# Anomalous Residual Surface Conductivity in a Superconductor with Strong
Spin-Orbit Coupling

J. R. Chamorro  These authors contributed equally to this work.  Department of
Chemistry, The Johns Hopkins University, Baltimore, MD 21218, USA  Institute
for Quantum Matter, Department of Physics and Astronomy, The Johns Hopkins
University, Baltimore, MD 21218, USA  P. Chauhan  These authors contributed
equally to this work.  Institute for Quantum Matter, Department of Physics and
Astronomy, The Johns Hopkins University, Baltimore, MD 21218, USA  C. Sun
Institute for Quantum Matter, Department of Physics and Astronomy, The Johns
Hopkins University, Baltimore, MD 21218, USA  N. Varnava  Department of
Physics & Astronomy, Rutgers University, Piscataway, NJ 08854, USA  M. J.
Winiarski  Faculty of Applied Physics and Mathematics and Advanced Materials
Center, Gdansk University of Technology, ul. Narutowicza 11/12, 80-233 Gdansk,
Poland  N. Ng  Department of Chemistry, The Johns Hopkins University,
Baltimore, MD 21218, USA  Institute for Quantum Matter, Department of Physics
and Astronomy, The Johns Hopkins University, Baltimore, MD 21218, USA  H. K.
Vivanco  Department of Chemistry, The Johns Hopkins University, Baltimore, MD
21218, USA  Institute for Quantum Matter, Department of Physics and Astronomy,
The Johns Hopkins University, Baltimore, MD 21218, USA  L. A. Pressley
Department of Chemistry, The Johns Hopkins University, Baltimore, MD 21218,
USA  Institute for Quantum Matter, Department of Physics and Astronomy, The
Johns Hopkins University, Baltimore, MD 21218, USA  C. M. Pasco  Department of
Chemistry, The Johns Hopkins University, Baltimore, MD 21218, USA  Institute
for Quantum Matter, Department of Physics and Astronomy, The Johns Hopkins
University, Baltimore, MD 21218, USA  D. Vanderbilt  Department of Physics &
Astronomy, Rutgers University, Piscataway, NJ 08854, USA  Yi Li  Institute for
Quantum Matter, Department of Physics and Astronomy, The Johns Hopkins
University, Baltimore, MD 21218, USA  N. P. Armitage  Institute for Quantum
Matter, Department of Physics and Astronomy, The Johns Hopkins University,
Baltimore, MD 21218, USA  T. M. McQueen<EMAIL_ADDRESS>Department of
Chemistry, The Johns Hopkins University, Baltimore, MD 21218, USA  Institute
for Quantum Matter, Department of Physics and Astronomy, The Johns Hopkins
University, Baltimore, MD 21218, USA  Department of Materials Science and
Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA

###### Abstract

Conventional BCS superconductors are expected to exhibit a conductivity with
vanishing dissipation with decreasing temperature. While bulk physical
properties measurements indicate PdPb2 is a conventional superconductor with a
$T_{c}$ of 3.0 K, measurements of surface impedance through the microwave
cavity perturbation technique indicate a large, non-vanishing dissipative
component below $T_{c}$ that is at odds with conventional superconductivity.
We demonstrate PdPb2 to be a possible topological superconductor with a fully
gapped bulk and a dissipative Majorana fluid surface.

Topological superconductors can host Majorana fermions inside vortex cores and
on their surfaces [1]. They have been proposed as platforms for topological
quantum computing [2, 3]. There are a number of ways of realizing such
Majorana fermions, such as topological insulator-superconductor
heterostructures [4, 5, 6, 7, 8], doping-induced superconductivity in
topological insulators[9, 10, 11, 12], and superconductivity-proximitized
nanowires[13, 14, 15, 16]. There are also recent proposals of intrinsic
topological superconductors, such as in $\beta$-Bi2Pd[17, 18, 19] and
FeTe1-xSex[20, 21, 22].

Analogous to a topological insulator, an intrinsic topological superconductor
is expected to show surface behavior markedly different from that of the bulk.
Topological surface states, if present in the normal state, as is the case in
$\beta$-Bi2Pd and FeTe1-xSex, may be proximitized by the superconducting bulk,
and are expected to possess an unconventional, odd-parity gap function that
may give rise to Majorana bound states within vortices. Alternatively, under
the right symmetry conditions, the bulk of the superconductor may itself be
topological, and can give rise to topological surface states below $T_{c}$
[8]. This kind of topological superconductor is fully gapped in the bulk, but
is expected to show non-superconducting surface metallicity. The metallic
surfaces in such cases are expected to host Majorana fermions as opposed to
massless Dirac fermions, as in topological insulators [8].

In this Letter, we present evidence for the existence of non-superconducting
metallic surface states in centrosymmetric, tetragonal PdPb2 below its bulk
superconducting transition temperature of $T_{c}=3$ K. Measurements of the
bulk indicate a fully gapped superconducting state, which are in constrast to
measurements of the surface impedance through the microwave cavity
perturbation technique that indicate significant low frequency dissipation by
surface carriers below $T_{c}$, an observation contrary to the expectations
for a conventional superconductor. Through extensive sample characterization,
we rule out extrinsic origins for the observed phenomenology, and propose
PdPb2 to be a candidate topological superconductor based on an analysis of the
$\mathbb{Z}_{2}$ invariant of the normal state band structure.

Figure 1: A Heat capacity data of PdPb2 at both $\mu_{0}H=0$ T and 2 T. The 2
T data has been fit to determine the electronic and phonon contributions to
the heat capacity in the normal state. The inset shows a BCS fit, described in
the text, to the $\mu_{0}H=0$ T electronic heat capacity of PdPb2, which
indicates a bulk gap of $\Delta(0)=0.370(2)$ meV. B and C Field-dependent
magnetization curves of PdPb2 at various temperatures, with applied fields
along the [110] and [001] directions, respectively. D and E Temperature-
dependent resistivity curves of PdPb2 under various applied fields, with
applied fields along the [110] and [001] directions, respectively. F Extracted
upper critical fields along both directions, using values determined from the
fastest slope of the resistivity curves, shown in D and E. Fits are to the
Ginzburg-Landau equation. The inset shows the lower critical fields for both
directions, as determined from the magnetization curves after considering
demagnetization effects as explained in the Supplementary Material.

Data from measurements of heat capacity, magnetization, and resistivity of a
single crystal of PdPb2 grown by the Bridgman technique (details in
Supplementary Material[23]) are shown in Figure 1. The heat capacity at zero
applied magnetic field, shown in Figure 1 A, demonstrates a superconducting
phase transition at $T_{c}=3.0$ K, as per an equal-entropy approximation, in
agreement with previous reports [24, 25]. An applied field of $\mu_{0}H=2$ T
is sufficient to quench this transition down to the lowest measured
temperature of $T=0.2$ K. Fits to the $\mu_{0}H=2$ T data, using
$C/T=\gamma+\beta_{3}T^{2}+\beta_{5}T^{4}$, result in an electronic term
$\gamma=6.32(6)$ mJ/mol K2, and two phonon terms $\beta_{3}=1.62(1)$ mJ/mol K4
and $\beta_{5}=0.0184(2)$ mJ/mol K6. The second phonon term arises from the
presence of an Einstein mode with $T_{E}=49.5(4)$ K, with fits shown in the
Supplementary Material [23]. By subtracting these phonon terms from the
$\mu_{0}H=0$ T data, we are able to obtain the electronic heat capacity of
PdPb2, $C_{el}$. After normalizing $C_{el}$ by $\gamma$ and $T_{c}$, we may
fit the data to $C_{el}/T=A[\mathrm{exp}(-BT_{c})/T]$ in order to obtain the
magnitude of the superconducting gap $\Delta(0)$, where $A$ and $B$ are two
constants [26], and $B$ is given by $B=\Delta(0)/k_{B}T_{c}$ at temperatures
$T_{c}/T\geq 2$. Our fits, shown in the inset of Figure 1 A on a log scale,
indicate a bulk superconducting gap of $\Delta(0)=0.370(2)$ meV and a
$2\Delta(0)/k_{B}T_{c}=2.86$. The origin of this anomalously small value of
$2\Delta(0)/k_{B}T_{c}$ in relation to the expected BCS value of 3.53 is
unknown. The gap value is in agreement with the value of $\Delta(0)\approx
0.4$ meV obtained via microwave cavity measurements, as discussed below and in
the supplementary material [23]. Furthermore, the Sommerfield coefficient
$\gamma\rightarrow 0$ as the temperature $T\rightarrow 0\;\mathrm{K}$, marking
the absence of a finite residual electronic contribution to the heat capacity
in the bulk, as expected for a fully gapped superconductor.

Table 1:  Superconducting parameters of a PdPb2 crystal oriented along two crystallographic directions relative to the applied field. These include the lower critical field $H_{c1}^{*}$, upper critical field $H_{c2}$, thermodynamic critical field $H_{c}$, coherence length $\xi(T=0)$, penetration depth $\lambda(T=0)$, and the Ginzburg-Landau parameter $\kappa$. More information is available in the Supplementary Material [23]. Parameter | [110] | [001]
---|---|---
$H_{c1}^{*}$ (Oe) | 75(6) | 93(4)
$H_{c2}$ (Oe) | 1086(26) | 404(17)
$H_{c}$ (Oe) | 191 | 163
$\xi(T=0)$ (nm) | 55 | 90
$\lambda(T=0)$ (nm) | 221 | 158
$\kappa$ | 4.02 | 1.75

The results of magnetization and resistivity measurements of PdPb2 are shown
in Figure 1 B-F. Both measurements show a higher onset $T_{c}$ into a
superconducting state compared to heat capacity and microwave perturbation. It
is possible that the higher $T_{c}$ and breadth of the transition are due to
superconducting fluctuations above $T_{c}$. In order to to rule out extrinsic
origins for this behavior, as well as for the surface behavior discussed later
in this manuscript, we have performed rigorous measurements of crystal and
sample quality, such as powder and single crystal X-ray diffraction, scanning
electron microscope imaging, energy-dispersive X-ray spectroscopy, Laue
diffraction, and X-ray microtomography, the details of which can be found in
the Supplementary Material [23]. Both X-ray diffraction and energy-dispersive
X-ray spectroscopy indicate a nominal stoichiometry of PdPb2, with the latter
measurement indicating atomic ratios of 33.42(13)% Pd and
$66.58(22)\%\;\mathrm{Pb}$ in the best crystal.

Figure 2: A Temperature-dependent complex impedance $\tilde{Z}_{\mathrm{eff}}$
of PdPb2. A surface metal sheath with thickness $t$ is considered, giving rise
to an effective impedance which arises from both a metal sheath impedance
$R_{t}$ and the impedance of the underlying superconductor $Z_{sc}$. The real
($R_{s}$) normal fluid component of $\tilde{Z}_{s}$ reaches a finite value of
$\sim 0.16\mu\Omega$, contrary to the expectations for a fully gapped
superconductor. B The effective surface complex conductivity of PdPb2
decomposed as given by $\tilde{\sigma}=\sigma_{1}-i\sigma_{2}$, where
$\sigma_{1}$ and $\sigma_{2}$ are the normal fluid and superfluid responses,
respectively. $\sigma_{1}$ does not go to zero, as expected for a fully gapped
superconductor, and instead increases. C The temperature dependence of the
fraction of effective normal fluid in PdPb2. This value approaches 33% instead
of zero as $T\rightarrow 0$ K. The inset shows the extracted value of the
scattering rate, which plateaus at 0.14 THz at low temperatures. D The real
part of the conductivity is shown for several materials, including topological
superconductor UTe2 [27], $s$-wave superconductor Ti [28], $d$-wave
superconductor CeCoIn5 [29], and PdPb2. Just as in UTe2, $\sigma_{1}$
anomalously increases with decreasing temperature. The data for Ti, CeCoIn5,
and UTe2 were extracted from S. Bae, $et.al.$ [27]

Measurements were performed on two samples, cut from the same Bridgman-grown
crystal, with either the [110] or [001] faces exposed, as determined through
Laue diffraction. The extracted superconducting parameters are shown in Table
1. The $H_{c2}$ values for both directions, $H_{c2}[110]=0.1086$ T and
$H_{c2}[001]=0.0404$ T, are much lower than the expected Pauli limit for
PdPb2, which through $H_{P}(\mathrm{T})\sim 1.85T_{c}$(K), should be
approximately $\mu_{0}H=5.5\;\mathrm{T}$. PdPb2, therefore, does not appear to
show signs of triplet pairing or otherwise unconventional superconductivity in
the bulk. The derived Ginzburg-Landau parameter $\kappa=\lambda(0)/\xi(0)$,
exceeds $\kappa\geq 1/\sqrt{2}$ in both crystallographic directions,
indicating PdPb2 is a type-II superconductor.

