To combine *N* different uncorrelated measurements *ai* ± *σi* of the same physical quantity *a*18 when the measurements are believed to be Gaussian distributed about the true value *at rue*, the well-known result is that the best estimate *acomb* ± *σcomb* is given by

$$a\_{comb} = \Sigma (a\_l \ast w\_l) / \Sigma w\_l, \quad \sigma\_{comb} = 1 / \sqrt{\Sigma} w\_l,\tag{15.13}$$

where the weights are defined as *wi* = 1*/σ*2 *i* . This is readily derived from minimising with respect to *a* a weighted sum of squared deviations

$$S(a) = \Sigma (a\_l - a)^2 / \sigma\_l^2 \tag{15.14}$$

The extension to the case where the individual measurements are correlated (as is often the case for analyses using different techniques on the same data) is straightforward: *S(a)* becomes *(ai* − *a)* ∗ *Hij* ∗ *(aj* − *a)*, where *H* is the inverse covariance matrix for the *ai*. It provides **B**est **L**inear **U**nbiassed **E**stimates (BLUE)[70].

There are, however, practical details that complicate its application. For example, in the above formula, the *σi* are supposed to be the **true** accuracies of the measurements. Often, all that we have available are **estimates** of their values. Problems arise in situations where the uncertainty estimate depends on the measured value *ai*. For example, in counting experiments with Poisson statistics, it is typical to set the uncertainty as the square root of the observed number. Then a downward fluctuation in the observation results in an overestimated weight, and *acomb* is biassed downwards. If instead the uncertainty is estimated as the square root of the expected number *a*, the combined result is biassed upwards—the increased uncertainty reduces *S* at larger *a*. A way round this difficulty has been suggested by Lyons et al. [71]. Alternatively, for Poisson counting data a likelihood approach is preferable to a *χ*2-based method.

Another problem arises when the individual measurements are very correlated. When the correlation coefficient of two uncertainties is larger than *σ*1*/σ*2 (where *σ*1 is the smaller uncertainty), *acomb* lies outside the range of the two measurements. As the correlation coefficient tends to +1, the extrapolation becomes larger, and is sensitive to the exact values assumed for the elements of the covariance matrix. The situation is aggravated by the fact that *σcomb* tends to zero. This is usually dealt with by selecting one of the two analyses, rather than trying to combine them. However, if the estimated uncertainty increases with the estimated value, choosing the result with the smaller **estimated** uncertainty can again produce a downward bias. On the other hand, using the smaller **expected** uncertainty can cause us to ignore an analysis which had a particularly favourable statistical fluctuation, which produced a result

18It is of course much better to use all the **data** in a combined analysis, rather than simply to combine the **results**.

that was genuinely more precise than expected19 How to deal with this situation in general is an open question. It has features in common with the problem (inspired by ref. [55]) of measuring a voltage by choosing at random a voltmeter from a cupboard containing meters of different sensitivities.

Another example involves combining two measurements of a cross-section with small statistical uncertainties, but with large correlated uncertainties from the common luminosity. With this luminosity uncertainty included in the covariance matrix, BLUE can result in the combined value being outside the range of the individual measurements. For this situation, it is preferable to exclude the luminosity uncertainty from the covariance matrix, and to apply it to the combined result afterwards.

### *15.5.2 Two or More Parameters*

An extension of this procedure is for combining *N* pairs of correlated measurements (e.g. the gradient and intercept of a straight line fit to several sets of data, where for simplicity it is assumed that any pair is independent of every other pair). For several pairs of values *(ai, bi)* with inverse covariance matrices **M***i*, the best combined values *(acomb, bcomb)* have as their inverse covariance matrix **M** = **M***i*. This means that, if the covariance matrix correlation coefficients *ρi* of the different measurements are very different from each other, the uncertainty on *acomb* can be much smaller than that for any single measurement.

This situation applies for track fitting to hits in a series of groups of tracking chambers, where each set of close chambers provides a very poor determination of the track; but the combination involves widely spaced chambers and determines the track well. Using the profile likelihoods (e.g. for the intercept, profiled over the gradient) for combining different measurements loses the correlation information and can lead to a very poor combined estimate[37]. The alternative of ignoring the correlation information is also strongly discouraged.

The importance of retaining covariances is relevant for many combinations, e.g. for the determination of the amount of Dark Energy in the Universe from various cosmological data[73].

19For example, the ALEPH experiment at LEP produced a tighter-than-expected upper limit on the mass of *ντ* because they happened to observe *τ* decay configurations which were particularly sensitive to the *ντ* mass.

### *15.5.3 Data Consistency*

The standard procedure for combining data pays no attention to whether or not the data are consistent. If they are clearly inconsistent, then they should not all be combined. When they are somewhat inconsistent, the procedure adopted by the Particle Data Group[14] is to increase all the uncertainties by a common factor such that the overall *χ*2 per degree of freedom equals unity.20

The Particle Data Group prescription for expanding uncertainties in the case of discrepant data sets has complications when each of the data sets consists of two or more parameters[72].

### **15.6 Goodness of Fit**

### *15.6.1 Sparse Multi-Dimensional Data*

The standard method loved by most scientists uses the weighted sum of squares, commonly called *χ*2. This, however, is only applicable to binned data (i.e. in a one or more dimensional histogram). Furthermore it loses its attractive feature that its distribution is model-independent when there is not enough data, which is likely to be so in the multi-dimensional case.

Although the maximum likelihood method is very useful for parameter determination with **unbinned data**, the value of *Lmax* usually does not provide a measure of goodness of fit (see Sect. 15.2.2).

An alternative that is used for sparse one-dimensional data is the Kolmogorov-Smirnov (KS) approach[68], or one of its variants. However, in the presence of fitted parameters, simulation is again required to determine the expected distribution of the KS-distance. Also because of the problem of how to order the data, the way to use it in multi-dimensional situations is not unique.

The standard KS method uses the maximum deviation between two cumulative distributions; because of statistical fluctuations, this is likely to occur near the middle of the distributions. In cases where interesting New Physics is expected to occur at extreme values of some kinematic variable (e.g. *pT* ), variants of KS such as Anderson-Darling[69] that give extra weight to the distributions' tails may be more useful.

20This is somewhat conservative, in that even if there are no problems, about half the data sets would be expected to have this larger than unity.

### *15.6.2 Number of Degrees of Freedom*

If we construct the weighted sum of squares *S* between a predicted theoretical curve and some data in the form of a histogram, provided the Poisson distribution of the bin contents can be approximated by a Gaussian (and the theory is correct, the data are unbiased, the uncertainty estimates are correct, etc.), **asymptotically**21 *S* will be distributed as *χ*2 with the number of degrees of freedom *ν* = *n* − *f* , where *n* is the number of data points and *f* is the number of free parameters whose values are determined by minimising *S*.

The relevance of the asymptotic requirement can be seen by imagining fitting a more or less flat distribution by the expression *N(*1 + 10−6 cos*(x* − *x*0*))*, where the free parameters are the normalisation *N* and the phase *x*0. It is clear that, although *x*0 is left free in the fit, because of the 10−6 factor, it will have a negligible effect on the fitted curve, and hence will not result in the typical reduction in *S* associated with having an extra free parameter. Of course, with an enormous amount of data, we would have sensitivity to *x*0, and so asymptotically it does reduce *ν* by one unit, but not for smaller amounts of data.

Another example involves neutrino oscillation experiments[54]. In a simplified two neutrino scenario, the neutrino energy spectrum is fitted by a survival probability *P* of the form

$$P = 1 - \sin^2 2\theta \,\,\sin^2(C\*\Delta m^2),\tag{15.15}$$

where *C* is a known function of the neutrino energy and the length of its flight path, *m*2 is the difference in mass squared of the relevant neutrino species, and *θ* is the neutrino mixing angle. For small values of *C* ∗ *m*2, this reduces to

$$P \approx 1 - \sin^2 2\theta \left( C \ast \Delta m^2 \right)^2 \tag{15.16}$$

Thus the survival probability depends on the two parameters only via their product sin 2*θ m*2. Because this combination is all that we can hope to determine, we effectively have only one free parameter rather than two. Of course, an enormous amount of data can manage to distinguish between sin *C* ∗ *m*2 and *C* ∗*m*2, and so asymptotically we have two free parameters as expected.

### **15.7 Discovery Issues**

Searches for new particles are an exciting endeavour, and continue to play a large role at the LHC at CERN, in neutrino experiments, in searches for dark matter, etc. The 2007 and 2011 PHYSTAT Workshops at CERN[7, 9] were devoted specifically

21The examples in this section go beyond the requirement that we need enough events for the Poisson distribution to be well approximated by a Gaussian.

to statistical issues that arise in discovery-orientated analyses at the LHC. Ref [74] deals with statistical issues that occur in Particle Physics searches for new phenomena; as an example, it includes the successful search for the Higgs boson at the LHC. A more detailed description of the plans for the Higgs search before its discovery is in ref. [75].

### *15.7.1 H***0***, or H***0** *Versus H***1***?*

In looking for new physics, there are two distinct types of approach. We can compare our data just with the null hypothesis *H*0, the SM of Particle Physics; alternatively we can see whether our data are more consistent with *H*0 or with an alternative hypothesis *H*1, some specific manifestation of new physics, such as a particular form of quark and/or lepton substructure. The former is known as 'goodness of fit', while the term 'hypothesis testing' is often reserved for the latter.

Each of these approaches has its own advantage. By not specifying a specific alternative,22 the goodness of fit test may be capable of detecting any form of deviation from the SM. On the other hand, if we are searching for some specific new effect, a comparison of *H*0 and *H*1 is likely to be a more sensitive way for that particular alternative. Also, the 'hypothesis testing' approach is less likely to give a false discovery claim if the assumed form of *H*0 has been slightly mis-modelled.

### *15.7.2 p-Values*

In order to quantify the chance of the observed effect being due to an uninteresting statistical fluctuation, some statistic is chosen for the data. The simplest case would be the observed number *n*0 of interesting events. Then the *p*-value is calculated, which is simply the probability that, given the expected background rate *b* from known sources, the observed value would fluctuate up to *n*0 or larger. In more complicated examples involving several relevant observables, the data statistic may be a likelihood ratio *L*0*/L*1 for the likelihood of the null hypothesis *H*0 compared with that for a specific alternative *H*1.

To compute the *p*-value of the observed or of possible data, the distribution *f (t)* of the data statistic *t* under the relevant hypothesis is required. In some cases this can be obtained analytically, but in more complicated situations, *f (t)* may require simulation. For *t* being −2 ln*L*0*/Lbest* , Cowan et al have given useful asymptotic

22Even a test of the null hypothesis may not be completely independent of ideas about alternatives. Thus in an event counting experiment, new physics usually results in an **increase** in rate, unless we are looking for neutrino oscillations, in which case a **decrease** would be significant. Also, sometimes the statistic used for a goodness of fit test of *H*0 may be the likelihood ratio for *H*0 as compared with a specific alternative *H*1.

formulae for *f (t)*[76]; here *Lbest* is the value of the likelihood when the parameters in *H*0 are set at their best values.

A small value of *p* indicates that the data are not very compatible with the theory (which may be because the detector's response or the background is poorly modeled, rather than the theory being wrong).

Particle Physicists usually convert *p* into the number of standard deviations *σ* of a Gaussian distribution, beyond which the one-sided tail area corresponds to *p*; statisticians refer to this as the *z*-score, but physicists call it significance. Thus 5*σ* corresponds to a *p*-value of 3 ∗ 10−7. This is done simply because it provides a number which is easier to remember, and not because Gaussians are relevant for every situation.

Unfortunately, *p*-values are often misinterpreted as the probability of the theory being true, given the data. It sometimes helps colleagues clarify the difference between *p(A*|*B)* and *p(B*|*A)* by reminding them that the probability of being pregnant, given the fact that you are female, is considerably smaller than the probability of being female, given the fact that you are pregnant. Reference [77] contains a series of articles by statisticians on the use (and misuse) of *p*-values.

Sometimes *S/*√ *B* or *S/*√*(S* +*B)* or the like (where *S* is the number of observed events above the estimated background *B*) is used as an approximate measure of significance. These approximations can be very poor, and their use is in general not recommended.23

### *15.7.3 CLs*

This is a technique[58] which is used for situations in which a discovery is not made, and instead various parameter values are excluded. For example the failure to observe SUSY particles can be converted into mass ranges which are excluded (at some confidence level).

Figure 15.5 (again) illustrates the expected distributions for some suitably chosen statistic *t* under two different hypotheses: the null *H*0 in which there is only standard known physics, and *H*1 which also includes some specific new particle, such as a SUSY neutralino. In Fig. 15.5c, the new particle is produced prolifically, and an experimental observation of *t* should fall in one peak or the other, and easily distinguishes between the two hypotheses. In contrast, Fig. 15.5a corresponds to very weak production of the new particle and it is almost impossible to know whether the new particle is being produced or not.

23For example, if selections to enhance signal with respect to background were optimised using *S/*√*B*, extremely hard cuts might be chosen, yielding expected numbers of events *S* = 0*.*1 and *B* = 10−3. This results in *S/*√*B* = 10, which sounds very good, but in fact this selection is disastrous.

The conventional method of claiming new particle production would be if the observed *t* fell well above the main peak of the *H*0 distribution; typically a *p*0 value corresponding to 5*σ* would be required (see Sect. 15.7.7). In a similar way, new particle production would be excluded if *t* were below the main part of the *H*1 distribution. Typically a 95% exclusion region would be chosen (i.e. *p*1 ≤ 0*.*05), where *p*1 is by convention the left-hand tail of the *H*1 distribution, as shown in Fig. 15.5b.

The *CLs* method aims to provide protection against a downward fluctuation of *t* in Fig. 15.5a resulting in a claim of exclusion in a situation where the experiment has no sensitivity to the production of the new particle; this could happen in 5% of experiments. It achieves this by defining24

$$CL\_s = p\_l/(1 - p\_0),\tag{15.17}$$

and requiring *CLs* to be below 0.05. From its definition, it is clear that *CLs* cannot be smaller than *p*1, and hence is a conservative version of the frequentist quantity *p*1. It tends to *p*1 when *t* lies above the *H*0 distribution, and to unity when the *H*0 and *H*1 distributions are very similar. The reduced*CLs* exclusion region is shown by the dotted diagonal line in Fig. 15.7; the price to pay for the protection provided by *CLs* is that there is built-in conservatism when *p*1 is small but *p*0 has intermediate values i.e. there are more cases in which no decision is made. Most statisticians are appalled by the use of *CLs*, because they consider that it is meaningless to take the ratio of two *p*-values.

It is deemed not to be necessary to protect against statistical fluctuations giving rise to discovery claims in situations with no sensitivity, because that should happen only at the 3 ∗ 10−7 rate (the one-sided 5*σ* Gaussian tail area).

Figure 15.7 is also useful for understanding the Punzi sensitivity definition (see Sect. 15.4.4). For any specified distributions of the statistic *t* for *H*0 and *H*1, the possible *(p*0*, p*1*)* values lie on a curve or straight line which extends from (0,1) to (1,0). With more data, the *t* distributions separate, and the curve moves closer to the *p*0 and *p*1 axes. The amount of data required to satisfy the Punzi requirement of always claiming a discovery or an exclusion is when no part of the curve is in the "no decision" region of Fig. 15.7.

24Given the fact that *CLs* is the ratio of two *p*-values, the choice of symbol *CLs* (standing for 'confidence level of signal') is not optimal. Another source of confusion is that in definitions of *CLs* the ways the *p*-values are defined vary, so the formulae can look different but the underlying concept is the same.

A subtlety with Eq. (15.17) is that *p*0 there is the probability of obtaining a measurement **greater than** the observed one, rather than the usual 'greater than or equal to'. This is to make 1 − *p*0 the probability of a value smaller than or equal to the observed one, in analogy with the definition of *p*1. It makes a difference when the observation is a small discrete number.

**Fig. 15.7** Plot of *p*0 against *p*1 for comparing a data statistic *t* with two hypotheses *H*0 and *H*1, whose expected *pdf* 's for *t* are given by two Gaussians of peak separation *μ*, and of equal width *σ*. For a given pair of *pdf* 's for *t*, the allowed values of *(p*0*, p*1*)* lie on a curve or straight line (shown solid in the diagram). The expected density for the data along a curve is such that its projection along the *p*0-axis (or *p*1-axis) is expected to be uniform for the hypothesis *H*0 (or *H*1 respectively). As the separation increases, the curves approach the *p*0 and *p*1 axes. Rejection of *H*0 is for *p*0 less than, say, 3 ∗ 10−7; here it is shown as 0.05 for ease of visualisation. Similarly exclusion of *H*1 is shown as *p*1 *<* 0*.*1. Thus the *(p*0*, p*1*)* square is divided into four regions: the largest rectangle is when there is no decision, the long one above the *p*0-axis is for exclusion of *H*1, the high one beside the *p*1-axis is for rejection of *H*0, and the smallest rectangle is when the data lie between the two *pdf* 's. For *μ/σ* = 3*.*33, there are no values of *(p*0*, p*1*)* in the "no decision" region. In the *CLs* procedure, rejection of *H*1 is when the *t* statistic is such that *(p*0*, p*1*)* lies below the diagonal dotted straight line

### *15.7.4 Comparing Two Hypotheses Via χ***2**

Assume that there is a histogram with 100 bins, and that a *χ*2 method is being used for fitting it with a function with one free parameter. The expected value of *χ*2 is 99±14. Thus if *p*0, the best value of the parameter, yields a *χ*2 of 85, this would be regarded as very satisfactory. However, a theoretical colleague has a model which predicts that the parameter should have a different value *p*1, and wants to know what the data have to say about that. This is tested by calculating the *χ*2 for that *p*1, which yields a value of 110. There appear to be two contradictory conclusions:

• *p*1 is satisfactory: This is based on the fact that the relevant *χ*2 of 110 is well within the expected range of 99 ± 14.

• *p*1 is ruled out: The uncertainty on *p* is estimated by seeing how much it must change from its optimum value in order to make *χ*2 increase by **1**. For this data, *χ*2*(p*1*)* is **25** units larger than *χ*2*(p*0*)*, and so, assuming that the behaviour of *χ*2 in the neighbourhood of the minimum is parabolic, *p*1 is ruled out at the ∼5 standard deviation level.

Unfortunately, many physicists, over-impressed by the fact that *χ*2*(p*1*)* appears to be satisfactory, are reluctant to accept that *p*0 is strongly favoured by the data.

A similar argument applies to comparing a given set of data with 2 separate hypotheses e.g. fitting a histogram with an exponential or a straight line. Again the **difference** between the *χ*2 quantities provides better discrimination between the hypotheses than do the **individual** *χ*2 values[78]. Another example of using the difference in *χ*2's is given in the next section.

There are of course other ways available for comparing two hypotheses. e.g. likelihood ratio, Bayes factor, Bayesian information criterion, etc. For a fuller discussion, see ref. [79]. A description of their application in cosmology can be found in ref. [80]. Problems in choosing priors for the Bayes factor approach for selecting among hypotheses are discussed by Heinrich[81].

### *15.7.5 Peak Above Smooth Background*

When comparing two hypotheses with our data, we can use the numerical values of the two *χ*2 quantities with a view to making some decision about the hypotheses. For example, we may be fitting a smooth distribution by a power series, and wonder whether we need a quadratic term, or whether a linear expression would suffice. Alternatively we may want to assess whether a mass spectrum favours the existence of a peak on top of a smooth background, as compared with just the smooth background. Qualitatively, if the extra term(s) are unnecessary, they will result in a relatively small reduction in *χ*2, while if they really are required, the reduction could be larger.

It is sometimes possible to be quantitative about the expected reduction when the extra terms are not needed[82]. If we are in the asymptotic regime, and if the hypotheses are nested,25 and if the extra parameters of the larger hypothesis are defined under the smaller one, and in that case do not lie on the boundary of their allowed region, then the difference in *χ*2 should itself be distributed as a *χ*2, with the number of degrees of freedom equal to the number of extra parameters.

An example that satisfies this is provided by the different order polynomials. The hypotheses are nested, in that the linear situation is a special case of a quadratic, where the coefficient of the quadratic term is zero. Thus the extra parameter is defined and within the (infinite) allowed range. Then, provided we have a large

25This means that for suitable values of the parameters the larger hypothesis reduces to the smaller one.

amount of data, we expect the difference in *χ*2 to have one degree of freedom, so a value larger than around 5 would be unlikely.

A contrast is provided by a smooth background *C(x)* compared with a background plus peak, *C(x)* + *A* exp [−0*.*5 ∗ *(x* − *x*0*)* 2*/σ*2]. The extra parameters for the peak are its amplitude, position and width: *A, x*0 and *σ* respectively. Again the hypotheses are nested, in that *C(x)*is just a special case of the peak plus background, with *A* = 0. However, although *A* is defined in the background only case, *x*0 and *σ* are not, as their values become completely irrelevant when *A* = 0. Furthermore, unless the peak plus background fit allows *A* to be negative, zero is on the boundary of its allowed region. We thus should not expect the difference of the *χ*2 quantities itself to be distributed as a *χ*2 [83–85]. To assess the significance of a particular *χ*2 difference, this unfortunately means that we have to obtain its distribution ourselves, presumably by Monte Carlo. If we want to find out probabilities of statistical fluctuations at the 10−6 level, this requires a lot of simulation, and probably needs us to use something better than brute force.

The problem of non-standard limiting distributions for *χ*2 tests has a substantial statistical literature (see, for example, refs. [86] and [87].)

### *15.7.6 Incorporating Nuisance Parameters*

The calculation of *p*-values is complicated in practice by the existence of nuisance parameters. (For the simple situation described in Sect. 15.7.2, there could be some uncertainty in the estimated background.) There are numerous ways of incorporating them. These include:

region. Clearly if it is desired to establish a discovery from *p*-values around 10−7 or smaller, then *γ* should be chosen at least an order of magnitude below this.

The properties of these and other methods are compared by Demortier [84], while Cranmer [88] and Cousins et al.[89] have discussed some of them in the context of searches at the LHC.

The role of systematic effects is likely to be more serious here than for upper limits discussed in Sect. 15.4.5. This is because in upper limit situations the number of events is usually small, and so statistical uncertainties dominate. In contrast, discovery claims have *p*-values of 3 ∗ 10−7 or smaller, and so tails of distributions are likely to be important.

### *15.7.7 Why* **5***σ?*

Unfortunately the usually accepted criterion for claiming a discovery in Particle Physics is that *p* should correspond to at least 5*σ*. Statisticians almost invariably ask why such a stringent level is used. One answer is past experience: all too often interesting effects at the 3*σ* or 4*σ* level have gone away as more data are collected. Another is the multiple comparison problem, or "Look Elsewhere Effect" (LEE). While the chance of obtaining a 5*σ* effect in one bin of a particular histogram ("local *p*-value") is really small, it is to be remembered that histograms have many bins,26 they could be plotted with different selection criteria and different binning,27 and there are very many other histograms that were or could have been looked at in the course of the experiment.28 Thus the chance of a 5*σ* fluctuation occurring somewhere in the data ("global *p*-value") is much larger than might at first appear. Calculating a global *p*-value may require an excessive amount of Monte-Carlo simulation. Reference [90] circumvents this for asymptotic situations by providing a formula for extrapolating the LEE correction factor from a lower significance level; this requires considerably less simulation.

Finally, physicists subconsciously incorporate Bayesian priors in assessing how likely they feel that they have discovered something new, and hence whether they

26In calculating a *p*-value in such a case, it is very desirable to take into account the number of chances for a statistical fluctuation to occur anywhere in the histogram (or anywhere in the search procedure, for more complicated analyses). At very least, it should be made clear what the basis of the calculated *p*-value is.

27If a blind analysis is performed, such decisions are made before looking at the data, and so this aspect of the "look elsewhere" effect is reduced.

28The extent to which other people's searches should be included in an allowance for the "look elsewhere" effect depends on the implied question being addressed. Thus are we considering the chance of obtaining a statistical fluctuation in any of the analyses we have performed; or by anyone analysing data in our experiment; or by any Particle Physicist this year? Because of the ambiguity of which specific question is being addressed, which is often not explicitly mentioned, we recommend not including an extra "look elsewhere" factor for this.

should claim a discovery. Thus, in deciding between the possibilities of a new discovery or of an undetected systematic effect, our priors might favour the latter, and hence strong evidence for discovery is required from the data.29

However it is not necessarily equitable to use a uniform standard for large general-purpose experiments and for small ones with a specific aim; or for looking for a process which is expected (e.g. *H*0 → *μ*+*μ*−), as compared with a more speculative search, such as lepton substructure[91]. But physicists and especially journal editors seem to like a defined rule rather than a flexible criterion, so this bolsters the 5*σ* standard. In any case, it is largely a semantic issue, in that physicists finding a 4*.*5*σ* effect would clearly report it, using judiciously chosen wording to describe the interpretation of their observation.