The microwave cavity perturbation technique was used to determine the
temperature-dependent complex surface impedance, $\tilde{Z}_{s}(T)$, of a
single crystal of PdPb2. Measurements were performed in a superconducting
NbTi, $T_{c}\approx 10$ K, cylindrical cavity resonator with a resonance
frequency of the TE011 mode at 18.66 GHz. The cavity perturbation shifts,
marked by a change in complex resonance frequency
$\Delta\tilde{\omega}/\omega_{0}$, were measured upon insertion of the sample.
For a sample in the skin depth regime, $\Delta\tilde{\omega}/\omega_{0}$ can
be related to the impedance $\tilde{Z}_{s}=R_{s}+iX_{s}$ via
$\frac{\Delta\tilde{\omega}}{\omega_{0}}=\xi\tilde{Z}_{s}+\lim_{|\tilde{\sigma}|\to\infty}\frac{\Delta\tilde{\omega}}{\omega_{0}}$,
where $\xi$ is the resonator constant and
$\lim_{|\tilde{\sigma}|\to\infty}\frac{\Delta\tilde{\omega}}{\omega_{0}}$ is
the metallic shift[23]. The decomposed surface impedance components, surface
resistance $R_{s}$ and surface reactance $X_{s}$, for PdPb2 are shown as a
function of temperature in Figure 2 A. Both $R_{s}$ and $X_{s}$ show a sharp
change at $T=3.0\;\mathrm{K}$, consistent with a transition into a
superconducting state, and reduce with decreasing temperature to plateaued
values of $R_{s}\sim 0.16~{}\mu\Omega$ and $X_{s}\sim 1.60~{}\mu\Omega$. The
non-zero surface resistance of $\sim 0.16~{}\mu\Omega$ implies the presence of
a significant dissipative channel that is odds with conventional
electrodynamics. As discussed below, it may be consistent with a normal
surface fluid when the sample is in superconducting state.

For a bulk homogeneous system, the low temperature dissipation is best
quantified via the complex conductivity $\tilde{\sigma}(T)$, which can be
extracted in the local electrodynamics regime, from the complex surface
impedance by $\tilde{Z}_{s}=\sqrt{i\omega\mu_{0}/\tilde{\sigma}}$. The
decomposed complex conductivity $\tilde{\sigma}=\sigma_{1}-i\sigma_{2}$, where
$\sigma_{1}$ and $\sigma_{2}$ are the normal fluid and superfluid responses,
respectively, is shown in Figure 2 B. For a conventional superconductor,
$\sigma_{1}$ is expected to show a Hebel-Schlicter peak near $T_{c}$ before
decreasing with temperature to a minimum, such that
$\sigma_{1}(0)/\sigma_{n}=0$. For d-wave and bulk nodal superconductors, the
ratio $0\leq\sigma_{1}(0)/\sigma_{n}\leq 1$ can arise as a result of an
underlying nodal gap function. PdPb2, in contrast, shows an anomalous ratio of
$\sigma_{1}(0)/\sigma_{n}>1.4$. Even at the lowest measured temperatures of
$T_{c}/T>3$, the effective value of $\sigma_{1}$ is greater than its value in
the normal state, indicating that PdPb2 hosts a significant normal dissipative
fluid that coexists with fully gapped superconductivity.

The normal fluid components of the effective complex conductivity for several
superconductors are shown in Figure 2 D, as extracted from S. Bae, et. al.
[27]. These are effective conductivities, since they are calculated as if the
system is homogeneous. In the case of elemental Ti, which is an s-wave
superconductor with $T_{c}=0.39$ K, $\sigma_{1}$ decreases monotonically to
zero as all of $\sigma_{n}\rightarrow\sigma_{2}$, i.e. all of the normal ﬂuid
becomes superﬂuid below $T_{c}$. In the case of CeCoIn5, a known d-wave
superconductor, the normal ﬂuid component of the complex conductivity
decreases to a ﬁnite, non-zero value, as the superconducting gap function
possesses nodes. These nodes are sources of dissipation and low energy
excitations. Both PdPb2 and topological superconductor candidate UTe2 show an
anomalous response, where $\sigma_{1}$ increases with decreasing temperature
and subsequently plateaus. In order to determine whether PdPb2 possesses non-
trivial topology in its electronic band structure, we performed density
functional theory (DFT) calculations that are discussed below.

The anomalous residual low temperature dissipation could arise either from the
bulk or the surface of this material. We investigate each of these
possibilities in turn. To further explore the anomalous behavior of the
complex conductivity in the case of a homogeneous system, we can describe it
using a two-fluid model in terms of the normal fluid and superfluid responses,
respectively:

$\tilde{\sigma}(T)=\frac{ne^{2}}{m^{*}}\left(\frac{f_{s}(T)}{i\omega}+\frac{f_{n}(T)\tau(T)}{1+i\omega\tau(T)}\right)$

where $n$ is the total electron density, $m^{*}$ is the effective mass of the
electrons, $\tau$ is the effective normal fluid scattering lifetime, $f_{n}$
is the normal fluid fraction and $f_{s}=1-f_{n}$ is the superfluid fraction.
As $\tau$ is always a real positive number, the normal fluid fraction must
satisfy $f_{n}\geq 2/(1+\sqrt{1+(\sigma_{2}/\sigma_{1})^{2}})$. For
conventional superconductors, as $T\rightarrow 0$ K, the ratio
$\sigma_{2}/\sigma_{1}\rightarrow\infty$, implying $f_{n}\rightarrow 0$. As
shown in Figure 2 B, this ratio approaches $\sigma_{2}/\sigma_{1}\rightarrow
5$ in PdPb2 as $T\rightarrow 0$, giving a minimum residual normal fluid
fraction $f_{n}\geq 33\%$, i.e. one-third of the normal state value, as shown
in Figure 2 C. This result is similar to one observed recently in the
topological superconductor candidate UTe2 [27]. Again, this is an effective
density calculated from a model for the conductivity that assumes that system
has a homogeneous electrodynamic response. Similar to UTe2, PdPb2 possesses
signiﬁcant dissipation on the surface against the backdrop of a fully gapped
bulk superconducting state. Furthermore, as shown in the inset of Figure 2 C,
we determine from the above equation the inverse scattering rate for the
anomalous fluid, which decreases to a plateau at low temperature to a value of
$\tau^{-1}\approx 0.14$ THz. This value is too low to create an impurity-
induced normal fluid scenario.

A possible origin for the anomalous effective conductivity and significant
dissipative response is a surface origin of a dissipative normal conduction
channel. If the surface of the bulk superconductor has a normal conductor
sheath then the expression for extracting a bulk conductivity from the surface
impedance becomes invalid. The extracted conductivity can naturally show
anomalous features due to contributions from the normal conduction channel.
One would need to account for such a thin normal fluid layer at the surface in
the effective impedance of the sample. For a thin normal conductor layer with
2D resistance $R_{t}$ on top of a bulk superconductor with impedance $Z_{sc}$
the effective impedance of the system is given to good approximation by
$Z_{\text{{eff}}}=Z_{sc}R_{t}/(Z_{sc}+R_{t})$[23]. We assume that the bulk
superconductor has a purely imaginary impedance $Z_{sc}=iX_{sc}$(reasonable
for a fully gapped 3D superconductor at low temperatures). Then normal
channel’s response follows from the measured signal as
$R_{t}=\frac{R_{s}^{2}+X_{s}^{2}}{X_{s}}$. Figure 2 A shows the impedance
$R_{t}$ of the thin normal layer with $R_{t}\sim 16~{}\mu\Omega$ for
$T\rightarrow 0$ K. $R_{t}$ reduces monotonically with increasing temperature.
One can see that it is reasonably temperature independent in the low
temperature region where this analysis applies.

Figure 3: The calculated electronic band structure of PdPb2, calculated using
the local density approximation and with spin-orbit coupling considered. The
first Brillouin zone for body-centered tetragonal is shown, under the $a>c$
lattice parameter condition. The parities at $\Gamma(\delta_{\Gamma})$ and
$M(\delta_{M})$ are shown as positive and negative signs. A change in parity
from one band to the next is shown in red. The $\mathbb{Z}_{2}$ topological
invariant $\nu_{0}$ is shown for each band, which is calculated as the product
of the parities at $\Gamma$ and $M$ for that band, along with the product of
those two parities for all previous bands. Non-trivial invariants of
$\nu_{0}=1$ are shown in blue.

The DFT calculated electronic band structure, with spin-orbit coupling
included, is shown in Figure 3. PdPb2 has been predicted to be a symmetry-
enforced semimetal with line crossings between the two high symmetry points of
the first Brillouin zone $\Gamma$ and $M$ [30, 31]. It has also been predicted
to be a topological insulator based on the absence of a linear combination
(NLC) of the elementary band representations (EBRs) across the Brillouin zone
[30], though it is not an insulator. Our calculated band structure, as well as
those previously calculated, indeed show band crossings along the $\Lambda$
path along $k_{z}$ between $\Gamma$ and $M$, with point group $4mm$. Since
PdPb2 possesses time-reversal symmetry, its bulk topology is characterized by
a $\mathbb{Z}_{2}$ invariant [32, 33, 34]. As it further possesses inversion
symmetry, the $\mathbb{Z}_{2}$ invariant can be calculated readily by
considering the product of the parities of all of the bands up to and
including the ones that cross the Fermi level at both $\Gamma$ and $M$ [35].
Only these two special points in the Brillouin zone determine the topological
invariant for body-centered tetragonal, as of the eight time-reversal
invariant momentum (TRIM) points in three-dimensions, $\Gamma$ and $M$ are the
only two with odd coefficients ($1\Gamma,4N,2X,1M$). The band parities at
$\Gamma$ and $M$, and the resulting topological invariant $\nu_{0}$, which
also considers the product of the parities of all bands beneath the one in
question, are shown in Figure 3. Our calculations indicate that four of the
five bands that cross the Fermi level have non-trivial invariants of
$\nu_{0}=1$. PdPb2 is therefore a $\mathbb{Z}_{2}$ metal in the normal state,
a designation also used to describe other topological superconductor
candidates such as FeTe1-xSex[20, 21, 22], $\beta$-Bi2Pd[17, 18, 19], doped
Bi2Se3 [12, 36], Tl5Te3 [37], and more recently the AV3Sb5 (A = K, Rb, and Cs)
family of materials [38, 39, 40, 41]. More in depth theoretical studies are
needed to disentangle the influence of the topological band crossings near the
Fermi level on the topology and physical properties.

While our calculations do not reveal the presence of surface states near the
Fermi level in the normal state (not shown), the non-trivial invariant of
bands that cross the Fermi level in PdPb2 could result in a topological
superconductor [42]. Strong spin-orbit coupling arising from the heavy
elements Pd and Pb can drive the system into a topological ground state
characterized by a fully gapped bulk superconducting state with topologically
non-trivial Majorana surface states. We believe that low temperature microwave
dissipation is a generic signature of such surface states. PdPb2 therefore
adds on to a short list of three-dimensional topological superconductor
candidates.

In conclusion, we have discovered an anomalous, large, dissipative surface
electrodynamic response in the centrosymmetric superconductor PdPb2. A natural
explanation of this phenomenon is that this material is a topological
superconductor with surface Majoranas states. The ease with which large, high
quality single crystals can be grown can make this material ideal for
understanding the origin of this anomalous behavior.

## Acknowledgments

This work was supported as part of the Institute for Quantum Matter, an Energy
Frontier Research Center funded by the U.S. Department of Energy, Office of
Science, Office of Basic Energy Sciences, under Award DE-SC0019331. J. R. C.
acknowledges support of the Gompf Family Fellowship from the JHU Department of
Chemistry. J. R. C. is grateful to M. A. Siegler for assistance collecting
single-crystal X-ray diffraction data. This work utilized synthetic
capabilities in the Platform for the Accelerated Realization, Analysis, and
Discovery of Interface Materials (NSF DMR-1539918), a National Science
Foundation Materials Innovation Platform. The Magnetic Properties Measurement
System used for data collection was funded by the National Science Foundation,
Division of Materials Research, Major Research Instrumentation Program, under
Award No. 1828490. The dilution refrigerator was funded by the National
Science Foundation, Division of Materials Research, Award No. 0821005.
Electronic band structure calculations were conducted using computational
resources at the Maryland Advanced Research Computing Center (MARCC).

## References

  * Hasan and Kane [2010] M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
  * Lian  _et al._ [2018] B. Lian, X.-Q. Sun, A. Vaezi, X.-L. Qi, and S.-C. Zhang, Topological quantum computation based on chiral Majorana fermions, Proceedings of the National Academy of Sciences 115, 10938 (2018).
  * Ivanov [2001] D. A. Ivanov, Non-Abelian Statistics of Half-Quantum Vortices in $\mathit{p}$-Wave Superconductors, Phys. Rev. Lett. 86, 268 (2001).
  * Xu  _et al._ [2015] J.-P. Xu, M.-X. Wang, Z. L. Liu, J.-F. Ge, X. Yang, C. Liu, Z. A. Xu, D. Guan, C. L. Gao, D. Qian, Y. Liu, Q.-H. Wang, F.-C. Zhang, Q.-K. Xue, and J.-F. Jia, Experimental Detection of a Majorana Mode in the core of a Magnetic Vortex inside a Topological Insulator-Superconductor ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}/{\mathrm{NbSe}}_{2}$ Heterostructure, Phys. Rev. Lett. 114, 017001 (2015).
  * Sun  _et al._ [2016] H.-H. Sun, K.-W. Zhang, L.-H. Hu, C. Li, G.-Y. Wang, H.-Y. Ma, Z.-A. Xu, C.-L. Gao, D.-D. Guan, Y.-Y. Li, C. Liu, D. Qian, Y. Zhou, L. Fu, S.-C. Li, F.-C. Zhang, and J.-F. Jia, Majorana Zero Mode Detected with Spin Selective Andreev Reflection in the Vortex of a Topological Superconductor, Phys. Rev. Lett. 116, 257003 (2016).
  * He  _et al._ [2017] Q. L. He, L. Pan, A. L. Stern, E. C. Burks, X. Che, G. Yin, J. Wang, B. Lian, Q. Zhou, E. S. Choi, K. Murata, X. Kou, Z. Chen, T. Nie, Q. Shao, Y. Fan, S.-C. Zhang, K. Liu, J. Xia, and K. L. Wang, Chiral Majorana fermion modes in a quantum anomalous Hall insulator–superconductor structure, Science 357, 294 (2017).
  * Xu  _et al._ [2014] J.-P. Xu, C. Liu, M.-X. Wang, J. Ge, Z.-L. Liu, X. Yang, Y. Chen, Y. Liu, Z.-A. Xu, C.-L. Gao, D. Qian, F.-C. Zhang, and J.-F. Jia, Artificial Topological Superconductor by the Proximity Effect, Phys. Rev. Lett. 112, 217001 (2014).
  * Fu and Kane [2008] L. Fu and C. L. Kane, Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator, Phys. Rev. Lett. 100, 096407 (2008).
  * Wray  _et al._ [2010] L. A. Wray, S.-Y. Xu, Y. Xia, Y. S. Hor, D. Qian, A. V. Fedorov, H. Lin, A. Bansil, R. J. Cava, and M. Z. Hasan, Observation of topological order in a superconducting doped topological insulator, Nature Physics 6, 855 (2010).
  * Smylie  _et al._ [2016] M. P. Smylie, H. Claus, U. Welp, W.-K. Kwok, Y. Qiu, Y. S. Hor, and A. Snezhko, Evidence of nodes in the order parameter of the superconducting doped topological insulator ${\mathrm{Nb}}_{x}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ via penetration depth measurements, Phys. Rev. B 94, 180510 (2016).
  * Hosur  _et al._ [2011] P. Hosur, P. Ghaemi, R. S. K. Mong, and A. Vishwanath, Majorana Modes at the Ends of Superconductor Vortices in Doped Topological Insulators, Phys. Rev. Lett. 107, 097001 (2011).
  * Sasaki  _et al._ [2011] S. Sasaki, M. Kriener, K. Segawa, K. Yada, Y. Tanaka, M. Sato, and Y. Ando, Topological Superconductivity in ${\mathrm{Cu}}_{x}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, Phys. Rev. Lett. 107, 217001 (2011).
  * Das  _et al._ [2012] A. Das, Y. Ronen, Y. Most, Y. Oreg, M. Heiblum, and H. Shtrikman, Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions, Nature Physics 8, 887 (2012).
  * Mourik  _et al._ [2012] V. Mourik, K. Zuo, S. M. Frolov, S. R. Plissard, E. P. A. M. Bakkers, and L. P. Kouwenhoven, Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices, Science 336, 1003 (2012).
  * Stanescu and Tewari [2013] T. D. Stanescu and S. Tewari, Majorana fermions in semiconductor nanowires: fundamentals, modeling, and experiment, Journal of Physics: Condensed Matter 25, 233201 (2013).
  * Stanescu  _et al._ [2011] T. D. Stanescu, R. M. Lutchyn, and S. Das Sarma, Majorana fermions in semiconductor nanowires, Phys. Rev. B 84, 144522 (2011).
  * Li  _et al._ [2019] Y. Li, X. Xu, M.-H. Lee, M.-W. Chu, and C. L. Chien, Observation of half-quantum flux in the unconventional superconductor $\beta$-Bi2Pd, Science 366, 238 (2019).
  * Lv  _et al._ [2017] Y.-F. Lv, W.-L. Wang, Y.-M. Zhang, H. Ding, W. Li, L. Wang, K. He, C.-L. Song, X.-C. Ma, and Q.-K. Xue, Experimental signature of topological superconductivity and Majorana zero modes on $\beta$-Bi2Pd thin films, Science Bulletin 62, 852 (2017).
  * Sakano  _et al._ [2015] M. Sakano, K. Okawa, M. Kanou, H. Sanjo, T. Okuda, T. Sasagawa, and K. Ishizaka, Topologically protected surface states in a centrosymmetric superconductor $\beta$-PdBi2, Nature Communications 6, 8595 (2015).
  * Zhang  _et al._ [2018] P. Zhang, K. Yaji, T. Hashimoto, Y. Ota, T. Kondo, K. Okazaki, Z. Wang, J. Wen, G. D. Gu, H. Ding, and S. Shin, Observation of topological superconductivity on the surface of an iron-based superconductor, Science 360, 182 (2018).
  * Xu  _et al._ [2016] G. Xu, B. Lian, P. Tang, X.-L. Qi, and S.-C. Zhang, Topological Superconductivity on the Surface of Fe-Based Superconductors, Phys. Rev. Lett. 117, 047001 (2016).
  * Machida  _et al._ [2019] T. Machida, Y. Sun, S. Pyon, S. Takeda, Y. Kohsaka, T. Hanaguri, T. Sasagawa, and T. Tamegai, Zero-energy vortex bound state in the superconducting topological surface state of Fe(Se,Te), Nature Materials 18, 811 (2019).
  * [23] See supplemental material at [url].
  * Pattalwar  _et al._ [1988] S. M. Pattalwar, R. N. Dixit, S. Y. Shete, and B. K. Basu, Low-temperature specific heat of PdPb2, Phys. Rev. B 38, 7067 (1988).
  * Havinga  _et al._ [1972] E. Havinga, H. Damsma, and P. Hokkeling, Compounds and pseudo-binary alloys with the CuAl2(C16)-type structure I. Preparation and X-ray results, Journal of the Less Common Metals 27, 169 (1972).
  * Tari [2003] A. Tari,  _The specific heat of matter at low temperatures_ (Imperial College Press, 2003).
  * Bae  _et al._ [2021] S. Bae, H. Kim, Y. S. Eo, S. Ran, I. lin Liu, W. T. Fuhrman, J. Paglione, N. P. Butch, and S. M. Anlage, Anomalous normal fluid response in a chiral superconductor UTe2, Nat. Commun. 12, 10.1038/s41467-021-22906-6 (2021).
  * Thiemann  _et al._ [2018] M. Thiemann, M. Dressel, and M. Scheffler, Complete electrodynamics of a BCS superconductor with $\mu\mathrm{eV}$ energy scales: Microwave spectroscopy on titanium at mK temperatures, Phys. Rev. B 97, 214516 (2018).
  * Truncik  _et al._ [2013] C. J. S. Truncik, W. A. Huttema, P. J. Turner, S. Özcan, N. C. Murphy, P. R. Carrière, E. Thewalt, K. J. Morse, A. J. Koenig, J. L. Sarrao, and D. M. Broun, Nodal quasiparticle dynamics in the heavy fermion superconductor CeCoIn5 revealed by precision microwave spectroscopy, Nature Communications 4, 2477 (2013).
  * Bradlyn  _et al._ [2017] B. Bradlyn, L. Elcoro, J. Cano, M. G. Vergniory, Z. Wang, C. Felser, M. I. Aroyo, and B. A. Bernevig, Topological quantum chemistry, Nature 547, 298 (2017).
  * Vergniory  _et al._ [2019] M. G. Vergniory, L. Elcoro, C. Felser, N. Regnault, B. A. Bernevig, and Z. Wang, A complete catalogue of high-quality topological materials, Nature 566, 480 (2019).
  * Fu  _et al._ [2007] L. Fu, C. L. Kane, and E. J. Mele, Topological Insulators in Three Dimensions, Phys. Rev. Lett. 98, 106803 (2007).
  * Moore and Balents [2007] J. E. Moore and L. Balents, Topological invariants of time-reversal-invariant band structures, Phys. Rev. B 75, 121306 (2007).
  * Roy [2010] R. Roy, Characterization of three-dimensional topological insulators by two-dimensional invariants, New Journal of Physics 12, 065009 (2010).
  * Fu and Kane [2007] L. Fu and C. L. Kane, Topological insulators with inversion symmetry, Phys. Rev. B 76, 045302 (2007).
  * Liu  _et al._ [2015] Z. Liu, X. Yao, J. Shao, M. Zuo, L. Pi, S. Tan, C. Zhang, and Y. Zhang, Superconductivity with Topological Surface State in SrxBi2Se3, Journal of the American Chemical Society 137, 10512 (2015).
  * Arpino  _et al._ [2014] K. E. Arpino, D. C. Wallace, Y. F. Nie, T. Birol, P. D. C. King, S. Chatterjee, M. Uchida, S. M. Koohpayeh, J.-J. Wen, K. Page, C. J. Fennie, K. M. Shen, and T. M. McQueen, Evidence for Topologically Protected Surface States and a Superconducting Phase in $[{\mathrm{Tl}}_{4}]({\mathrm{Tl}}_{1-x}{\mathrm{Sn}}_{x}){\mathrm{Te}}_{3}$Using Photoemission, Specific Heat, and Magnetization Measurements, and Density Functional Theory, Phys. Rev. Lett. 112, 017002 (2014).
  * Ortiz  _et al._ [2019] B. R. Ortiz, L. C. Gomes, J. R. Morey, M. Winiarski, M. Bordelon, J. S. Mangum, I. W. H. Oswald, J. A. Rodriguez-Rivera, J. R. Neilson, S. D. Wilson, E. Ertekin, T. M. McQueen, and E. S. Toberer, New kagome prototype materials: discovery of ${\mathrm{KV}}_{3}{\mathrm{Sb}}_{5},{\mathrm{RbV}}_{3}{\mathrm{Sb}}_{5}$, and ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$, Phys. Rev. Materials 3, 094407 (2019).
  * Ortiz  _et al._ [2021] B. R. Ortiz, P. M. Sarte, E. M. Kenney, M. J. Graf, S. M. L. Teicher, R. Seshadri, and S. D. Wilson, Superconductivity in the ${\mathbb{Z}}_{2}$ kagome metal ${\mathrm{KV}}_{3}{\mathrm{Sb}}_{5}$, Phys. Rev. Materials 5, 034801 (2021).
  * Ortiz  _et al._ [2020] B. R. Ortiz, S. M. L. Teicher, Y. Hu, J. L. Zuo, P. M. Sarte, E. C. Schueller, A. M. M. Abeykoon, M. J. Krogstad, S. Rosenkranz, R. Osborn, R. Seshadri, L. Balents, J. He, and S. D. Wilson, $\mathrm{Cs}{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$: A ${\mathbb{Z}}_{2}$ Topological Kagome Metal with a Superconducting Ground State, Phys. Rev. Lett. 125, 247002 (2020).
  * Yang  _et al._ [2020] S.-Y. Yang, Y. Wang, B. R. Ortiz, D. Liu, J. Gayles, E. Derunova, R. Gonzalez-Hernandez, L. Šmejkal, Y. Chen, S. S. P. Parkin, S. D. Wilson, E. S. Toberer, T. McQueen, and M. N. Ali, Giant, unconventional anomalous Hall effect in the metallic frustrated magnet candidate, KV3Sb5, Science Advances 6, eabb6003 (2020).
  * Fu and Berg [2010] L. Fu and E. Berg, Odd-Parity Topological Superconductors: Theory and Application to CuxBi2Se3, Phys. Rev. Lett. 105, 097001 (2010).