Statisticians also ask whether models can really be trusted to describe the extreme tails of distributions. In general, this may be so—counting experiments are expected to follow Poisson distributions, with small corrections for possible long timescale drifts in detector calibrations; and particle decays usually are described by exponential distributions in time. However, the situation is much less clear for nuisance parameters, where uncertainty estimates may be less rigorous, and their distribution is often assumed to be Gaussian (or truncated Gaussian) by default. The effect of these uncertainties on very small *p*-values needs to be investigated caseby-case.

It is important to remember that *p*-values merely test the null hypothesis. There are more sensitive ways of looking for new physics when a specific alternative is relevant. Thus a very small *p*-value on its own is usually not enough to make a convincing case for discovery.

### *15.7.8 Repetitions in Time*

Often experiments accumulate data over several years. The same search for a new effect may typically be repeated once or twice each year as more data are collected. Does this constitute another factor of ∼20 in the number of opportunities for a statistical fluctuation to appear? Our reply is "No". If there had been a 6*σ* signal with the early data (which resulted in a claim for discovery), which had then become only 3*σ* with more data, this would be grounds for downplaying the earlier discovery claim. Thus at any time, there is essentially only one set of data (everything) that is relevant.

For a *p*-value to be meaningful, it is important that the time at which the experiment stops collecting data is determined not by the significance of the observed signal but by external factors (e.g. accelerator being decommissioned, ending of funding, etc.). Indeed there is a theorem that states that, provided data is

29If I were performing an experiment to look for violations of energy conservation, I would require more than 5*σ*, because my prior for energy being conserved is very large.

collected for long enough, it is possible to reach any arbitrary level of significance against a hypothesis that is in fact true.

### *15.7.9 Combining p-Values*

In looking for a given new effect, there may be several separate and uncorrelated analyses which are relevant. These could correspond to different decay modes for the new particle; or different experiments looking for the same signal. Thus, if the *p*-values for the null hypothesis (i.e. no new physics) for the separate analyses were 10−6 and 0*.*1, what is the corresponding *p*-value for the pair of results?30

The unambiguous answer is that there is no unique recipe for combining them[92, 93]. There is no single way of taking a uniform distribution in two variables, and finding a transformation *pcomb(p*1*, p*2*)* that converts it into a uniform distribution of the single variable *pcomb*.

Two popular recipes involve asking what is the probability that the smaller *p*value will be 10−6 or smaller; or that the product is below *p*1 ∗ *p*2 = 10−7. (Note that these probabilities are **not** 10−6 and 10−7 respectively.) None of the possible methods has the property that in combining three *p*-values, the same answer is obtained if *p*1 is first combined with *p*2, and then the result is combined with *p*3; or whether some different ordering is used.

Another problem is the lack of other information that might be relevant. For example, the *p*-values might arise from *χ*2's with different numbers of degrees of freedom *ν* e.g. *χ*2 1 = 90 for 100 degrees of freedom, and *χ*2 2 = 20 for *ν* = 1. The second has a very small *p*-value, so many combination methods (including the two mentioned above) would conclude that overall the data do not look consistent with the null hypothesis. However, another plausible-sounding method is to add the separate *χ*2 values and also the individual *ν*, 31 to obtain a total *χ*2 = 110 for *ν* = 101, which sounds perfectly satisfactory. The resolution of this discrepancy of interpretation depends on the nature of the two tests. If the second analysis with *χ*2 = 20 corresponded to just one extra measurement like the previous 100, then it seems reasonable to combine the *χ*2 values and the *ν*, and to conclude that overall there is indeed nothing surprising. But on the other hand, if the second measurement was genuinely different, and an alternative way of looking for some discrepancy, then it may be more appropriate to combine the *p*-values by one of the earlier methods, which suggest that the overall consistency with theory is not good. It

30Rather than combining *p*-values, it is of course much better to use the complete sets of original data (if available) for obtaining the combined result.

31The method described earlier involving the product of the *p*-values is equivalent to converting each *p* to a *χ*2, assuming that *ν* = 2, regardless of whether this was the actual number of degrees of freedom, and then adding the *χ*2 and also the *ν*.

is this extra information about the nature of the two tests that determines which combination method might be appropriate.

It is clearly important to decide in advance what combination method should be used, without reference to the specific data being analysed.

### **15.8 Blind Analyses**

These are becoming increasingly popular as a means of avoiding personal bias affecting the result. They involve keeping part of the data unseen by the analysers, until the data selection procedure and the analysis method have been completely defined, all correction procedures specified, etc.

One of the early suggestions to use a blind analysis in a Particle Physics experiment was due to Luis Alvarez. An experiment at Stanford had looked for quarks, by measuring the residual charge on small spheres that were levitated in a superconducting magnet. If a single free quark were present in a sphere, the residual charge would be a third or two-thirds of the electron's charge.  A potential problem was that large corrections had to be applied to the raw data in order to extract the final result for the charge. The suspicion was that maybe the experimenters were (subconsciously) applying corrections until the value turned out to be 'satisfactory'. The blind approach involved the computer adding a random number to the raw value of the charge, which would then be corrected until the experimentalists were satisfied, and only then would the computer subtract the random number to reveal the final answer for that sphere.32

There are various methods of performing blind analyses[95] most of which aim to allow the experimentalists to look at some of the real data, in order to perform checks that nothing is terribly wrong. Some of these are:

32This suggestion was implemented, but in fact no subsequent results were published. The current consensus is that this 'discovery' of free quarks is probably spurious.

If several different groups within the same collaboration are performing similar analyses for extracting some specific parameter, then it is desirable to fix the procedure for selecting which result to present, or alternatively how to combine the separate results. This should be done before the results are seen, and is worth doing even if the individual analyses were not "blind".

A question that arises with blind analyses is whether it should be permitted to modify the analysis after the data had been unblinded. It is generally agreed that this should not be done, unless everyone would regard it as ridiculous not to do so. For example, if a search for rare events yielded 10 candidates over the course of a year's run, all of which occurred on Sunday mornings at precisely 1.17 a.m., it would be prudent to do some further investigation before publishing. If 'postunblinding' modification of the procedure is performed, this should be made clear in any publication.

### **15.9 Topics that Deserve More Attention**

### *15.9.1 Statistical Software*

Particle physicists tend to write their own software for performing statistical computations. Although this has educational merits, it is inefficient use of one's time. The data-manipulation system of programmes ROOT/RooFit/RooStats contains many useful statistical routines[96]. Tools also exist for implementing many methods for separating signal from background[43, 44].

A problem with these is that they are too easy to use. In the hands of a noncritical user, the required input data instructions may contain some error, with the consequence that they will produce the solution to a different procedure than the intended one. It is very important to check that the result obtained is not unreasonable.

### *15.9.2 Deep Learning*

This involves the use of sophisticated techniques[45] for achieving nearly optimal extraction of information from data, but which are still relatively unfamiliar to many scientists. It is important to develop a set of protocols to ensure that they perform in a reliable manner, and are not introducing subtle biases of which users are unaware.

### *15.9.3 Unfolding Data or Smearing Theory?*

Observed experimental distributions are almost always smeared versions of 'the true distributions of Nature'. It is simpler to compare theory and data by smearing the theory, rather than trying to unfold the experimental effects from the data, as the latter is a less stable procedure and also introduces correlations among the bins of the unfolded distribution. Some fields tend to favour deconvolution; this is partly because it is rarer for them to have a dominant theoretical model with which the data is to be compared. Unfolding does have the advantage that it provides an estimate of the 'true' distribution, with which any future theory can be compared. Also it can be looked at by a physicist, but we are not accustomed to readily interpreting data where the contents of the histogram bins are highly correlated.

There are some situations where unfolding is desirable. For example, it allows the comparison of distributions from different experiments, with different resolutions. Another is using experimental data for tuning Monte Carlo generators; smearing the data at each step of the optimisation increases the computation time too much.

Even for checking in future whether new theories are compatible with data does not necessarily require unfolding. Provided that the smearing matrix of the detector is provided, the future data can be smeared, and then compared with the actual (not unfolded) data. However, including the effects of systematics can be a complication.

Sessions at the 2011 PHYSTAT workshop[9] and at CERN's PHYSTAT*ν* meeting[12] were devoted to unfolding. Blobel[97] has reviewed the topic, while ref. [98] contains a statistician's view of the statistical issues involved in unfolding.

### *15.9.4 Visualisation*

The combination of the human eye and brain is very powerful at detecting patterns in data (even if sometimes they are not there!) This can be useful in deciding how to analyse the data; as a check on whether the result of an analysis is plausible; whether a machine learning method for separating signal from background is performing sensibly; etc. Such human inspection of data is feasible if there are only a small number (below 4) of relevant variables. Techniques for inspecting multidimensional data would be valuable.

### *15.9.5 Non-parametric Methods*

These are so unknown to most Particle Physicists that they are usually unaware when they are using them. Simple examples include:

These all avoid the need to specify a particular parametric form, and hence the values of any parameters. In general such a method is less powerful than a parametric one, if the latter were available and relevant.

### *15.9.6 Collaboration with Statisticians*

Other scientists seem to be better than particle physicists about involving statisticians in the analysis of their data. This is partly due to the fact that we like to try out statistical techniques ourselves; that we consider our data is too complicated for other people to deal with; and that we are somewhat over-protective of our data, and are reluctant to share it with others. None of this is particularly convincing, and it is clear that we would benefit from the involvement of professional statisticians. The advantages of having them participating in the recent PHYSTAT meetings have been obvious.

In the past, Particle Physicists have on occasion asked rather specific questions to Statisticians they happened to know. Statisticians prefer to be much more directly involved with the data itself. With analyses becoming more and more complex, it will be highly desirable for them to be affiliated with experimental groups.

### **15.10 Conclusion**

Although the statistical aspects of many particle physics analyses are already at a sophisticated level, it is clear that there are many practical statistical issues to be resolved. With the increasing complexity of scientific investigations, more active collaboration with statisticians and machine learning experts will result in a better understanding of the relevant techniques and improved analyses in the future.

**Acknowledgements** I wish to acknowledge the patience and expertise of David Cox, Brad Efron, Jerry Friedman and David van Dyk, and also of other Statisticians too numerous to list, in explaining statistical issues to me; the ones who have contributed to the PHYSTAT meetings have been particularly helpful. My understanding of the practical application of statistical techniques has improved considerably as a result of discussions with many experimental Particle Physics colleagues, and in particular with the members of the CDF and CMS Statistics Committees. I especially wish to thank Bob Cousins, Luc Demortier and Joel Heinrich for their careful reading and valuable comments on the original version of this article. To all of you, I am most grateful.

The Leverhulme Foundation kindly provided a grant which partially supported the original version this work.

### **References**

O. Behnke at al (eds), "Data Analysis in High Energy Physics: A Practical Guide to Statistical Methods", Wiley (2013),

Glen Cowan, "Statistical Data Analysis", Oxford University Press (1998).

F. E. James, "Statistical Methods in Experimental Physics", World Scientific Publishing Co (2007).

L. Lista, "Statistical Methods for Data Analysis in Particle Physics", Springer (2017). Louis Lyons, "Statistics for Nuclear and Particle Physics", Cambridge University Press (1986). See also https://www-cdf.fnal.gov/physics/statistics/notes/Errata2.pdf for an Update. Byron Roe, "Probability and Statistics in Experimental Physics", Springer Verlag (1991).

"Statistical issues towards PHYSTAT*ν* 2019", NuPhys2018: Prospects in Neutrino Physics, https://indico.ph.qmul.ac.uk/indico/conferenceDisplay.py?confId=289

21. CERN European Schools, https://physicschool.web.cern.ch/physicschool/ESHEP/previous\_ eshep.html;

CERN Latin-American Schools, https://physicschool.web.cern.ch/physicschool/CLASHEP/ previous\_clashep.html; and

CERN Asia-Pacific Schools, http://aepshep.org/previous-schools.html.