* Rosch (1983) Rosch, E. 1983. Prototype classification and logical classification: The two systems. In E. K. Scholnick, (Ed), New Trends in Conceptual Representation: Challenges to Piaget’s Theory?, pp. 73-86. Hillsdale NJ: Erlbaum.
  * Rubens & Kurlbaum (1900) Rubens, H. and Kurlbaum, S. B. (1900). Über die Emission langwelliger Wärmestrahlen durch den schwarzen Körper bei verschiedenen Temperaturen. Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse, pp. 929-941.
  * Saunders (2003) Saunders, S. (2003). Physics and Leibniz’s principles. In K. Brading and E. Castellani (Eds.), Symmetries in Physics: Philosophical Reflections. Cambridge, UK: Cambridge University Press.
  * Schrödinger (1926a) Schrödinger, E. (1926). Zur Einsteinschen Gastheorie. Physikalische Zeitschrift 27, pp. 95-101.
  * Schrödinger (1926b) Schrödinger, E. (1926). Quantisierung als Eigenwertproblem. Annalen der Physik 384, pp. 361-376. doi: 10.1002/andp.19263840404.
  * Surov (2021) Surov, I. A. (2021). Quantum cognitive triad: Semantic geometry of context representation. Foundations of Science volume 26, pp. 947-975. doi: ’url10.1007/s10699-020-09712-x.
  * Van Rijsbergen (2004) Van Rijsbergen, C. J. (2004). The Geometry of Information Retrieval. Cambridge University Press: Cambridge, United Kingdom.
  * Widdows (2004) Widdows, D. (2004). Geometry and Meaning. Stanford: CSLI publications.
  * Wien (1897) Wien, W. (1897). XXX. On the division of energy in the emission-spectrum of a black body. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Series 5, Volume 43, pp. 214-220.
  * Zanette (2006) Zanette, H. D. (2006). Zipf’s law and the creation of musical context. Musicae Scientiae 10, pp. 3-18. doi: 10.1177/102986490601000101.
  * Zipf (1935) Zipf, G. K. (1935). The Psycho-Biology of Language. Boston: Houghton Mifflin Co.
  * Zipf (1949) Zipf, G. K. (1949). Human Behavior and the Principle of Least Effort. Cambridge: Addison Wesley.


EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2014-236 LHCb-PAPER-2014-052 February 18, 2015

Search for the lepton flavour violating decay
$\tau^{-}\rightarrow\mu^{-}\mu^{+}\mu^{-}$

The LHCb collaboration†††Authors are listed at the end of this paper.

A search for the lepton flavour violating decay
$\tau^{-}\rightarrow\mu^{-}\mu^{+}\mu^{-}$ is performed with the LHCb
experiment. The data sample corresponds to an integrated luminosity of
$1.0$$\mbox{\,fb}^{-1}$ of proton-proton collisions at a centre-of-mass energy
of 7$\mathrm{\,Te\kern-1.00006ptV}$ and $2.0$$\mbox{\,fb}^{-1}$ at
8$\mathrm{\,Te\kern-1.00006ptV}$. No evidence is found for a signal, and a
limit is set at $90\%$ confidence level on the branching fraction, ${\cal
B}(\tau^{-}\rightarrow\mu^{-}\mu^{+}\mu^{-})<4.6\times 10^{-8}$.

Published as JHEP 02 (2015) 121

© CERN on behalf of the LHCb collaboration, licence CC-BY-4.0.

##  1 Introduction

Lepton flavour violating processes are allowed within the context of the
Standard Model (SM) with massive neutrinos, but their branching fractions are
of order $10^{-40}$ [1, 2] or smaller, and are beyond the reach of any
currently conceivable experiment. Observation of charged lepton flavour
violation (LFV) would therefore be an unambiguous signature of physics beyond
the Standard Model (BSM), but no such process has been observed to date [3].

A number of BSM scenarios predict LFV at branching fractions approaching
current experimental sensitivities [4], with LFV in $\tau^{-}$ decays often
enhanced with respect to $\mu^{-}$ decays due to the large difference in mass
between the two leptons (the inclusion of charge-conjugate processes is
implied throughout). If charged LFV were to be discovered, measurements of the
branching fractions for a number of channels would be required to determine
the nature of the BSM physics. In the absence of such a discovery, improving
the experimental constraints on the branching fractions for LFV decays would
help to constrain the parameter spaces of BSM models.

This paper reports on an updated search for the LFV decay
$\tau^{-}\rightarrow\mu^{-}\mu^{+}\mu^{-}$ with the LHCb experiment [5] at the
CERN LHC. The previous LHCb analysis of this channel produced the first result
on a search for LFV $\tau^{-}$ decays at a hadron collider [6]. Using
$1.0$$\mbox{\,fb}^{-1}$ of proton-proton collision data collected at a centre-
of-mass energy of 7$\mathrm{\,Te\kern-1.00006ptV}$, a limit was set on the
branching fraction, ${\cal
B}\left(\tau^{-}\rightarrow\mu^{-}\mu^{+}\mu^{-}\right)<8.0\times 10^{-8}$ at
90% confidence level (CL). The current best experimental upper limits are
${\cal B}\left(\tau^{-}\rightarrow\mu^{-}\mu^{+}\mu^{-}\right)<2.1\times
10^{-8}$ at 90% CL from Belle [7] and ${\cal
B}\left(\tau^{-}\rightarrow\mu^{-}\mu^{+}\mu^{-}\right)<3.3\times 10^{-8}$ at
90% CL from BaBar [8]. In the analysis presented here, an additional LHCb data
set, corresponding to $2.0$$\mbox{\,fb}^{-1}$ of integrated luminosity
collected at 8$\mathrm{\,Te\kern-1.00006ptV}$, is added to the previous data
set, and a number of new analysis techniques are introduced.

The search for LFV in $\tau^{-}$ decays at LHCb takes advantage of the large
inclusive $\tau^{-}$ production cross-section at the LHC, where $\tau^{-}$
leptons are produced almost entirely from the decays of $b$ and $c$ hadrons.
Using the $b\overline{b}$ and $c\overline{c}$ cross-sections measured by LHCb
[9, 10] and the inclusive $b\rightarrow\tau$ and $c\rightarrow\tau$ branching
fractions [3], the inclusive $\tau^{-}$ cross-section is estimated to be
$85\,\upmu$b at 7$\mathrm{\,Te\kern-1.00006ptV}$.

Selection criteria are implemented for the signal mode,
$\tau^{-}\rightarrow\mu^{-}\mu^{+}\mu^{-}$, and for the calibration and
normalisation channel, which is $D_{s}^{-}\rightarrow\phi\pi^{-}$ with
$\phi\rightarrow\mu^{+}\mu^{-}$, referred to in the following as
$D_{s}^{-}\rightarrow\phi\left(\mu^{+}\mu^{-}\right)\pi^{-}$. To avoid
potential bias, $\mu^{-}\mu^{+}\mu^{-}$ candidates with mass within $\pm
30{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ (approximately three times the
expected mass resolution) of the known $\tau^{-}$ mass are initially excluded
from the analysis. Discrimination between a potential signal and the
background is performed using a three-dimensional binned distribution in two
multivariate classifiers and the mass of the $\tau^{-}$ candidate. One
classifier is based on the three-body decay topology and the other on muon
identification.

##  2 Detector and triggers

The LHCb detector [5] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region, a large-area silicon-strip detector located upstream of a
dipole magnet with a bending power of about $4{\rm\,Tm}$, and three stations
of silicon-strip detectors and straw drift tubes placed downstream of the
magnet. The tracking system provides a measurement of momentum, $p$, with a
relative uncertainty that varies from 0.4% at low momentum to 0.6% at
100${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The minimum distance of a track to
a primary vertex, the impact parameter (IP), is measured with a resolution of
$\left(15+29/\mbox{$p_{\rm T}$}\right)\,\upmu\rm m$, where $p_{\rm T}$ is the
component of $p$ transverse to the beam, in
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov detectors
(RICH) [11]. Photon, electron and hadron candidates are identified by a
calorimeter system consisting of scintillating-pad and preshower detectors, an
electromagnetic calorimeter and a hadronic calorimeter. Muons are identified
by a system composed of alternating layers of iron and multiwire proportional
chambers [12].