Nature **560** (2018) 41;

A. J. Larkoski, I. Moult and B. Nachman "Deep Learning and Its Application to LHC Physics" (2017) http://arxiv.org/abs/arXiv:1709.04464;

I. Goodfellow, Y. Bengio and A. Courville, "Deep Learning" (20116), MIT Press.

Mathematical Statistics. **19** (2) (1948) 279, doi:10.1214/aoms/1177730256

W. Verkerke and D. Kirkby, "The RooFit toolkit for data modeling" (2003), arXiv:physics/0306116;

L. Moneta et al., "The RooStats Project", 13*th* Int. Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT2010), arXiv:1009.1003.PoSACAT:057

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# **Chapter 16 Integration of Detectors into a Large Experiment: Examples from ATLAS and CMS**

**Daniel Froidevaux**

### **16.1 Introduction**

### *16.1.1 The Context*

The Large Hadron Collider (LHC) is the proton-proton accelerator which began operation in 2010 in the existing LEP tunnel at CERN in Geneva, Switzerland. It represents the next major step in the high-energy frontier beyond the Fermilab Tevatron (proton-antiproton collisions at a centre-of-mass energy of 2 TeV), with its design centre-of-mass energy of 14 TeV and luminosity of 1034 cm−2s−1. The high design luminosity is required because of the small cross-sections expected for many of the benchmark processes (Higgs-boson production and decay, new physics scenarios such as supersymmetry, extra dimensions, etc.) used to optimise the design of the general-purpose detectors over a period of 15 years or so. To achieve this luminosity and minimise the impact of simultaneous inelastic collisions occurring at the same time in the detectors (a phenomenon usually called pileup), the LHC beam crossings are 25 ns apart in time, resulting in 23 inelastic interactions per crossing on average at design luminosity. Two general-purpose experiments, ATLAS and CMS, were proposed for operation at the LHC in 1994 [1], and approved for construction in 1995. The experimental challenges undertaken by these two projects of unprecedented size and complexity in the field of high-energy physics, the construction and integration achievements realised over the years 2000– 2008, and the expected performance of the commissioned detectors are described in a variety of detailed documents, such as the detector papers [2, 3]. In this chapter, much of the description of the lessons learned based on this huge effort, and of

D. Froidevaux (-)

CERN, Geneva, Switzerland e-mail<EMAIL_ADDRESS>
© The Author(s) 2020 C. W. Fabjan, H. Schopper (eds.), *Particle Physics Reference Library*, https://doi.org/10.1007/978-3-030-35318-6\_16

the comparisons in terms of expected performance have been taken and somewhat updated from a recent review [4]. For completeness, it is important to mention also the two more specialised and smaller experiments, ALICE [5] and LHCb [6]. In 2019, at a moment when the accelerator and experiments have just completed very successfully the so-called run-2 with 4 years of operation at a centre-of-mass energy of 13 TeV, and after run-1 with operation at lower energies topped with the discovery of the Higgs boson, it is interesting to look back not only on the period of construction and integration with its great expectations, a period which is the main focus of this chapter, but also on almost 10 years of operation and data-taking with its own challenges and of course with the excitement stemming from the analysis of real data.

The prime motivation of the LHC is to elucidate the nature of electroweak symmetry breaking, for which the Higgs mechanism is presumed to be responsible. The experimental study of the Higgs mechanism can also shed light on the consistency of the Standard Model at energy scales above 1 TeV. The Higgs boson is generally expected to have a mass below about 200 GeV [7]. This expectation could be relaxed if there are problems in the interpretation of the precision electroweak data [8] or if there are additional contributions to the electroweak observables [9]. A variety of models without Higgs bosons have also been proposed more recently, together with mechanisms of partial unitarity restoration in longitudinal vector boson scattering at the TeV scale [10]. All these possibilities may appear to be remote, but they serve as a reminder that the existence of a light Higgs boson cannot be taken for granted.

Theories or models beyond the Standard Model invoke additional symmetries (supersymmetry) or new forces or constituents (strongly-broken electroweak symmetry, technicolour). It is generally hoped that discoveries at the LHC could provide insight into a unified theory of all fundamental interactions, for example in the form of supersymmetry or of extra dimensions, the latter requiring modification of gravity at the TeV scale. There are therefore several compelling reasons for exploring the TeV scale and the search for supersymmetry is perhaps the most attractive one, particularly since preserving the naturalness of the electroweak mass scale requires supersymmetric particles with masses below about 1 TeV.

### *16.1.2 The Main Initial Physics Goals of ATLAS and CMS at the LHC*

There have been many studies of the LHC discovery potential as a function of the integrated luminosity and the ones released just before data-taking [11, 12] have focussed on the first few years, over which about 10 fb−1 of integrated luminosity were expected to be accumulated by each experiment.

With some optimism that the performance of the ATLAS and CMS detectors would be understood rapidly and would be close to expectations, the expectations

at the time were that a Standard Model Higgs boson could be discovered at the LHC with a significance above 5*σ* over the full mass range of interest and for an integrated luminosity of only 5 fb−1, as shown in Fig. 16.1. This discovery potential should, however, be taken with a grain of salt, since the evidence for a light Higgs boson of mass in the 110–130 GeV range would not only have to be combined over both experiments but also over several channels with very different final states (*H* → *γ γ* decays in association with various jet topologies, *ttH* production with *H* → *bb* decay and *qqH* production with *H* → *τ τ* decay). Achieving the required sensitivity in each of these channels would require an excellent understanding of the detailed performance of most elements of these complex detectors and would therefore require sufficient experimental data and time.

The discovery potential for supersymmetry was expected to be very substantial in the very first months of data-taking, since only 100 pb−1 of integratedluminosity would be sufficient to discover squarks or gluinos with masses below about 1.3 TeV [1, 11, 13], a large increase in sensitivity with respect to that ultimately achieved at the Tevatron. This sensitivity would increase to 1.7 TeV for an integrated luminosity of 1 fb−1 and to about 2.2 TeV for 10 fb−1, as shown in Fig. 16.2.

The few examples above illustrate the wide range of physics opened up by the seven-fold increase in energy from the Tevatron to the LHC. Needless to say, all Standard Model processes of interest, QCD jets, vector bosons and especially top quarks, would be produced in unprecedented abundance at the LHC, as illustrated in Table 16.1, and would therefore be studied with high precision by ATLAS and CMS.

**Table 16.1** For a variety of physics processes expected to be the most abundantly produced at the LHC, expected numbers of events recorded by ATLAS and CMS for an integrated luminosity of 1 fb−1 per experiment

### *16.1.3 A Snapshot of the Current Status of the ATLAS and CMS Experiments*

From the year 2000 to end of 2009, the experiments have had to deal in parallel with a very complex set of tasks requiring a wide diversity of skills and personnel:

• the construction of the major components of the detectors was complete or nearing completion at the end of 2006, after a very long period of research

**Fig. 16.3** Left: picture of the ATLAS barrel toroid superconducting magnet with its eight coils of 25 m length and of the ATLAS barrel calorimeter with its liquid Argon electromagnetic calorimeter and its scintillating tile hadronic calorimeter, as installed in the experimental cavern. Right: picture of the first end-cap LAr cryostat, including the electromagnetic, hadronic and forward calorimeters, as it is lowered into its docking position on one side of the ATLAS pit

**Fig. 16.4** Left: picture of the CMS superconducting solenoid, as integrated with the barrel muon system (outside) and with the barrel hadron calorimetry (inside). Right: picture of the insertion of the CMS silicon-strip tracker into the barrel crystal calorimeter

and development, including validation in terms of survival to irradiation and preparation of industrial manufacturing;

components were able to record significant samples of data, albeit at low energy and with insufficient statistics to fully commission the trigger and reconstruction algorithms dedicated to provide the signatures required for the initial Standard Model measurements and searches for new physics.

In parallel with the rapidly evolving integration, installation and commissioning effort at the experimental sites, the collaborations have also reorganised themselves to evolve as smoothly and efficiently as possible from a distributed construction project with a strong technical co-ordination team to a running experiment with the emphasis shifting to monitoring of the detector and trigger operation, understanding of the detector performance in the real LHC environment and producing the first physics results. A small but significant part of the human and financial resources are already focusing on the necessary upgrades to the experiments required by the LHC luminosity upgrade programme.

This chapter has been structured in the following way: Sect. 16.2 presents an overview of the ATLAS and CMS projects in terms of their main design characteristics, describes briefly the magnet systems, and summarises the main lessons learned from the 15-year long research and development and construction period. The next three sections, Sects. 16.3–16.5, describe in more detail the main features and challenges related respectively to the inner tracker, to the calorimetry and to the muon spectrometer, in the specific case of the ATLAS experiment. The subsequent two sections, Sects. 16.6 and 16.7, discuss in broad terms the various aspects of, respectively, the trigger and data acquisition system and the computing and software, again in the context of the ATLAS experiment. The next section, Sect. 16.8, summarises and compares briefly the expected performances at the time of beginning of data-taking of the main ATLAS and CMS systems. The last and final section, Sect. 16.9, gives a very brief overview of the performance and physics results achieved over the past 10 years.

### **16.2 Overall Detector Concept and Magnet Systems**

This section presents an overview of the ATLAS and CMS detectors, based on the main physics arguments which guided the conceptual design, and describes the magnet systems, which have driven many of the detailed design aspects of the experiments.

### *16.2.1 Overall Detector Concept*

Figures 16.5 and 16.6 show the overall layouts respectively of the ATLAS and CMS detectors and Table 16.2 lists the main parameters of each experiment. Both experiments are designed somewhat as cylindrical onions consisting of:

**Fig. 16.5** Overall layout of the ATLAS detector

**Fig. 16.6** Overall layout of the CMS detector

To complete the coverage of the central part of the experiments (often called barrel), so-called end-cap detectors (calorimetry and muon spectrometers) are added on each side of the barrel cylinders.

The sizes of ATLAS and CMS are determined mainly by the fact that they are designed to identify most of the very energetic particles emerging from the proton-proton collisions and to measure as efficiently and precisely as feasible their trajectories and momenta. The interesting particles are produced over a very wide range of energies (from a few hundred MeV to a few TeV) and over the full solid angle. They need therefore to be detected down to very small polar angles (*θ*) with respect to the incoming beams (a fraction of a degree, corresponding to pseudorapidities *η* of up to 5, where *η* = −log[tan*(θ/*2*)*]; pseudorapidity is more commonly used at hadron colliders because the rates for most hard-scattering processes of interest are constant as a function of *η*). Most of the energy of the colliding protons is however dissipated in shielding and collimators close to the focussing quadrupoles (on each side of the experimental caverns, which house the experiments). The overall radiation levels will therefore be very high: many components in the detectors will become activated and will require special handling during maintenance, particularly near the beams.

For all the above reasons, both experiments have been designed following similar guiding principles:

• No particle of interest should escape unseen (except neutrinos, which will therefore be identified because their presence will cause an imbalance in the energy-momentum conservation laws governing the interactions measured in the experiments). The consequences of this simple statement are profound and farreaching when one goes beyond simple sketches and simulations to the details of the real experiment:

	- CMS has chosen the highest possible magnetic field (4 T) combined with an inner tracker consisting solely of Silicon pixel detectors (nearest to the interaction vertex) and of Silicon microstrip detectors providing very high granularity at all radii. The occupancy of these detectors is below 2–3% even at the LHC design luminosity and the impact of pile-up is therefore minimal;
	- ATLAS has invested a very large fraction of its resources into three superconducting toroid magnets and a set of very precise muon chambers, constantly monitored with optical alignment devices, to measure the muon momenta very accurately over the widest possible coverage (|*η*| *<* 2*.*7) and momentum range (4 GeV to several TeV). This system provides a stand-alone muon momentum measurement of sufficient quality for all benchmark physics processes up to the highest luminosities envisaged for the LHC operation;

For reasons of size, cost and radiation hardness, both experiments have limited the coverage of their lepton identification and measurements to the approximate pseudorapidity range |*η*| *<* 2*.*5 (or a polar angle of 9.4◦ with respect to the beams). The implementation of these requirements has also had a very large impact on the design and technology choices of both experiments:

The first level of trigger (or L1 trigger) in the ATLAS and CMS experiments is based on custom-built hardware extracting as quickly as possible the necessary information from the calorimeters and muon spectrometer and provides a decision in 2.5 to 3μs, during which most of the time is spent in signal transmission from the detector (to make the trigger decision) and to the detector (to propagate this decision back to the front-end electronics). This reduces the event rate to about 100 kHz with a very high efficiency for most of the events of interest for physics analysis. During this very long (for relativistic particles) time, the hundreds of thousands of very sensitive and sophisticated radiation-hard electronics chips situated throughout the detectors have to store the successive waves of data produced every 25 ns in pipelines and keep track of the time stamps of all the data so that the correct information can be retrieved when the decision from the L1 trigger is received. The synchronisation of a vast number of frontend electronics channels over very large volumes has been a major challenge for the design of the overall trigger and timing control of the experiments.