The trigger [13] consists of a hardware stage, based on information from the
calorimeter and muon systems, followed by a software stage, which applies a
full event reconstruction. Candidate events are first required to pass the
hardware trigger, which selects muons with a transverse momentum
$\mbox{$p_{\rm T}$}>1.48{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ in the
7$\mathrm{\,Te\kern-1.00006ptV}$ data or $\mbox{$p_{\rm
T}$}>1.76{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ in the
8$\mathrm{\,Te\kern-1.00006ptV}$ data. In the software trigger, at least one
of the final-state particles is required to have both $\mbox{$p_{\rm
T}$}>0.8{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and IP $>100\,\upmu\rm m$ with
respect to all of the primary $pp$ interaction vertices (PVs) in the event.
Finally, the tracks of two or more of the final-state particles are required
to form a vertex that is significantly displaced from the PVs.

##  3 Monte Carlo simulation

In the simulation, $pp$ collisions are generated using Pythia [14,
*Sjostrand:2007gs] with a specific LHCb configuration [15]. Decays of hadronic
particles are described by EvtGen [16], in which final-state radiation is
generated using Photos [17]. For the
$\tau^{-}\rightarrow\mu^{-}\mu^{+}\mu^{-}$ signal channel, the final-state
particles are distributed according to three-body phase-space. The interaction
of the generated particles with the detector and its response are implemented
using the Geant4 toolkit [18, *Agostinelli:2002hh] as described in Ref. [20].

As the $\tau^{-}$ leptons produced in the LHCb acceptance originate almost
exclusively from heavy quark decays, they can be classified in one of five
categories according to the parent particle. The parent particle can be the
following: a $b$ hadron; a $D_{s}^{-}$ or $D^{-}$ meson that is produced
directly in a proton-proton collision or via the decay of an excited charm
meson; or a $D_{s}^{-}$ or $D^{-}$ meson resulting from the decay of a $b$
hadron. Events from each category are generated separately and are combined in
accordance with the measured cross-sections and branching fractions.
Variations of the cross-sections and branching fractions within their
uncertainties are considered as sources of systematic uncertainty.

##  4 Event selection

Candidate $\tau^{-}\rightarrow\mu^{-}\mu^{+}\mu^{-}$ decays are selected by
requiring three tracks that combine to give a mass close to that of the
$\tau^{-}$ lepton, and that form a vertex that is displaced from the PV. The
tracks are required to be well-reconstructed muon candidates with
$\mbox{$p_{\rm T}$}>300$ ${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ that have a
significant separation from the PV. There must be a good fit to the three-
track vertex, and the decay time of the candidate forming the vertex has to
satisfy $ct>100\,\upmu\rm m$. As the $\tau^{-}$ leptons are produced
predominantly in the decays of charm mesons, where the $Q$-values are
relatively small (and so the charm meson and the $\tau^{-}$ are almost
collinear in the laboratory frame), a requirement on the pointing angle,
$\theta$, between the momentum vector of the three-track system and the vector
joining the primary and secondary vertices is used to remove poorly
reconstructed candidates ($\cos\theta>0.99$). Contamination from pairs of
tracks originating from the same particle is reduced by removing same-sign
muon pairs with mass lower than 250${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$.

The decay
$D_{s}^{-}\rightarrow\eta\left(\mu^{+}\mu^{-}\gamma\right)\mu^{-}{\bar{\nu}_{\mu}}$
is a source of irreducible background near the signal region, and therefore
candidates with a $\mu^{+}\mu^{-}$ invariant mass below $450$
${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ are removed. Signal candidates
containing muons that result from the decay of the $\phi(1020)$ meson are
removed by excluding $\mu^{+}\mu^{-}$ masses within $\pm
20{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known $\phi(1020)$ meson
mass.

The signal region is defined by a $\pm
20{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ window (approximately two times
the expected mass resolution) around the known $\tau^{-}$ mass. Candidates
with $\mu^{-}\mu^{+}\mu^{-}$ invariant mass between 1600 and
1950${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ are kept to allow evaluation of
the background contributions in the signal region. In the following, the wide
mass windows on either side of the signal region are referred to as the data
sidebands. The signal region for the normalisation channel,
$D_{s}^{-}\rightarrow\phi\left(\mu^{+}\mu^{-}\right)\pi^{-}$, which has a
similar topology to that of the $\tau^{-}\rightarrow\mu^{-}\mu^{+}\mu^{-}$
decay, is defined by a $\pm 20{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ window
around the $D_{s}^{-}$ mass, with the $\mu^{+}\mu^{-}$ mass required to be
within $\pm 20{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the $\phi(1020)$
meson mass. Where appropriate, the rest of the selection criteria are
identical to those for the signal channel, with one of the muon candidates
replaced by a pion candidate.

##  5 Signal and background discrimination

Three classifiers are used to discriminate between signal and background: an
invariant mass classifier that uses the reconstructed mass of the $\tau^{-}$
candidate; a geometric classifier, ${\rm\mathcal{M}_{3body}}$; and a particle
identification classifier, ${\rm\mathcal{M}_{PID}}$.

The multivariate classifier ${\rm\mathcal{M}_{3body}}$ is based on the
geometry and kinematic properties of the final-state tracks and the
reconstructed $\tau^{-}$ candidate. It aims to reject backgrounds from
combinations of tracks that do not share a common vertex and those from multi-
body decays with more than three final-state particles. The variables used in
the classifier include the vertex fit quality, the displacement of the vertex
from the PV, the pointing angle $\theta$, and the IP and fit $\chi^{2}$ of the
tracks. An ensemble-selected (blended) [21], custom boosted decision tree
(BDT) classifier is used [22, 23], as described in the following. In the
blending method the input variables are combined [24] into one BDT, two Fisher
discriminants [25], four neural networks [26], one function-discriminant
analysis [27] and one linear discriminant [28]. Each classifier is trained
using simulated signal and background samples, where the composition of the
background is a mixture of $b\bar{b}\rightarrow\mu\mu X$ and
$c\bar{c}\rightarrow\mu\mu X$ processes according to their relative abundances
as measured in data. As each category of simulated signal events has different
kinematic properties, a separate set of classifiers is trained for each. One
third of the available signal sample is used at this stage, along with one
half of the background sample. The classifier responses, along with the
original input variables, are then used as input to the custom BDT classifier,
which is trained on the remaining half of the background sample and a third of
the signal sample, with the five categories combined, to give the final
classifier response. The responses of the classifier on the training and the
test samples are found to be in good agreement, suggesting no overtraining of
the classifier is present. As the responses of the individual classifiers are
not fully correlated, blending the output of the classifiers improves the
sensitivity of the analysis in our data sample by 6% with respect to that
achievable by using the best single classifier. The ${\rm\mathcal{M}_{3body}}$
classifier response is calibrated using the
$D_{s}^{-}\rightarrow\phi\left(\mu^{+}\mu^{-}\right)\pi^{-}$ control channel
to correct for differences in response between data and simulation. Figure 1
shows good agreement between
$D_{s}^{-}\rightarrow\phi\left(\mu^{+}\mu^{-}\right)\pi^{-}$ data and
simulation for one of the input variables to ${\rm\mathcal{M}_{3body}}$ and
for the classifier response. A systematic uncertainty of 2% is assigned to
account for any remaining differences. The classifier response is found to be
uncorrelated with mass for both the signal sample and the data sidebands.

\begin{overpic}[width=432.48048pt]{dataMC_FD.pdf}
\put(40.0,100.0){\small{(a)}} \end{overpic}

\begin{overpic}[width=432.48048pt]{dataMC.pdf} \put(40.0,100.0){\small{(b)}}
\end{overpic}

Figure 1: Distribution of (a) $D_{s}^{-}$ flight distance and (b)
${\rm\mathcal{M}_{3body}}$ response for
$D_{s}^{-}\rightarrow\phi\left(\mu^{+}\mu^{-}\right)\pi^{-}$ candidates at
8$\mathrm{\,Te\kern-0.90005ptV}$. The dashed (red) lines indicate the data and
the solid (black) lines indicate the simulation. The data is background-
subtracted using the sPlot technique [29].

The multivariate classifier ${\rm\mathcal{M}_{PID}}$ uses information from the
RICH detectors, the calorimeters and the muon detectors to obtain the
likelihood that each of the three final-state particles is compatible with the
muon hypothesis. The value of the ${\rm\mathcal{M}_{PID}}$ response is taken
as the smallest likelihood of the three muon candidates. The
${\rm\mathcal{M}_{PID}}$ classifier uses a neural network that is trained on
simulated events to discriminate muons from other charged particles. The
${\rm\mathcal{M}_{PID}}$ classifier response is calibrated using muons from
$J/\psi\rightarrow\mu^{+}\mu^{-}$ decays in data.

For the ${\rm\mathcal{M}_{3body}}$ and ${\rm\mathcal{M}_{PID}}$ responses, a
binning is chosen via the $\textrm{CL}_{\textrm{s}}$ method [30, *Junk_99] by
maximising the difference between the median $\textrm{CL}_{\textrm{s}}$ values
under the background-only hypothesis and the signal-plus-background
hypothesis, whilst minimising the number of bins. The binning optimisation is
performed separately for the 7$\mathrm{\,Te\kern-1.00006ptV}$ and
8$\mathrm{\,Te\kern-1.00006ptV}$ data sets, because there are small
differences in event topology with changes of centre-of-mass energy. The
optimisation does not depend on the signal branching fraction. The bins at
lowest values of ${\rm\mathcal{M}_{3body}}$ and ${\rm\mathcal{M}_{PID}}$
response do not contribute to the sensitivity and are excluded from the
analysis. The distributions of the responses of the two classifiers, along
with their binning schemes, are shown in Fig. 2.

\begin{overpic}[width=432.48048pt]{m3body_2011_log.pdf}
\put(40.0,115.0){\small{(a)}} \end{overpic}

\begin{overpic}[width=432.48048pt]{mPID_2011_log.pdf}
\put(40.0,115.0){\small{(b)}} \end{overpic}

\begin{overpic}[width=432.48048pt]{m3body_2012_log.pdf}
\put(40.0,117.0){\small{(c)}} \end{overpic}

\begin{overpic}[width=432.48048pt]{mPID_2012_log.pdf}
\put(40.0,117.0){\small{(d)}} \end{overpic}

Figure 2: Distribution of (a) ${\rm\mathcal{M}_{3body}}$ and (b)
${\rm\mathcal{M}_{PID}}$ response for 7$\mathrm{\,Te\kern-0.90005ptV}$ data
and (c) ${\rm\mathcal{M}_{3body}}$ and (d) ${\rm\mathcal{M}_{PID}}$ response
for 8$\mathrm{\,Te\kern-0.90005ptV}$ data. The binnings correspond to those
used in the extraction of the final results. The short-dashed (red) lines show
the response of the data sidebands, whilst the long-dashed (blue) and solid
(black) lines show the response of simulated signal events before and after
calibration. In all cases the first bin is excluded from the analysis.

The expected shapes of the invariant mass spectra for the
$\tau^{-}\rightarrow\mu^{-}\mu^{+}\mu^{-}$ signal in the
7$\mathrm{\,Te\kern-1.00006ptV}$ and 8$\mathrm{\,Te\kern-1.00006ptV}$ data
sets are taken from fits to the
$D_{s}^{-}\rightarrow\phi\left(\mu^{+}\mu^{-}\right)\pi^{-}$ control channel
in data. Figure 3 shows the fit to the 8$\mathrm{\,Te\kern-1.00006ptV}$ data.
No particle identification requirements are applied to the pion. The signal
distribution is modelled with the sum of two Gaussian functions with a common
mean, where the narrower Gaussian contributes 70% of the total signal yield,
while the combinatorial background is modelled with an exponential function.
The expected width of the $\tau^{-}$ signal in data is taken from simulation,
scaled by the ratio of the widths of the $D_{s}^{-}$ peaks in data and
simulation.

Figure 3: Invariant mass distribution of $\phi(\mu^{+}\mu^{-})\pi^{-}$
candidates in 8$\mathrm{\,Te\kern-0.90005ptV}$ data. The solid (blue) line
shows the overall fit, the long-dashed (green) and short-dashed (red) lines
show the two Gaussian components of the $D^{-}_{s}$ signal and the dot-dashed
(black) line shows the combinatorial background contribution.

##  6 Backgrounds

The background processes for the $\tau^{-}\rightarrow\mu^{-}\mu^{+}\mu^{-}$
decay consist mainly of heavy meson decays yielding three muons in the final
state, or one or two muons in combination with two or one misidentified
particles. There are also a large number of events with one or two muons from
heavy meson decays combined with two or one muons from elsewhere in the event.
Decays containing undetected final-state particles, such as
$K^{0}_{\rm\scriptscriptstyle L}$ mesons, neutrinos or photons, can give large
backgrounds, which vary smoothly in the signal region. The most important
background channel of this type is found to be
$D_{s}^{-}\rightarrow\eta\left(\mu^{+}\mu^{-}\gamma\right)\mu^{-}{\bar{\nu}_{\mu}}$,
about $90\%$ of which is removed by the requirement on the dimuon mass. The
small remaining contribution from this process has a mass distribution similar
to that of the other backgrounds in the mass range considered in the fit. The
dominant contributions to the background from misidentified particles are from
$D_{(s)}^{-}\rightarrow K^{+}\pi^{-}\pi^{-}$ and
$D_{(s)}^{-}\rightarrow\pi^{+}\pi^{-}\pi^{-}$ decays. However, these events
populate mainly the region of low ${\rm\mathcal{M}_{PID}}$ response and are
reduced to a negligible level by the exclusion of the first bin.

The expected numbers of background events within the signal region, for each
bin in ${\rm\mathcal{M}_{3body}}$ and ${\rm\mathcal{M}_{PID}}$, are evaluated
by fitting an exponential function to the candidate mass spectra outside of
the signal windows using an extended, unbinned maximum likelihood fit. The
parameters of the exponential function are allowed to vary independently in
each bin. The small differences obtained if the exponential curves are
replaced by straight lines are included as systematic uncertainties. The
$\mu^{-}\mu^{+}\mu^{-}$ mass spectra are fitted over the mass range
1600–1950${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, excluding windows of
width $\pm 30$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ around the expected
signal mass. The resulting fits to the data sidebands for the highest
sensitivity bins are shown in Fig. 4 for 7 and
8$\mathrm{\,Te\kern-1.00006ptV}$ data separately.

\begin{overpic}[width=455.24408pt]{Bkg2011.pdf} \put(50.0,120.0){\small{(a)}}
\put(117.0,125.0){\footnotesize{${\rm\mathcal{M}_{3body}}$ $\in[0.80,1.0]$}}
\put(117.0,115.0){\footnotesize{${\rm\mathcal{M}_{PID}}$ $\in[0.75,1.0]$}}
\end{overpic}

\begin{overpic}[width=455.24408pt]{Bkg2012.pdf} \put(50.0,120.0){\small{(b)}}
\put(117.0,125.0){\footnotesize{${\rm\mathcal{M}_{3body}}$ $\in[0.94,1.0]$}}
\put(117.0,115.0){\footnotesize{${\rm\mathcal{M}_{PID}}$ $\in[0.80,1.0]$}}
\end{overpic}

Figure 4: Invariant mass distributions and fits to the mass sidebands in (a)
7$\mathrm{\,Te\kern-0.90005ptV}$ and (b) 8$\mathrm{\,Te\kern-0.90005ptV}$ data
for $\mu^{+}\mu^{-}\mu^{-}$ candidates in the bins of
${\rm\mathcal{M}_{3body}}$ and ${\rm\mathcal{M}_{PID}}$ response that contain
the highest signal probabilities.

##  7 Normalisation

The observed number of $\tau^{-}\rightarrow\mu^{-}\mu^{+}\mu^{-}$ candidates
is converted into a branching fraction by normalising to the
$D_{s}^{-}\rightarrow\phi\left(\mu^{+}\mu^{-}\right)\pi^{-}$ calibration
channel according to

${{\cal B}\left(\tau^{-}\rightarrow\mu^{-}\mu^{+}\mu^{-}\right)}=\frac{{\cal
B}\left(D_{s}^{-}\rightarrow\phi\left(\mu^{+}\mu^{-}\right)\pi^{-}\right)}{{\cal
B}\left(D_{s}^{-}\rightarrow\tau^{-}\bar{\nu}_{\tau}\right)}\times
f^{D_{s}}_{\tau}\times\frac{\rm{\epsilon\mathstrut_{cal}^{R}}}{\rm\epsilon\mathstrut_{sig}^{R}}\times\frac{\rm{\epsilon\mathstrut_{cal}^{T}}}{\rm\epsilon\mathstrut_{sig}^{T}}\times\frac{N_{\rm
sig}}{N_{\rm cal}}\equiv\alpha N_{\rm sig}\,,$ (1)

where $\alpha$ is the overall normalisation factor, $N_{\rm sig}$ is the
number of observed signal events and all other terms are described below.
Table 1 gives a summary of all contributions to the factor $\alpha$; the
uncertainties are taken to be uncorrelated. The branching fraction of the
normalisation channel is determined from known branching fractions as

${\cal
B}\left(D_{s}^{-}\rightarrow\phi\left(\mu^{+}\mu^{-}\right)\pi^{-}\right)=\frac{{\cal
B}\left(D_{s}^{-}\rightarrow\phi\left(K^{+}K^{-}\right)\pi^{-}\right)}{{\cal
B}\left(\phi\rightarrow K^{+}K^{-}\right)}{\cal
B}\left(\phi\rightarrow\mu^{+}\mu^{-}\right)=\left(1.32\pm 0.10\right)\times
10^{-5}\,,$

where ${\cal B}\left(\phi\rightarrow K^{+}K^{-}\right)$ and ${\cal
B}\left(\phi\rightarrow\mu^{+}\mu^{-}\right)$ are taken from Ref. [3] and
${\cal B}\left(D_{s}^{-}\rightarrow\phi\left(K^{+}K^{-}\right)\pi^{-}\right)$
is taken from Ref. [32]. The branching fraction ${\cal
B}\left(D_{s}^{-}\rightarrow\tau^{-}\bar{\nu}_{\tau}\right)$ is taken from
Refs. [3, 33].

The quantity $f^{D_{s}}_{\tau}$ is the fraction of $\tau^{-}$ leptons that
originate from $D_{s}^{-}$ decays. The value of $f^{D_{s}}_{\tau}$ at
7$\mathrm{\,Te\kern-1.00006ptV}$ is calculated using the $b\bar{b}$ and
$c\bar{c}$ cross-sections as measured by LHCb [9, 10] at
7$\mathrm{\,Te\kern-1.00006ptV}$ and the inclusive $b\rightarrow D_{s}$,
$c\rightarrow D_{s}$, $b\rightarrow\tau$ and $c\rightarrow\tau$ branching
fractions [3]. For the value of $f^{D_{s}}_{\tau}$ at
8$\mathrm{\,Te\kern-1.00006ptV}$ the $b\bar{b}$ cross-section is updated to
the 8$\mathrm{\,Te\kern-1.00006ptV}$ LHCb measurement [34] and the $c\bar{c}$
cross-section measured at 7$\mathrm{\,Te\kern-1.00006ptV}$ is scaled by a
factor of $\nicefrac{{8}}{{7}}$, consistent with Pythia simulations. The
uncertainty on this scaling factor, which is negligible, is found by taking
the difference between the value obtained from the nominal parton distribution
functions and that from the average of their corresponding error sets [35].

The reconstruction and selection efficiencies, $\rm\epsilon^{R}$, are products
of the detector acceptances for the decay of interest, the muon identification
efficiencies and the selection efficiencies. The combined muon identification
and selection efficiencies are determined from the yield of simulated events
after the full selections are applied. The ratio of efficiencies is corrected
to account for the differences between data and simulation in track
reconstruction, muon identification, the $\phi(1020)$ mass window requirement
in the normalisation channel and the $\tau^{-}$ mass range. The removal of
candidates in the least sensitive bins in the ${\rm\mathcal{M}_{3body}}$ and
${\rm\mathcal{M}_{PID}}$ classifier responses is also taken into account.

The trigger efficiencies, $\rm\epsilon^{T}$, are evaluated from simulation and
their systematic uncertainties are determined from the differences between the
trigger efficiencies of $B^{-}\rightarrow J/\psi(\mu^{+}\mu^{-})K^{-}$ decays
measured in data and in simulation, using muons with momentum values typical
of $\tau^{-}\rightarrow\mu^{-}\mu^{+}\mu^{-}$ signal decays. The trigger
efficiency for the 8$\mathrm{\,Te\kern-1.00006ptV}$ data set is corrected to
account for differences in trigger conditions across the data taking period,
resulting in a relatively large systematic error.

The yields of $D_{s}^{-}\rightarrow\phi\left(\mu^{+}\mu^{-}\right)\pi^{-}$
candidates in data, $N_{\rm cal}$, are determined from the fits to
reconstructed $\phi\left(\mu^{+}\mu^{-}\right)\pi^{-}$ mass distributions
shown in Fig. 3. The variations in the yields when the relative contributions
of the two Gaussian components are allowed to vary in the fits are considered
as systematic uncertainties.

Table 1: Terms entering into the normalisation factors, $\alpha$, and their
combined statistical and systematic uncertainties.

$\begin{array}[]{cr@{\hspace{1mm}\pm\hspace{1mm}}lr@{\hspace{1mm}\pm\hspace{1mm}}l}\hline\cr\hline\cr&\lx@intercol\hfil
7\mathrm{\,Te\kern-1.00006ptV}\hfil\lx@intercol&\lx@intercol\hfil
8\mathrm{\,Te\kern-1.00006ptV}\hfil\lx@intercol\\\ \hline\cr{\cal
B}\left(D_{s}^{-}\rightarrow\phi\left(\mu^{+}\mu^{-}\right)\pi^{-}\right)&\lx@intercol\hfil\left(1.32\right.\hskip
2.84526pt\pm\hskip 2.84526pt&\lx@intercol\left.0.10\right)\times
10^{-5}\hfil\lx@intercol\\\ {\cal
B}\left(D_{s}^{-}\rightarrow\tau^{-}\bar{\nu}_{\tau}\right)&\lx@intercol\hfil\left(5.61\right.\hskip
2.84526pt\pm\hskip 2.84526pt&\lx@intercol\left.0.24\right)\times
10^{-2}\hfil\lx@intercol\\\ f^{D_{s}}_{\tau}&0.78\hskip 2.84526pt\pm\hskip
2.84526pt&0.04&0.80\hskip 2.84526pt\pm\hskip 2.84526pt&0.03\\\
\rm{\epsilon\mathstrut_{cal}}^{R}/\rm{\epsilon\mathstrut_{sig}}^{R}&0.898\hskip
2.84526pt\pm\hskip 2.84526pt&0.060&0.912\hskip 2.84526pt\pm\hskip
2.84526pt&0.054\\\
\rm{\epsilon\mathstrut_{cal}}^{T}/\rm{\epsilon\mathstrut_{sig}}^{T}&0.659\hskip
2.84526pt\pm\hskip 2.84526pt&0.006&0.525\hskip 2.84526pt\pm\hskip
2.84526pt&0.040\\\ N_{\rm cal}&28\,200\hskip 2.84526pt\pm\hskip
2.84526pt&440&52\,130\hskip 2.84526pt\pm\hskip 2.84526pt&700\\\
\alpha&\left(7.20\right.\hskip 2.84526pt\pm\hskip
2.84526pt&\left.0.98\right)\times 10^{-9}&\left(3.37\right.\hskip
2.84526pt\pm\hskip 2.84526pt&\left.0.50\right)\times 10^{-9}\\\
\hline\cr\hline\cr\end{array}$