### *16.2.2 Magnet Systems*

The magnet systems of the ATLAS and CMS experiments [14] were at the heart of the conceptual design of the detector components and they have driven many of the fundamental geometrical parameters and of the broad technology choices for the components of the detectors. The large bending power required to measure muons of 1 TeV momentum with a precision of 10% has led both collaborations to choose superconducting technology for their magnets to limit the size of the experimental caverns and the overall costs. The choice of magnet system for CMS was based on the elegant idea of fulfilling at the same time with one magnet a high magnetic field in the tracker volume for all precision momentum measurements, including muons, and a high enough return flux in the iron outside the magnet to provide a muon trigger and a second muon momentum measurement for the experiment. This is achieved with a single solenoid of a large enough radius to contain most of the CMS calorimeter system. In contrast, the choice of magnet system for ATLAS was driven by the requirement to achieve a high-precision standalone momentum measurement of muons over as large an acceptance in momentum and *η*-coverage as possible. This is achieved using an arrangement of a smallradius thin-walled solenoid, integrated into the cryostat of the barrel electromagnetic calorimeter, surrounded by a system of three large air-core toroids, situated outside the ATLAS calorimeter systems and generating the magnetic field for the muon spectrometer. The main parameters of these magnet systems are listed in Table 16.3 and their stored energies are compared to those of previous large-scale magnets in high-energy physics experiments in Fig. 16.7.

In CMS, the length of the solenoid was driven by the need to achieve excellent momentum resolution over the required *η*-coverage and its diameter was chosen such that most of the calorimetry is contained inside the coil. In ATLAS, the

**Table 16.3** Main parameters of the CMS and ATLAS magnet systems

**Fig. 16.7** Ratio of stored energy over mass, *E/M*, versus stored energy, *E*, for various magnets built for large high-energy physics experiments

position of the solenoid in front of the barrel electromagnetic calorimeter has demanded a careful optimisation of the material in order to minimise its impact on the calorimeter performance and its length has been defined by the design of the overall calorimeter and inner tracker systems, leading to significant non-uniformity of the field at the end of the tracker volume.

The main advantages and drawbacks of the chosen magnet systems can be summarised as follows, considering successively the inner tracker, calorimeter and muon system performances (see Sect. 16.8):

• the higher field strength and uniformity of the CMS solenoid provide better momentum resolution and better uniformity over the full *η*-coverage for the inner tracker;

In terms of construction, the magnet systems have each turned out to be a major project in its own right with very direct and strong involvement from the Technical Coordination team [15] and from major national laboratories and funding agencies. A detailed account of the construction of these magnets is beyond the scope of this review and this section can be concluded by simply stating that during the course of the past few years, all these magnets have undergone very successfully extensive commissioning steps, sustained operation at full current, in particular for cosmicray data-taking in 2008/2009, and stable operation with beam in the LHC machine at the end of 2009.

#### **<IP_ADDRESS> Radiation Levels**

At the LHC, the primary source of radiation at full luminosity comes from collisions at the interaction point. In the tracker, charged hadron secondaries from inelastic proton-proton interactions dominate the radiation backgrounds at small radii while further out other sources, such as neutrons, become more important. Table 16.4 shows projected radiation levels in key areas of the detector.

In ATLAS, most of the energy from primaries is dumped into two regions: the TAS (Target Absorber Secondaries) collimators protecting LHC quadrupoles and the forward calorimeters. The beam vacuum system spans the length of the detector and in the forward region is a major source of radiation backgrounds. Primary particles from the interaction point strike the beam-pipe at very shallow angles, such that the projected material depth is large. Studies have shown that the beamline material contributes more than half of the radiation backgrounds in the muon system. The deleterious effects of background radiation fall into a number of general categories: increased background and occupancies, radiation damage and ageing of

**Table 16.4** The 1 MeV neutron equivalent fluence (*F*neq) and doses in key areas of the ATLAS detector after 500 fb−1 of data (estimated to be approximately 7 years of operation at design luminosity)

Also given are the charged-particle fluxes in the tracker and fluxes and single-plane rates in the muon spectrometer

detector components and electronics, single-event upsets and single-event damage, and creation of radionuclides which will impact access and maintenance scenarios.

### *16.2.3 Lessons Learned from the Construction Experience*

It is fair to say that most of the physicists and engineers involved in the ATLAS and CMS construction were faced with a challenge of this scope and size for the first time. It seems therefore appropriate to put some emphasis in this article on the lessons learned from the construction of these detectors. This section describes the general lessons learned and the next sections will give more explicit examples in many cases when describing the experience from the construction of the detector components.

The lessons learned are of varying nature, many are organisational, many are technical and some are sociological. Some are specific to the LHC, some are specific to the way international high-energy physics collaborations work, and some are of a general enough nature that they might well apply to any complex high-tech project of this size. It is therefore hard to classify them in a clear logical order, and this review has attempted to rank them from the general and common to the specific and unique to the LHC.

### **<IP_ADDRESS> Time-Scales, Project Phases and Schedule Delays**

If there has been one lesson learned from the days in the early 1990s when ATLAS and CMS came into being as detector concepts, it is certainly that the research and development phase of projects of this complexity are impossible to plan with real certainty about the time-scales involved. Modern tools for project management are of little help here because the vagaries of the initial phase do not generally obey the simple laws of project schedules and charts. These can be a posteriori explained of course:

Experience has shown however that success was far from guaranteed in this phase, with causes for delays or outright initial failures ranging from being forced to award contracts to the lowest bidder, to incomplete technical specifications, to handling and packaging issues during manufacturing, particularly for polyimidebased products, of which there are many thousands of m2 in both experiments. This material shows up under various forms (especially in flexible printed circuit boards for various applications) and is a basic insulating material with excellent electrical and mechanical properties, with very high tolerance to radiation, but unfortunately also with a high propensity to absorb moisture and thereby lead to unexpected changes in even the course of a well-defined manufacturing process. Serious technical problems in this area have affected the manufacturing schedule of major components of both experiments (hybrids for semi-conductor detectors, flexible parts of printed-circuit boards, large-size electrodes for electromagnetic calorimetry), but other issues such as welding, brazing and general integrity and leak-tightness of thin-walled cooling pipes have also been a concern for several of the components in each experiment.

In addition, several of the more significant contracts were seriously affected by changes in the industrial boundary conditions (insolvency, change of ownership). The recommended purchasing strategy of having multiple suppliers for large contracts, to minimise the consequences from a possible failure in the case of a single supplier, has not always been the optimal one (high-quality silicon sensors are perhaps the most prominent example).

The detailed construction planning can be consulted in the various Technical Design Reports (TDR), most of which were submitted from 1996 to 1998 to seek approval for construction of the major detector components. This called for completion of this construction phase by mid-2001 to mid-2003. At the time when a big schedule and financial crisis shook the LHC project in fall 2001 (see below), it was already clear that many detector components would not be on schedule by a significant margin.

The 2-year delay in the completion of the accelerator resulting from this crisis was also needed by the experiments, as can be seen from Table 16.5, which illustrates the major construction milestones originally planned at the time of the TDRs and actually achieved. When trying to assess the significance of the differences between the dates achieved for the delivery of major components of

**Table 16.5** Main construction milestones for the ATLAS and CMS detectors

Shown are the milestones for the delivery of major components to CERN, as planned at the time of the Technical Design Reports (TDR), and the actual delivery milestones achieved

the experiments and those planned 9 years ago, it is important to remember the prominent events, at CERN and within the collaborations, which happened during these years:

### **<IP_ADDRESS> Physicists and Engineers: How to Strike the Right Balance?**

This is a very delicate issue because there exists no precise recipe to solve this problem. The ATLAS and CMS experiments were born from the dreams of physicists but are based today on the calculations and design efforts from some of the best teams of engineers and designers in the world. One should not forget that, originally (in 1987), even the physicists thought that only a muon spectrometer behind an iron dump was guaranteed to survive the irradiation and that most tracking technologies were doomed at the highest luminosities of the LHC [16].

Although a strong central and across-board (from mechanics to electronics, controls and computing) engineering effort would have been desirable from the very start (i.e. around 1993), a standard centralised and very systematic engineering approach alone, as is frequently used in large-scale astronomy projects, could not have been used for several reasons:

tracking detectors, number of cells in the electromagnetic calorimeter, overall strength and uniformity of the magnetic field, etc.). The number of coils to be constructed in the ATLAS superconducting toroid and the peak field of the CMS central solenoid are two examples of early and fundamental parameters of the experiments, which were studied for quite some time and had a significant bearing on the overall cost of the experiments;

In retrospect, however, there has emerged as a clear lesson, that the management of the experiments should have evolved at an earlier stage the decision-making process from a physicist-centric one at the beginning, when little was known about the detailed design of all the components, to a more engineer-centric one, as the details were fleshed out more and more. Establishing engineering envelopes and assembly drawings for the different systems, routing the very large and diverse amount of services needed to operate complex detectors distributed everywhere across the available space, and designing, validating and procuring common solutions for many of the electronics and controls components are examples, which clearly illustrate this need. The collaborations have indeed encountered difficulties to recognise such needs and to react to them at the appropriate moment in time.

#### **<IP_ADDRESS> International and Distributed: A Strength or a Weakness?**

ATLAS and CMS are truly international and distributed collaborations, even if the engineering and/or manufacturing of some of the major components of both experiments have been entrusted to large laboratories situated all across the world. Modern technology (web access to document servers, video-conferencing facilities, more uniform standards, such as the use of the metric system, for drawings, specifications and quality assurance methods, electronic reporting tools) has been instrumental in improving the efficiency of the various strands of these collaborations, an admittedly weak point of such organisations. There are two major weaknesses intrinsic to collaborations structured as ATLAS and CMS with distributed funding resources:

The strengths of this international and distributed approach far outweigh however its deficiencies over a much more centralised one, such as that adopted for the Super-Conducting Super Collider with a centralised funding and management in Waxahachie (Texas) about 15 years ago:

It is fair to say that, without the motivation and dedication of many of our colleagues all over the world, who fought and won their own battles at all required levels (technical, funding, human resources, organisational), and of their funding agencies, the construction of ATLAS and CMS would not have reached its astounding and successful completion with only small parts of each experiment deferred. Dealing with significant deferrals has always been damaging to the atmosphere of large collaborations of this type and the fact that both experiments are now essentially complete should certainly be attributed to the credit of all their participants.

A particular mention should go here to our Russian colleagues, who have not only strongly contributed intellectually to the experiments, as all the others, from the very beginning, but who also staffed continuously, together with other Eastern European colleagues and also colleagues from Asia, a very large fraction of the teams needed to assemble, equip, test and commission the major detector components. This was quite striking during the installation period from just listening to the conversations occurring in the lifts bringing people and equipment up and down the experimental shafts.

• the concept of deliverables has also turned out to the advantage of the projects. Each set of institutes in each country have been asked to deliver a certain fraction of specific components of the detector systems, ranging from a modest (but critical!) scope, such as the fabrication of the C-fibre cylinders for the barrel semi-conductor tracker in ATLAS, to a very large (and very visible to the whole collaboration!) scope, such as the CMS crystal production in several commercial companies, or as the ATLAS super-conducting solenoid built in Japanese industry, in close collaboration with institutes from the same country, which are full-fledged members of the collaboration.