##  8 Results

Tables 2 and 3 give the expected and observed numbers of candidates in the
signal region, for each bin of the classifier responses. No significant excess
of events over the expected background is observed. Using the
$\textrm{CL}_{\textrm{s}}$ method [30, *Junk_99] and Eq. 1, the observed
$\textrm{CL}_{\textrm{s}}$ value and the expected $\textrm{CL}_{\textrm{s}}$
distribution are calculated as functions of the assumed branching fraction, as
shown in Fig. 5. The systematic uncertainties on the signal and background
estimates, which have a very small effect on the final limits, are included
following Ref. [30, *Junk_99]. The expected limit at $90\%~{}(95\%)$ CL for
the branching fraction is ${\cal
B}\left(\tau^{-}\rightarrow\mu^{-}\mu^{+}\mu^{-}\right)<5.0~{}(6.1)\times
10^{-8}$, while the observed limit at $90\%~{}(95\%)$ CL is

${\cal
B}\left(\tau^{-}\rightarrow\mu^{-}\mu^{+}\mu^{-}\right)<4.6~{}(5.6)\times
10^{-8}.$

Whilst the above limits are given for the phase-space model of $\tau^{-}$
decays, the kinematic properties of the decay would depend on the physical
processes that introduce LFV. Reference [36] gives a model-independent
analysis of the decay distributions in an effective field-theory approach
including BSM operators with different chirality structures. Depending on the
choice of operator, the observed limit varies within the range
$(4.1-6.8)\times 10^{-8}$ at $90\%$ CL. The weakest limit results from an
operator that favours low $\mu^{+}\mu^{-}$ mass, since the requirement to
remove the
$D_{s}^{-}\rightarrow\eta\left(\mu^{+}\mu^{-}\gamma\right)\mu^{-}{\bar{\nu}_{\mu}}$
background excludes a large fraction of the relevant phase-space.

In summary, the LHCb search for the LFV decay
$\tau^{-}\rightarrow\mu^{-}\mu^{+}\mu^{-}$ is updated using all data collected
during the first run of the LHC, corresponding to an integrated luminosity of
3.0$\mbox{\,fb}^{-1}$. No evidence for any signal is found. The measured
limits supersede those of Ref. [6] and, in combination with results from the B
factories, improve the constraints placed on the parameters of a broad class
of BSM models [37].

Table 2: Expected background candidate yields in the 7$\mathrm{\,Te\kern-0.90005ptV}$ data set, with their uncertainties, and observed candidate yields within the $\tau^{-}$ signal window in the different bins of classifier response. The classifier responses range from $0$ (most background-like) to $+1$ (most signal-like). The first bin in each classifier response is excluded from the analysis. ${\rm\mathcal{M}_{PID}}$ response |  ${\rm\mathcal{M}_{3body}}$ response | Expected | Observed
---|---|---|---
| 0.28 – | 0.32 |  3.17 $\pm$ | 0.66 | 4
| 0.32 – | 0.46 |  9.2 $\pm$ | 1.1 | 6
0.40 – 0.45 | 0.46 – | 0.54 |  2.89 $\pm$ | 0.63 | 6
| 0.54 – | 0.65 |  3.17 $\pm$ | 0.66 | 4
| 0.65 – | 0.80 |  3.64 $\pm$ | 0.72 | 2
| 0.80 – | 1.00 |  3.79 $\pm$ | 0.80 | 3
| 0.28 – | 0.32 |  4.22 $\pm$ | 0.78 | 6
| 0.32 – | 0.46 |  8.3 $\pm$ | 1.1 | 10
0.45 – 0.54 | 0.46 – | 0.54 |  2.3 $\pm$ | 0.57 | 4
| 0.54 – | 0.65 |  2.83 $\pm$ | 0.63 | 8
| 0.65 – | 0.80 |  2.72 $\pm$ | 0.69 | 5
| 0.80 – | 1.00 |  4.83 $\pm$ | 0.90 | 7
| 0.28 – | 0.32 |  2.33 $\pm$ | 0.58 | 6
| 0.32 – | 0.46 |  8.3 $\pm$ | 1.1 | 8
0.54 – 0.63 | 0.46 – | 0.54 |  2.07 $\pm$ | 0.53 | 1
| 0.54 – | 0.65 |  3.29 $\pm$ | 0.68 | 1
| 0.65 – | 0.80 |  2.96 $\pm$ | 0.65 | 4
| 0.80 – | 1.00 |  3.11 $\pm$ | 0.69 | 3
| 0.28 – | 0.32 |  2.69 $\pm$ | 0.62 | 1
| 0.32 – | 0.46 |  7.5 $\pm$ | 1.0 | 5
0.63 – 0.75 | 0.46 – | 0.54 |  2.06 $\pm$ | 0.53 | 3
| 0.54 – | 0.65 |  2.00 $\pm$ | 0.55 | 5
| 0.65 – | 0.80 |  3.16 $\pm$ | 0.66 | 2
| 0.80 – | 1.00 |  4.67 $\pm$ | 0.84 | 2
| 0.28 – | 0.32 |  2.19 $\pm$ | 0.55 | 2
| 0.32 – | 0.46 |  3.38 $\pm$ | 0.76 | 5
0.75 – 1.00 | 0.46 – | 0.54 |  1.52 $\pm$ | 0.46 | 3
| 0.54 – | 0.65 |  1.28 $\pm$ | 0.47 | 1
| 0.65 – | 0.80 |  2.78 $\pm$ | 0.65 | 1
| 0.80 – | 1.00 |  4.42 $\pm$ | 0.83 | 7
Table 3: Expected background candidate yields in the 8$\mathrm{\,Te\kern-0.90005ptV}$ data set, with their uncertainties, and observed candidate yields within the $\tau^{-}$ signal window in the different bins of classifier response. The classifier responses range from $0$ (most background-like) to $+1$ (most signal-like). The first bin in each classifier response is excluded from the analysis. ${\rm\mathcal{M}_{PID}}$ response |  ${\rm\mathcal{M}_{3body}}$ response | Expected | Observed
---|---|---|---
| 0.26 – | 0.34 |  39.6 $\pm$ | 2.3 | 39
| 0.34 – | 0.45 |  32.2 $\pm$ | 2.1 | 34
| 0.45 – | 0.61 |  28.7 $\pm$ | 2.0 | 28
0.40 – 0.54 | 0.61 – | 0.70 |  9.7 $\pm$ | 1.2 | 5
| 0.70 – | 0.83 |  11.4 $\pm$ | 1.3 | 7
| 0.83 – | 0.94 |  7.3 $\pm$ | 1.1 | 6
| 0.94 – | 1.00 |  6.0 $\pm$ | 1.0 | 0
| 0.26 – | 0.34 |  13.6 $\pm$ | 1.4 | 8
| 0.34 – | 0.45 |  12.1 $\pm$ | 1.3 | 12
| 0.45 – | 0.61 |  8.3 $\pm$ | 1.0 | 13
0.54 – 0.61 | 0.61 – | 0.70 |  2.60 $\pm$ | 0.62 | 1
| 0.70 – | 0.83 |  1.83 $\pm$ | 0.60 | 5
| 0.83 – | 0.94 |  2.93 $\pm$ | 0.72 | 6
| 0.94 – | 1.00 |  2.69 $\pm$ | 0.63 | 3
| 0.26 – | 0.34 |  13.5 $\pm$ | 1.4 | 7
| 0.34 – | 0.45 |  10.9 $\pm$ | 1.2 | 11
| 0.45 – | 0.61 |  9.7 $\pm$ | 1.2 | 12
0.61 – 0.71 | 0.61 – | 0.70 |  3.35 $\pm$ | 0.69 | 2
| 0.70 – | 0.83 |  4.60 $\pm$ | 0.89 | 5
| 0.83 – | 0.94 |  4.09 $\pm$ | 0.81 | 4
| 0.94 – | 1.00 |  2.78 $\pm$ | 0.68 | 1
| 0.26 – | 0.34 |  7.8 $\pm$ | 1.1 | 6
| 0.34 – | 0.45 |  7.00 $\pm$ | 0.99 | 8
| 0.45 – | 0.61 |  6.17 $\pm$ | 0.95 | 6
0.71 – 0.80 | 0.61 – | 0.70 |  1.57 $\pm$ | 0.56 | 2
| 0.70 – | 0.83 |  2.99 $\pm$ | 0.72 | 0
| 0.83 – | 0.94 |  3.93 $\pm$ | 0.81 | 0
| 0.94 – | 1.00 |  3.22 $\pm$ | 0.68 | 1
| 0.26 – | 0.34 |  5.12 $\pm$ | 0.86 | 3
| 0.34 – | 0.45 |  4.44 $\pm$ | 0.79 | 6
| 0.45 – | 0.61 |  3.80 $\pm$ | 0.78 | 5
0.80 – 1.00 | 0.61 – | 0.70 |  2.65 $\pm$ | 0.68 | 2
| 0.70 – | 0.83 |  3.05 $\pm$ | 0.67 | 2
| 0.83 – | 0.94 |  1.74 $\pm$ | 0.54 | 2
| 0.94 – | 1.00 |  3.36 $\pm$ | 0.70 | 3
Figure 5: Distribution of $\textrm{CL}_{\textrm{s}}$ values as a function of
the assumed branching fraction for $\tau^{-}\rightarrow\mu^{-}\mu^{+}\mu^{-}$,
under the hypothesis to observe background events only. The dashed line
indicates the expected limit and the solid line the observed one. The light
(yellow) and dark (green) bands cover the regions of 68% and 95% confidence
for the expected limit.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC
(China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland);
INFN (Italy); FOM and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA
(Romania); MinES and FANO (Russia); MinECo (Spain); SNSF and SER
(Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (USA). The Tier1
computing centres are supported by IN2P3 (France), KIT and BMBF (Germany),
INFN (Italy), NWO and SURF (The Netherlands), PIC (Spain), GridPP (United
Kingdom). We are indebted to the communities behind the multiple open source
software packages on which we depend. We are also thankful for the computing
resources and the access to software R&D tools provided by Yandex LLC
(Russia). Individual groups or members have received support from EPLANET,
Marie Skłodowska-Curie Actions and ERC (European Union), Conseil général de
Haute-Savoie, Labex ENIGMASS and OCEVU, Région Auvergne (France), RFBR
(Russia), XuntaGal and GENCAT (Spain), Royal Society and Royal Commission for
the Exhibition of 1851 (United Kingdom).