This concept has certainly maximised the overall funding received by ATLAS and CMS, because each funding agency has to a certain extent been asked and has agreed to take responsibility for the delivery of certain detector components without assigning to these a specific cost, since the real costs vary from country to country, and even the ratios of costs between different countries inevitably vary, because of the approximately uniform costs of raw materials as compared to the wildly differing costs of skilled and unskilled labour. Since the infrastructure of the experiments is a mixture of low and high technology components, most participating countries have in the end been able to contribute efficiently in kind to the common projects of interest to the whole collaboration.

detector operation, monitoring of the data quality and data preparation, leading to the analysis work required to understand precisely the behaviour of the detectors and extract as efficiently as possible the exciting physics ahead of us. The years spent together and the difficulties overcome over a 15-year long period of design and construction have certainly cemented the collaborations in a spirit of respect and mutual understanding of all their diverse components. This will surely turn out to be an excellent preparation for the forthcoming challenges when faced with real experimental data.

### **<IP_ADDRESS> A Well Integrated and Strong Technical Co-ordination Team**

It is clear that without such a team the experiments would most probably have faced insurmountable construction delays and integration problems. The Technical Co-ordination team must in a sense be perceived as the strong backbone of the experiment by all the physicists in the community. This was indeed the case in the installation phase of the experiments, at a time when it had to smoothly execute a complex suite of integration and installation operations for detector components arriving from all over the world. But this was less the case 10–15 years ago, at a time when the physicists and engineers in this team were sometimes perceived as a nuisance disrupting the delicate balance of the collaboration and were criticised in different ways:

In retrospect, these reviews are indeed necessary, whether or not all of their recommendations and outcomes have turned out to be of a specific concrete usefulness, because they have usually forced the project teams to collect documentation, take stock, step back and think about issues sometimes obscured by the more immediate and pressing problems at hand.

Although the construction of the individual detector components can be argued to have been quite successful under the umbrella of deliverables and in the absence of a fully centralised management of the experiment resources, there are obviously a variety of tasks, which have to be solved by a strong centralised team of designers, engineers and physicists. As in any such process, this team is much better accepted if it is built up at least partially from people within the collaboration, who are already well integrated in and known to the collaboration. Despite all the grumbling and moaning, the efforts of the Technical Co-ordination team have been crucial to the success of the ATLAS and CMS projects:

• finding common (often commercial) solutions does not come easily to large numbers of inventive and often opinionated physicists. Common solutions across the experiments are even harder to achieve, although they have turned out to be profitable to all parties in a number of areas. Clearly the strong research and development programme launched in 1989 by CERN for the development of the LHC detector technologies has been a key element in the definition of the various detector concepts (radiation-hard silicon detectors and electronics, electromagnetic and hadronic calorimetry, various tracking technologies, etc.).

In the areas where such common (often commercial) solutions have been adopted in many cases in the past, the successes of the research and development programme have been less spectacular (data transmission, specialised trigger processors, various offline software developments), most probably because the solutions emerging today were not easy to predict from the technology trends of 20 years ago, when the worldwide web, mobile phones, inexpensive desktop computing and high-speed networks did not exist.

The Technical Co-ordination team has certainly been very instrumental in encouraging the collaboration to adopt common technical solutions and has also delegated to the appropriate persons in the collaboration the mandate to negotiate and agree these common solutions across the experiments: the frame contracts with major micro-electronics suppliers, the gas systems, the power supplies, the electronics crates and racks and the slow controls infrastructure hardware and database software can be quoted as some of the more prominent examples.

• establishing a strong quality assurance and review process across the whole collaboration is a must at an early stage in such complex projects, where standard commercial products have often failed, sometimes for multiple reasons owing to the boundary conditions in the experimental caverns (radiation background and magnetic field).

As stated above, the review process (from conceptual engineering design reviews, to production readiness and production advancement reviews) can be very beneficial and even well accepted within the collaboration if it is kept lightweight and perceived as executed by people involved in the project as all the others rather than by an elite breed of top-level managers.

Most of the ATLAS and CMS Technical Design Reports quoted as references in this review address quality assurance with ambitions and specifications, which are fully justified on paper but much harder to implement in reality when facing time pressure and the inevitable lack of human resources to fulfill every aspect of the task. In relation to industry in particular, the effort required in monitoring production of delicate components had been totally underestimated or even ignored in the design phase. The reviews put in place by the Technical Coordination team have played an important role in keeping all aspects related to schedule, resources and quality assurance under control during the detector construction. They have also ensured that large groups with significant project responsibilities were not allowed to operate for too long in a stand-alone mode without synchronising with and reporting back to Technical Co-ordination, the management of the experiments and the collaboration at large. The risks involved in letting things go astray too much are simply unacceptable for projects of this complexity and size.

• As stated above, one weakness perhaps of the multiple dimensions under which ATLAS and CMS are viewed is that the funding agencies have often conducted their own necessary review processes in a way largely decoupled from the review process operated by the management of the experiments. This weakness stems from the lack of central control of expenditures because of the distributed funding and spending responsibilities. This can obviously lead to inefficiencies in the actual execution of the project and, worse, sometimes to conflicting messages given to the institutes concerning priorities, since those of a given funding agency may not always coincide with those of the experiment. The common funds necessary to the construction of significant components of the experiments, such as magnets, infrastructure, shielding, cryostats, etc., are a prominent example which comes to mind, when assessing which of the components of the experiments had the most difficulty in dealing with the multithreaded environment, in which the detector construction has been achieved.

Finally, it is in the very recent phase of assembly, installation and commissioning of the ATLAS and CMS detectors that the enormous efforts and contribution from the Technical Co-ordination teams have been most visible: they have had to organise the vast teams of sub-contractors and specialised personnel from the collaborating institutes and they have had to deal with the daily burden of making sure all the tasks were executed as smoothly as possible with safety as one of the paramount requirements.

### **16.3 Inner Tracking System**

### *16.3.1 Introduction*

The ATLAS tracker is designed to provide hermetic and robust pattern recognition, excellent momentum resolution and both primary and secondary vertex measurements [17] for charged tracks above a given *pT* threshold (nominally 0.5 GeV, but as low as 0.1 GeV in some ongoing studies of initial measurements with minimumbias events) and within the pseudorapidity range |*η*| *<* 2*.*5. It also provides electron identification over |*η*| *<* 2*.*0 and a wide range of energies (between 0.5 and 150 GeV). It is contained within a cylindrical envelope of length ±3512 mm and of radius 1150 mm, within the solenoidal magnetic field of 2 T. Figures 16.8 and 16.9 show the sensors and structural elements traversed by 10 GeV tracks in respectively the barrel and end-cap regions.

**Fig. 16.8** Drawing showing the sensors and structural elements traversed by a charged track of 10 GeV *pT* in the ATLAS barrel inner detector (*η* = 0*.*3). The track traverses successively the beryllium beam-pipe, the three cylindrical silicon-pixel layers with individual sensor elements of 50 × 400 μm2, the four cylindrical double layers (one axial and one with a stereo angle of 40 mrad) of barrel silicon-microstrip sensors (SCT) of pitch 80μm, and approximately 36 axial straws of 4 mm diameter contained in the barrel transition-radiation tracker modules within their support structure

The ATLAS tracker consists of three independent but complementary subdetectors. At inner radii, high-resolution pattern recognition capabilities are available using discrete space-points from silicon pixel layers and stereo pairs of silicon micro-strip (SCT) layers. At larger radii, the transition radiation tracker (TRT) comprises many layers of gaseous straw tube elements interleaved with transition radiation material. With an average of 36 hits per track, it provides continuous tracking to enhance the pattern recognition and improve the momentum resolution over |*η*| *<* 2*.*0 and electron identification complementary to that of the calorimeter over a wide range of energies.

Table 16.6 lists the main parameters of the ATLAS tracker:

• the radial position of the innermost measurement is essentially determined by the outer diameter of the beam pipe, which has been manufactured using expensive and delicate Beryllium material over an overall length of 7 m. The active part of the tracker has a half-length of 280 cm, slightly longer than that of its solenoid, resulting in significant field non-uniformities and momentum resolution degradation at each end.

**Fig. 16.9** Drawing showing the sensors and structural elements traversed by two charged tracks of 10 GeV *pT* in the ATLAS end-cap inner detector (*η* = 1*.*4 and 2.2). The end-cap track at *η* = 1*.*4 traverses successively the beryllium beam-pipe, the three cylindrical silicon-pixel layers with individual sensor elements of 50 × 400 μm2, four of the disks with double layers (one radial and one with a stereo angle of 40 mrad) of end-cap silicon-microstrip sensors (SCT) of pitch ∼80μm, and approximately 40 straws of 4 mm diameter contained in the end-cap transition radiation tracker wheels. In contrast, the end-cap track at *η* = 2*.*2 traverses successively the beryllium beam-pipe, only the first of the cylindrical silicon-pixel layers, two end-cap pixel disks and the last four disks of the end-cap SCT. The coverage of the end-cap TRT does not extend beyond |*η*| = 2

**Table 16.6** Main parameters of the ATLAS tracker system

The high-radiation environment imposes stringent conditions on the innerdetector sensors, on-detector electronics, mechanical structure and services. Over the 10-year design lifetime of the experiment, the pixel inner vertexing layer must be replaced after approximately 3 years of operation at design luminosity. The other pixel layers and the pixel disks must withstand a 1 MeV neutron equivalent fluence Fneq [18] of up to ∼8 × 1014 cm−2. The innermost parts of the SCT must withstand Fneq of up to 2 × 1014 cm−2. To maintain an adequate noise performance after radiation damage, the silicon sensors must be kept at low temperature (approximately −5 to −10 ◦C) implying coolant temperatures of ∼−25 ◦C. In contrast, the TRT is designed to operate at room temperature.

The above operating specifications imply requirements on the alignment precision which are summarised in Table 16.7 and which serve as stringent upper limits on the silicon-module build precision, the TRT straw-tube position, and the measured module placement accuracy and stability. This leads to:

**Table 16.7** Intrinsic measurement accuracies and mechanical alignment tolerances for the tracker sub-systems, as defined by the performance requirements of the ATLAS experiment

The numbers in the table correspond to the single-module accuracy for the pixels, to the effective single-module accuracy for the SCT and to the drift-time accuracy of a single straw for the TRT aArises from the 40 mrad stereo angle between back-to-back sensors on the SCT modules with axial (barrel) or radial (end-cap) alignment of one side of the structure. The result is pitchdependent for end-cap SCT modules

bThe quoted alignment accuracy is related to the TRT drift-time accuracy

(c) a trade-off between the low material budget needed for optimal performance and the significant material budget resulting from a stable mechanical structure with the services of a highly granular detector.

The design and construction of systems, capable of meeting the physics requirements and of providing stable and robust operation over many years, has been perhaps the most formidable challenge faced by the experiment because of the very harsh radiation conditions to be faced near the interaction point and of the conflicting requirements in terms of material budget between the physics and the design constraints. The latter arise mostly from the on-detector high-speed frontend electronics, which require a lot of power to be fed into a limited volume and therefore a large amount of heat to be removed from a very distributed set of local heat sources across the whole tracker.

This section describes briefly the ATLAS tracker and its main properties and discusses a few salient aspects from the construction experience and from the measured performance in laboratory and test beam of production modules in the various technologies. A few examples of the overall performance expected in the actual configuration of the experiment are presented in Sect. 16.8.1, where it is also compared to the expected performance of the CMS tracker.

### *16.3.2 Construction Experience*

### **<IP_ADDRESS> General Aspects**

The ATLAS tracker system has evolved considerably since the submission of the Technical Proposal in 1994 and even since the corresponding Technical Design Reports in 1997/1998. The evolution was dictated by many factors, some of which have already been alluded to in Sect. 16.2.3 and some of which are related to the specific design challenges posed:

Another more general example stems from the engineering choices made for the implementation of the on-detector and off-detector cooling systems: there are as many on-detector cooling schemes and pipe material choices as there are detector components. The cooling systems themselves are all operating under severe space limitations on-detector and at high pressure (from 3 to 6 bars). These systems range from room-temperature monophase C6F14 for the TRT to cold evaporative C3F8 for the SCT and pixels. Many problems have been encountered during the commissioning in situ and early operation of these systems, and it is fair to say a posteriori that this is one area where a stronger and more centralised engineering effort would have probably come up with a more uniform, more robust and redundant, and less risky implementation.

• Table 16.8 shows how optimistic the estimate of the material budget of the ATLAS tracker was at the time of the Technical Proposal in 1994 and how it has evolved since then to reach the values quoted in early 2008, after completion of the installation of all of its components. These values cannot be claimed to be final yet, although most of the remaining uncertainties are small and related to the exact routing details of the various services and of patch-panels for cable and pipe connections. These are situated within the tracker volume, but not always in the fiducial region where the detectors expect to perform precision tracking and electromagnetic calorimetry measurements (for example, the patch-panels for the pixel detector are outside this fiducial region). The material budget for the tracker has risen steadily over the years and the only significant decrease seen (from 1997 to now) is due to the rerouting of the pixel services from a large radius along the LAr barrel cryostat to a much smaller radius along the pixel

The numbers are given in fractions of radiation lengths (*X/X*0). Note that, for ATLAS, the reduction in material from 1997 to 2006 at *η* ≈ 1*.*7 is due to the rerouting of pixel services from an integrated barrel tracker layout with pixel services along the barrel LAr cryostat to an independent pixel layout with pixel services routed at much lower radius and entering a patch panel outside the acceptance of the tracker (this material appears now at *η* ≈ 3). Note also that the numbers do not represent all the material seen by particles before entering the active part of the electromagnetic calorimeter, since particles see in addition the barrel LAr cryostat and the solenoid coil (amounting to approximately 2*X*0 at *η* = 0) or the end-cap LAr cryostat at the larger rapidities

**Fig. 16.10** Material distribution (*X*0, *λ*) at the exit of the ATLAS tracker, including the services and thermal enclosures. The distribution is shown as a function of |*η*| and averaged over *φ*. The breakdown indicates the contributions of external services and of individual sub-detectors, including services in their active volume. These plots do not include additional material just in front of the electromagnetic calorimeter, which is quite large in ATLAS (LAr cryostats and, for the barrel, solenoid coil)

support tube, a significant change in the ATLAS tracker design, which occurred in 1999.

Figure 16.10 shows how this material budget is distributed as a function of pseudorapidity. The material closest to the beam (pixel detectors) is clearly the one most critical for the performance of the tracker and of the electromagnetic calorimetry: this amounts to between 10 and 50% X/X0. The material budget can also be broken down in terms of its functional components: a large contribution to the material budget arises from cooling and cables in areas where these services accumulate to be routed radially outwards, towards the cracks in the electromagnetic calorimetry foreseen for their passage. It is therefore not surprising that, until all the details of the granularity, technical components, routing, fixation schemes, etc., were known and incorporated into assembly drawings and detailed spreadsheets, the material budgets announced for this tracker of unprecedented scope and complexity were largely underestimated.

#### **<IP_ADDRESS> Silicon-Strip and Straw Tube Trackers**

The ATLAS SCT contains a total of 4088 modules corresponding to 6.3 million channels, of which 99.7% have been measured to be fully operational in terms of electrical and thermal performance in situ. The ATLAS TRT comprises approximately 350,000 channels, of which about 98.5% fully meet the operational specifications in terms of noise counting rate and of basic efficiency and highvoltage behaviour.

The ATLAS tracker was installed in three successive stages, from summer 2006 (barrel SCT/TRT tracker), to end 2006 (end-cap SCT/TRT trackers), and to spring 2007 (pixels). It is impossible to properly give credit here to all the work performed over the past 15 years to validate the design choices involving each and every one of the delicate components composing these tracking detectors. Only a few of the most prominent examples are quoted below:

#### **<IP_ADDRESS> Pixel Detectors**

The ATLAS pixel detector has been one of the last elements installed in the experiment, in great part for practical reasons, but also because this is the detector which has undergone the most difficult development path. It can perhaps be considered as the most striking example of the marvels achieved during the long and painstaking years of research and development: the pixel detector will survive over many years in the most hostile region of the experiment and deliver some of the most important data required to understand in detail what will be happening within a few tens of microns from the interaction point.

Fifteen years ago, at the time of the ATLAS Technical Proposal, very few physicists believed that these detectors could be built within the specifications required in terms of radiation hardness and of readout bandwidth and speed. Today, the data collected using cosmic rays (in 2008 and 2009) and early collisions (end of 2009) have demonstrated that the pixel detector works as expected. The future will tell how long the innermost layer will survive, but the collaboration is already proceeding towards a strategy of "replacement" of the innermost pixel layer on the timescale of 2015. This innermost layer is not expected to survive over the full timespan of the operation of the experiment, which should lead to integrated luminosities

**Table 16.9** Main parameters of the ATLAS pixel system

of close to 300 fb−1. Table 16.9 shows the most relevant parameters concerning the ATLAS pixel system.

Finally, Fig. 16.11 shows the results of test-beam measurements of the *Rφ* accuracy of production modules of the ATLAS pixel detector before and after being irradiated with a total equivalent fluence corresponding to about 1015 neutrons per cm2 [22]. These results are somewhat optimistic because they were obtained with analogue readout and at an ideal incidence angle, but they nevertheless demonstrate the extreme robustness of the pixel modules constructed for ATLAS. This is one striking example of the painstaking validation work done in the early phase of the construction years.

### **16.4 Calorimeter System**

The design of the ATLAS calorimeter system is to a large extent the end product of about 25 years of development and experience gained over several generations of high-energy colliders and general-purpose experiments, all of which have brought major advances in the understanding of the field. These advances range from the concept of full coverage in total transverse energy at UA1, to that of precision hadron calorimetry at ZEUS, and to that of very high granularity of the electromagnetic calorimeters and the use of energy-flow techniques in the LEP detectors [23].

**Fig. 16.11** Residuals from *Rφ* measurements of production-grade ATLAS pixel module before irradiation (left) and after being irradiated with a total equivalent fluence corresponding to about 1015 neutrons per cm2 (right), as obtained from test-beam data taken in 2004. The contribution of the track extrapolation to the width of the residuals is about 5μm (it should be subtracted in quadrature from the overall residual widths quoted in the figure to obtain the intrinsic resolution of the tested module)

**Fig. 16.12** Cut-away view of the ATLAS calorimeter system. The various calorimeter components are clearly visible, from the LAr barrel and end-cap electromagnetic calorimeters, to the scintillating tile barrel and extended barrel hadronic calorimeters, and to the LAr end-cap and forward hadronic calorimeters

The ATLAS calorimeter system, as depicted overall in Fig. 16.12, will play a crucial role at the LHC for two main reasons: first, its intrinsic resolution improves with energy, in contrast to magnetic spectrometers; second, it will provide the trigger primitives for all the high-*pT* objects of interest to the experiments except for the muons.

The integration of a hermetic and high-precision calorimeter system into the overall design of the ATLAS detector and its magnet systems has been a task of high complexity where compromises have had to be made, as will be shown in the first part of this section, which describes the basic requirements and features of the calorimeters. As illustrated in the second part, which highlights some aspects of the construction of the most critical element, namely the electromagnetic calorimeter, and of its measured performance in test beam, the impact of the main design choices and of the technology implementations on the performance has been very significant. A few examples of the overall performance expected in the actual configuration of the experiment are presented in Sect. 16.8.2, where it is also compared to the expected performance of the CMS calorimeter system.

### *16.4.1 General Considerations*

#### **<IP_ADDRESS> Performance Requirements**

The main performance requirements from the physics on the calorimeter system can be briefly summarised as follows:

will also thus be able to identify forward jets produced in vector-boson fusion processes.

#### **<IP_ADDRESS> General Features of Electromagnetic Calorimetry**

The ATLAS EM calorimeter [25] is divided into a barrel part covering approximately |*η*| *<* 1*.*5 and two end-caps covering 1*.*4 *<* |*η*| *<* 3*.*2, and its main parameters are listed in Table 16.10. Its fiducial coverage is without appreciable cracks, except in the transition region between the barrel and end-cap cryostats, where the measurement accuracy is degraded over 1*.*37 *<* |*η*| *<* 1*.*52 because of large energy losses in the material in front of the active EM calorimeter, which reaches up to 6 *X*0. The excellent uniformity of coverage is a direct consequence of the design of this lead/liquid Argon sampling calorimeter with accordion-shaped electrodes and absorbers. The total thickness of the EM calorimeter varies from a minimum of 24 X0 (at *η* ≈ 0) to a maximum of 35 X0 (at *η* ≈ 2*.*5). This depth is sufficient to contain EM showers at the highest energies (a few TeV) and preserve the energy resolution, in particular the constant term which is dominant above a few hundred GeV.

As can be seen from Table 16.10, the ATLAS EM calorimeter has been designed with both excellent lateral and longitudinal granularity, with samplings in depth optimised for energy loss corrections (presampler) and for shower pointing accuracy together with *γ* /*π*0 and electron/jet separation (strips). The intrinsic performance of the EM calorimeter is however significantly affected by the unavoidable amount of material which had to be incorporated in the tracker system (see Fig. 16.10), and also by the cryostats and the solenoid coil in the case of the ATLAS EM calorimeter (see Sect. 16.8.2 for more details).

#### **<IP_ADDRESS> General Features of Hadronic Calorimetry**

Figure 16.13 shows the total number of absorption lengths contained in the ATLAS hadronic calorimetry and in front of the muon system as a function of pseudorapidity. Good containment of jets of typically 1 TeV energy requires about 11 *λ* in the full calorimeter, a target which has been achieved over most of the pseudorapidity range.

For the central part of the hadronic calorimetry, which covers the range 0 *<* |*η*| *<* 1*.*7, the sampling medium consists of scintillator tiles and the absorber medium is steel. The tile calorimeter is composed of three parts, one central barrel and two extended barrels. The choice of this technology provides maximum radial depth for the least cost for ATLAS. The hadronic calorimetry is extended to

**Table 16.10** Main parameters of the ATLAS calorimeter system

(continued)

**Table 16.10** (continued)

larger pseudorapidities by a copper/liquid-argon calorimeter system, which covers the range 1*.*5 *<* |*η*| *<* 3*.*2, and by the forward calorimeters, a set of coppertungsten/liquid-argon detectors at larger pseudorapidities. The hadronic calorimetry thus reaches one of its main design goals, namely coverage over |*η*| *<* 4*.*9.

The ATLAS forward calorimeters are fully integrated into the cryostat housing the end-cap calorimeters, which reduces the neutron fluence in the muon system and, with careful design, affects very little the neutron fluence in the tracker volume. The main role of these calorimeters is to keep the tails in the measurement of missing transverse energy at a low level and to tag jets in the forward direction rather than to accurately measure their energy, so their geometry has been simplified and their readout costs have been minimised. The forward calorimeters are based on copper (front) and tungsten (back) absorber bodies and absorber rods, the latter being parallel to the beam and slotted into precisely machined holes. The gaps in these holes are filled with LAr and operated at an electric field of about 1 kV/mm.

**Fig. 16.13** Distribution of amount of material (in absorption lengths) for the ATLAS calorimetry (and in front of the muon system) as a function of *η*

### *16.4.2 Construction Experience and Measured Performance in Test Beam*

As has been described above, the ATLAS calorimeters comprise a variety of technologies, each with its own challenges and pitfalls, and only a few of the most prominent examples of lessons learned during construction can be given in this review.

The biggest challenge has clearly been the construction of the electromagnetic calorimeters. The technology chosen for the ATLAS EM calorimeter, although based on a well established technique had a number of innovative features, which resulted in some major production issues:

**Fig. 16.14** Linearity of response (left) and energy resolution (right) obtained for a production module of the ATLAS barrel EM calorimeter as a function of the incident electron beam energy

• radiation-tolerant electronics had to be produced for all components in the cavern. This comprises all the front-end electronics boards housed near the signal feed-throughs.

The ATLAS collaboration has performed an extensive programme of test-beam measurements to calibrate and characterise the EM calorimeter modules [26]. The original plans called for a test-beam calibration of about 20% of the modules. In the end, a smaller fraction of 15% of the ATLAS EM modules underwent detailed test-beam measurements, and a few recent results from these stand-alone calibration campaigns are presented here.

Figure 16.14 shows that a linearity of response of ±1 per mil has been obtained over an electron energy range from 20 to 180 GeV for an ATLAS barrel LAr EM module. To achieve this, while preserving the energy resolution (also shown in Fig. 16.14), requires a thorough understanding of the material in front of the active calorimeter and a careful evaluation of the weights and corrections to be applied to the raw cluster energy. The uniformity of response across the whole module has also been measured and found to contribute an r.m.s. of 0.4% to the global constant term, which is within the specifications set to the LAr EM calorimeter (see Sect. 16.8.2 for a more detailed discussion of the various contributions to the constant term for the EM calorimeters).

### **16.5 Muon Spectrometer System**

Muons are a very robust, clean and unambiguous signature of much of the physics that ATLAS has been designed to study. The ability to trigger and to reconstruct muons at the highest luminosities of the LHC has been incorporated into the design of the experiment from the very beginning [29]. In fact, the concepts chosen for measuring muon momenta have shaped the experiment more than any other physics consideration (see also Sect. 16.2.1).

As discussed already in Sect. 16.2.2, the choice of magnet was motivated by the method which would be used for the measurement of muons with momenta up to ∼ TeV scales. ATLAS has thus opted for a high-resolution, stand-alone measurement independently of the rest of the sub-detectors, resulting in a very large volume, with low material density, over which the muon measurement takes place. The ATLAS toroidal magnetic field provides a momentum resolution which is essentially independent of pseudorapidity up to a value of 2.7.

This section reviews the main features of the muon spectrometer system and discusses a few of the challenges encountered. A few examples of the overall performance expected in the actual configuration of the experiment are presented in Sect. 16.8.3, where it is also compared to the expected performance of the CMS muon system.

### *16.5.1 General Considerations*

The physics signatures that give rise to muons are numerous and varied. At the highest momenta, they include muons from new high-mass (multi-TeV) resonances such as heavy neutral gauge bosons, *Z* , as well as decays from heavy Higgs bosons. At the lowest end of the spectrum, B-physics relies on the reconstruction of muons with momentum down to a few GeV. The resulting requirements are:

There are also the requirements which result from the 25 ns spacing in time between successive beam crossings and from the neutron radiation environment of the experimental halls. Good timing resolution and the ability to identify the bunchcrossing in question, as well as redundancy in the measurements, are therefore also demanded of the muon detectors, which represent by far the largest and most difficult system to install in the experiment.

**Fig. 16.15** Cut-away view of the ATLAS muon spectrometer system. displaying the regions in which the different muon chamber technologies are used

The conceptual layout of the muon spectrometer is shown in Fig. 16.15 and the main parameters of the muon chambers are listed in Table 16.11. It is based on the magnetic deflection of muon tracks in the large superconducting air-core toroid magnets, instrumented with separate trigger and high-precision tracking chambers. Over the range |*η*| *<* 1*.*4, magnetic bending is provided by the large barrel toroid. For 1*.*6 *<* |*η*| *<* 2*.*7, muon tracks are bent by two smaller end-cap magnets inserted into both ends of the barrel toroid. Over 1*.*4 *<* |*η*| *<* 1*.*6, usually referred to as the transition region, magnetic deflection is provided by a combination of barrel and end-cap fields. This magnet configuration provides a field which is mostly orthogonal to the muon trajectories, while minimising the degradation of resolution due to multiple scattering. The anticipated high level of particle flux has had a major impact on the choice and design of the spectrometer instrumentation, affecting performance parameters such as rate capability, granularity, ageing properties, and radiation hardness. In the barrel region, tracks are measured in chambers arranged in three cylindrical layers around the beam axis; in the transition and end-cap regions, the chambers are installed in planes perpendicular to the beam, also in three layers.

#### **<IP_ADDRESS> Muon Chamber Types**

Over most of the *η*-range, a precision measurement of the track coordinates in the principal bending direction of the magnetic field is provided by Monitored Drift Tubes (MDT's). The mechanical isolation in the drift tubes of each sense wire from its neighbours guarantees a robust and reliable operation. At large pseudorapidities, Cathode Strip Chambers (CSC's, which are multiwire proportional chambers with

**Table 16.11** Main parameters of the ATLAS muon spectrometer

> Numbers in brackets for the MDT's and the RPC's refer to the final configuration of the detector in 2009

cathodes segmented into strips) with higher granularity are used in the innermost plane over 2 *<* |*η*| *<* 2*.*7, to withstand the demanding rate and background conditions. The stringent requirements on the relative alignment of the muon chamber layers are met by the combination of precision mechanical-assembly techniques and optical alignment systems both within and between muon chambers.

The trigger system covers the pseudorapidity range |*η*| *<* 2*.*4. Resistive Plate Chambers (RPC's) are used in the barrel and Thin Gap Chambers (TGC's) in the end-cap regions. The trigger chambers for the muon spectrometer serve a threefold purpose: provide bunch-crossing identification, provide well-defined *pT* thresholds, and measure the muon coordinate in the direction orthogonal to that determined by the precision-tracking chambers.

#### **<IP_ADDRESS> Muon Chamber Alignment and B-Field Reconstruction**

The overall performance over the large areas involved, particularly at the highest momenta, depends on the alignment of the muon chambers with respect to each other and with respect to the overall detector.

The accuracy of the stand-alone muon momentum measurement necessitates a precision of 30μm on the relative alignment of chambers both within each projective tower and between consecutive layers in immediately adjacent towers. The internal deformations and relative positions of the MDT chambers are monitored by approximately 12,000 precision-mounted alignment sensors, all based on the optical monitoring of deviations from straight lines. Because of geometrical constraints, the reconstruction and/or monitoring of the chamber positions rely on somewhat different strategies and sensor types in the end-cap and barrel regions, respectively.

The accuracy required for the relative positioning of non-adjacent towers to obtain adequate mass resolution for multi-muon final states, lies in the few millimetre range. This initial positioning accuracy is approximately established during the installation of the chambers. Ultimately, the relative alignment of the barrel and forward regions of the muon spectrometer, of the calorimeters and of the tracker will rely on high-momentum muon trajectories.

For magnetic field reconstruction, the goal is to determine the bending power along the muon trajectory to a few parts in a thousand. The field is continuously monitored by a total of approximately 1800 Hall sensors distributed throughout the spectrometer volume. Their readings are compared with magnetic-field simulations and used for reconstructing the position of the toroid coils in space, as well as to account for magnetic perturbations induced by the tile calorimeter and other nearby metallic structures.

The muon system consists of three large superconducting air-core toroid magnets, which are instrumented with different types of chambers to provide the two needed functions, namely high-precision tracking and triggering. The central (or barrel) region, |*η*| *<* 1*.*0, is covered by a large barrel magnet consisting of eight coils which surround the hadron calorimeter. In this region, tracks are measured in chambers arranged in three cylindrical layers (stations) around the beam axis. In the end-cap region, 1*.*4 *<* |*η*| *<* 2*.*7, muon tracks are bent in two smaller end-cap magnets inserted into both ends of the barrel toroid. The intermediate (transition) region, 1*.*0 *<* |*η*| *<* 1*.*4, is less straightforward, since here the barrel and endcap fields overlap, thus partially reducing the bending power. To keep a uniform resolution in this region, tracking chambers are place in strategic places to improve the quality and accuracy of the measurement. Due to financial constraints, one out of three sets of chambers in this region has been staged, thus leading to an inferior performance in the transition region for the first years of data-taking.

The layout of the ATLAS muon spectrometer system is shown in Fig. 16.15. A total of four types of detectors are used, the choice of technology being driven by the very large surface to be covered, by trigger and precision measurement requirements, and by the different radiation environments. Resistive Plate Chambers (RPC) in the barrel region (|*η*| *<* 1*.*05) and Thin Gap Chambers (TGC) in the endcap regions (1*.*05 *<* |*η*| *<* 2*.*4) are used for triggering purposes. These chambers provide a fast response with good time resolution but rather coarse position resolution. The precision measurements are performed by Monitored Drift Tubes (MDT) over most of the coverage. In the regions at large |*η*|, where background conditions are harsher and the rate of muon hits is therefore larger, Cathode Strip Chambers (CSC) are used.

The basic principle of the muon measurement in the ATLAS muon spectrometer is to obtain three segments (or super-points) along the muon trajectory. For momenta up to 300 GeV, the resolution is limited to a few percent by multiple scattering and fluctuations in the energy loss in the calorimeters, and can therefore be improved by combining the momentum measurement with that obtained in the Inner Detector. The momentum resolution goals quoted above at higher momenta imply a very high precision of 80μm on the individual hits, given the three-point measurement and the available bending power. The required precision on the muon momentum measurement also implies excellent knowledge of the magnetic field. The air-core toroid design leads to a magnetic field, which is modest in average magnitude (0.5 T), but is also inhomogeneous, and must therefore be measured and monitored with high precision (at the level of 20 G). The inhomogeneity of the field and its rapid variations cannot be approximated by simple analytical descriptions and have to be accounted for carefully, thereby enhancing the importance of the use of the inner detector information to reconstruct low-momentum muon tracks with low fake rates.

#### **<IP_ADDRESS> Alignment**

Alignment of the muon chambers with respect to each other and with respect to the overall detector is a critical ingredient, key to obtaining the desired performance over the large areas involved, particularly at the highest momenta. The high accuracy of the ATLAS stand-alone measurement necessitates a very high precision of 30μm on the alignment.

The chambers have however been installed with an accuracy of a few mm, and obviously, no attempt at repositioning the chambers once their installation is completed can realistically be made. Instead, intricate hardware systems have been designed to measure the relative positions between chambers contributing to the measurement of the same tracks, but also to monitor any displacements during the detector operation. These systems are designed to provide continuous monitoring of the positions of the chambers with or without collisions in the accelerator. The very strict requirement of a 30μm alignment has necessitated the design of a complex system, in which optical sensors are mounted with very high mechanical mounting precision (better than 20μm in the precise coordinate). The system uses ∼5000 alignment sensors, which are either installed on the chambers or in the socalled alignment bars (long instrumented Aluminium cylinders with deformations monitored to within 10μm, which constitute the alignment reference system in the end-caps). In addition, 1789 magnetic field sensors (3D Hall probes) are also being installed on the chambers to determine with high accuracy the position and shape of the conductors of each coil. From these accurate measurements, the field will be determined throughout the whole volume to an accuracy of about 20 G, provided all magnetic materials are also mapped and described accurately.

The final alignment values will clearly be obtained with the large statistics of muon tracks traversing the muon chambers (rates of about 10 kHz are expected at a luminosity of 1033 cm−2 s−1 for muons with *pT >* 6 GeV).

### *16.5.2 Construction Experience and Measured Performance in Laboratory and Test Beam*

The muon chambers are based on technologies, which were used in previous experiments: drift tubes and CSCs have been used widely in the past; RPCs were used in the L3 and Babar experiments, while TGCs were used in OPAL. Nevertheless, large R&D efforts have been necessary to address the special requirements of the LHC environment.

The high particle fluxes (mainly photons and neutrons) have necessitated searches for the right type of materials and gases, which prevent wire deposits in the case of drift tubes, while new operational modes were developed for the RPCs (proportional regime instead of the streamer regime used in previous experiments) and the TGCs (quasi-proportional mode instead of saturated mode), with the corresponding required changes in the front-end electronics.

In the case of the ATLAS muon spectrometer, the requirement of a precise standalone measurement limits the amount of material in order to minimise multiple scattering. This has led to the development of thin but precise Aluminium tubes, which are mounted on very light structures. The deformations of these structures can be monitored by a sophisticated alignment system, as well as the extensive use of paper honeycomb in the trigger chambers to limit the contribution of the detectors in the material description.

Beyond this, the greatest challenge came mostly from the very large, unprecedented areas that the muon chambers had to cover and the correspondingly large numbers of electronic channels. The ATLAS muon system contains approximately 25,000 m2 of active detection planes, and roughly one million electronic channels. The main parameters of the muon chambers are listed in Table 16.11.

The requirement of achieving all this within 'reasonable cost' was actually one of the biggest issues encountered. In terms of lessons learned from the construction process; beyond the general observations made in Sect. 16.2.3, three issues emerge as the most important ones:

consuming and eventually more space-consuming than planned. Whereas the first two issues can, at least in principle, be solved with additional manpower and increased costs, the space issue is a major one, which needs adequate planning right from the start. The space issue has been compounded by the fact that the muon system is traversed by the services of the other detectors, leading to issues of ownership of space and to problems in collecting all the necessary information for proper planning. This major complexity of the actual installation of the services has been one of the major challenges of the Technical Coordination team.

• Uniformity of technologies, power supplies and electronics. As already explained in the introduction, the size of the muon project has necessitated the distribution of the design and construction across different institutes and funding agencies. This necessarily leads to a multitude of different choices for numerous components, from the choice of high-voltage power supplies to basic choices of electronics (ASICs or FPGAs). A strong electronics coordination team is needed to alleviate many of these pressures and lead to an overall system, which will be much easier to maintain.