## References

  * [1] M. Raidal et al., Flavour physics of leptons and dipole moments, Eur. Phys. J. C57 (2008) 13, arXiv:0801.1826
  * [2] A. Ilakovac, A. Pilaftsis, and L. Popov, Charged lepton flavor violation in supersymmetric low-scale seesaw models, Phys. Rev. D87 (2013) 053014, arXiv:1212.5939
  * [3] Particle Data Group, K. A. Olive et al., Review of particle physics, Chin. Phys. C38 (2014) 090001
  * [4] W. J. Marciano, T. Mori, and J. M. Roney, Charged lepton flavour violation experiments, Ann. Rev. Nucl. Part. Sci 58 (2008) 315
  * [5] LHCb collaboration, A. Alves et al., The LHCb detector at the LHC, JINST 3 (2008) S08005
  * [6] LHCb collaboration, R. Aaij et al., Searches for violation of lepton flavour and baryon number in tau lepton decays at LHCb, Phys. Lett. B724 (2013) 36, arXiv:1304.4518
  * [7] Belle collaboration, K. Hayasaka et al., Search for lepton flavor violating $\tau$ decays into three leptons with 719 million produced $\tau^{+}\tau^{-}$ pairs, Phys. Lett. B687 (2010) 139, arXiv:1001.3221
  * [8] BaBar Collaboration, J. Lees et al., Limits on tau Lepton-Flavor Violating Decays in three charged leptons, Phys. Rev. D81 (2010) 111101, arXiv:1002.4550
  * [9] LHCb collaboration, R. Aaij et al., Measurement of $J/\psi$ production in $pp$ collisions at $\sqrt{s}=7$ TeV, Eur. Phys. J. C71 (2011) 1645, arXiv:1103.0423
  * [10] LHCb collaboration, R. Aaij et al., Prompt charm production in $pp$ collisions at $\sqrt{s}=7$ TeV, Nucl. Phys. B871 (2013) 1, arXiv:1302.2864
  * [11] M. Adinolfi et al., Performance of the LHCb RICH detector at the LHC, Eur. Phys. J. C73 (2013) 2431, arXiv:1211.6759
  * [12] A. A. Alves Jr. et al., Performance of the LHCb muon system, JINST 8 (2013) P02022, arXiv:1211.1346
  * [13] R. Aaij et al., The LHCb trigger and its performance in 2011, JINST 8 (2013) P04022, arXiv:1211.3055
  * [14] T. Sjöstrand, S. Mrenna, and P. Skands, PYTHIA 6.4 Physics and manual, JHEP 05 (2006) 026, arXiv:hep-ph/0603175
  * [15] I. Belyaev et al., Handling of the generation of primary events in Gauss, the LHCb simulation framework, Nuclear Science Symposium Conference Record (NSS/MIC) IEEE (2010) 1155
  * [16] D. J. Lange, The EvtGen particle decay simulation package, Nucl. Instrum. Meth. A462 (2001) 152
  * [17] P. Golonka and Z. Was, PHOTOS Monte Carlo: A precision tool for QED corrections in $Z$ and $W$ decays, Eur. Phys. J. C45 (2006) 97, arXiv:hep-ph/0506026
  * [18] Geant4 collaboration, J. Allison et al., Geant4 developments and applications, IEEE Trans. Nucl. Sci. 53 (2006) 270
  * [19] Geant4 collaboration, S. Agostinelli et al., Geant4: A simulation toolkit, Nucl. Instrum. Meth. A506 (2003) 250
  * [20] M. Clemencic et al., The LHCb simulation application, Gauss: Design, evolution and experience, J. of Phys: Conf. Ser. 331 (2011) 032023
  * [21] R. Caruana, A. Niculescu-Mizil, G. Crew, and A. Ksikes, Ensemble selection from libraries of models, in Proceedings of the Twenty-first International Conference on Machine Learning, ICML ’04, (New York, NY, USA), p. 18, ACM, 2004\.  doi: 10.1145/1015330.1015432
  * [22] A. Gulin, I. Kuralenok, and D. Pavlov, Winning the transfer learning track of Yahoo!’s Learning to Rank Challenge with YetiRank, JMLR: Workshop and Conference Proceedings 14 (2011) 63
  * [23] L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stone, Classification and regression trees, Wadsworth international group, Belmont, California, USA, 1984
  * [24] A. Hoecker et al., TMVA: Toolkit for Multivariate Data Analysis, PoS ACAT (2007) 040, arXiv:physics/0703039
  * [25] R. A. Fisher, The use of multiple measurements in taxonomic problems, Annals of Eugenics 7 (1936) 179
  * [26] P. Gay, B. Michel, J. Proriol, and O. Deschamps, Tagging Higgs bosons in hadronic LEP2 events with neural networks, in New computing techniques in physics research 4, (Pisa, Italy), pp. 725–730, World Scientific, 1995
  * [27] G. D. Garson, Discriminant function analysis, Statistical Associates Publishers, Ashboro, North Carolina, USA, 2012
  * [28] D0 collaboration, P. C. Bhat, Search for the top quark at D0 using multivariate methods, AIP Conf. Proc. 357 (1996) 308, arXiv:hep-ex/9507007
  * [29] M. Pivk and F. R. Le Diberder, sPlot: a statistical tool to unfold data distributions, Nucl. Instrum. Meth. A555 (2005) 356, arXiv:physics/0402083
  * [30] A. L. Read, Presentation of search results: The CL(s) technique, J. Phys. G28 (2002) 2693
  * [31] T. Junk, Confidence level computation for combining searches with small statistics, Nucl. Instrum. Meth. A434 (1999) 435, arXiv:hep-ex/9902006
  * [32] BaBar collaboration, P. del Amo Sanchez et al., Dalitz plot analysis of $D_{s}^{+}\rightarrow K^{+}K^{-}\pi^{+}$, Phys. Rev. D83 (2011) 052001, arXiv:1011.4190
  * [33] Belle collaboration, A. Zupanc et al., Measurements of branching fractions of leptonic and hadronic $D_{s}^{+}$ meson decays and extraction of the $D_{s}^{+}$ meson decay constant, JHEP 09 (2013) 139, arXiv:1307.6240
  * [34] LHCb collaboration, R. Aaij et al., Production of $J/\psi$ and $\Upsilon$ mesons in $pp$ collisions at $\sqrt{s}=8$ TeV, JHEP 06 (2013) 064, arXiv:1304.6977
  * [35] J. Pumplin et al., New generation of parton distributions with uncertainties from global QCD analysis, JHEP 0207 (2002) 012, arXiv:hep-ph/0201195
  * [36] B. Dassinger, T. Feldmann, T. Mannel, and S. Turczyk, Model-independent analysis of lepton flavour violating $\tau$ decays, JHEP 10 (2007) 039, arXiv:0707.0988
  * [37] Heavy Flavor Averaging Group (HFAG), Y. Amhis et al., Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of summer 2014, arXiv:1412.7515

LHCb collaboration

R. Aaij41, B. Adeva37, M. Adinolfi46, A. Affolder52, Z. Ajaltouni5, S. Akar6,
J. Albrecht9, F. Alessio38, M. Alexander51, S. Ali41, G. Alkhazov30, P.
Alvarez Cartelle37, A.A. Alves Jr25,38, S. Amato2, S. Amerio22, Y. Amhis7, L.
An3, L. Anderlini17,g, J. Anderson40, R. Andreassen57, M. Andreotti16,f, J.E.
Andrews58, R.B. Appleby54, O. Aquines Gutierrez10, F. Archilli38, A.
Artamonov35, M. Artuso59, E. Aslanides6, G. Auriemma25,n, M. Baalouch5, S.
Bachmann11, J.J. Back48, A. Badalov36, C. Baesso60, W. Baldini16, R.J.
Barlow54, C. Barschel38, S. Barsuk7, W. Barter47, V. Batozskaya28, V.
Battista39, A. Bay39, L. Beaucourt4, J. Beddow51, F. Bedeschi23, I. Bediaga1,
S. Belogurov31, K. Belous35, I. Belyaev31, E. Ben-Haim8, G. Bencivenni18, S.
Benson38, J. Benton46, A. Berezhnoy32, R. Bernet40, M.-O. Bettler47, M. van
Beuzekom41, A. Bien11, S. Bifani45, T. Bird54, A. Bizzeti17,i, P.M.
Bjørnstad54, T. Blake48, F. Blanc39, J. Blouw10, S. Blusk59, V. Bocci25, A.
Bondar34, N. Bondar30,38, W. Bonivento15,38, S. Borghi54, A. Borgia59, M.
Borsato7, T.J.V. Bowcock52, E. Bowen40, C. Bozzi16, T. Brambach9, D. Brett54,
M. Britsch10, T. Britton59, J. Brodzicka54, N.H. Brook46, H. Brown52, A.
Bursche40, J. Buytaert38, S. Cadeddu15, R. Calabrese16,f, M. Calvi20,k, M.
Calvo Gomez36,p, P. Campana18, D. Campora Perez38, A. Carbone14,d, G.
Carboni24,l, R. Cardinale19,38,j, A. Cardini15, L. Carson50, K. Carvalho
Akiba2, G. Casse52, L. Cassina20, L. Castillo Garcia38, M. Cattaneo38, Ch.
Cauet9, R. Cenci23, M. Charles8, Ph. Charpentier38, M. Chefdeville4, S.
Chen54, S.-F. Cheung55, N. Chiapolini40, M. Chrzaszcz40,26, X. Cid Vidal38, G.
Ciezarek41, P.E.L. Clarke50, M. Clemencic38, H.V. Cliff47, J. Closier38, V.
Coco38, J. Cogan6, E. Cogneras5, V. Cogoni15, L. Cojocariu29, G. Collazuol22,
P. Collins38, A. Comerma-Montells11, A. Contu15,38, A. Cook46, M. Coombes46,
S. Coquereau8, G. Corti38, M. Corvo16,f, I. Counts56, B. Couturier38, G.A.
Cowan50, D.C. Craik48, M. Cruz Torres60, S. Cunliffe53, R. Currie53, C.
D’Ambrosio38, J. Dalseno46, P. David8, P.N.Y. David41, A. Davis57, K. De
Bruyn41, S. De Capua54, M. De Cian11, J.M. De Miranda1, L. De Paula2, W. De
Silva57, P. De Simone18, C.-T. Dean51, D. Decamp4, M. Deckenhoff9, L. Del
Buono8, N. Déléage4, D. Derkach55, O. Deschamps5, F. Dettori38, A. Di Canto38,
H. Dijkstra38, S. Donleavy52, F. Dordei11, M. Dorigo39, A. Dosil Suárez37, D.
Dossett48, A. Dovbnya43, K. Dreimanis52, G. Dujany54, F. Dupertuis39, P.
Durante38, R. Dzhelyadin35, A. Dziurda26, A. Dzyuba30, S. Easo49,38, U.
Egede53, V. Egorychev31, S. Eidelman34, S. Eisenhardt50, U. Eitschberger9, R.
Ekelhof9, L. Eklund51, I. El Rifai5, Ch. Elsasser40, S. Ely59, S. Esen11,
H.-M. Evans47, T. Evans55, A. Falabella14, C. Färber11, C. Farinelli41, N.
Farley45, S. Farry52, RF Fay52, D. Ferguson50, V. Fernandez Albor37, F.
Ferreira Rodrigues1, M. Ferro-Luzzi38, S. Filippov33, M. Fiore16,f, M.
Fiorini16,f, M. Firlej27, C. Fitzpatrick39, T. Fiutowski27, P. Fol53, M.
Fontana10, F. Fontanelli19,j, R. Forty38, O. Francisco2, M. Frank38, C.
Frei38, M. Frosini17,g, J. Fu21,38, E. Furfaro24,l, A. Gallas Torreira37, D.
Galli14,d, S. Gallorini22,38, S. Gambetta19,j, M. Gandelman2, P. Gandini59, Y.
Gao3, J. García Pardiñas37, J. Garofoli59, J. Garra Tico47, L. Garrido36, D.
Gascon36, C. Gaspar38, R. Gauld55, L. Gavardi9, A. Geraci21,v, E. Gersabeck11,
M. Gersabeck54, T. Gershon48, Ph. Ghez4, A. Gianelle22, S. Gianì39, V.
Gibson47, L. Giubega29, V.V. Gligorov38, C. Göbel60, D. Golubkov31, A.
Golutvin53,31,38, A. Gomes1,a, C. Gotti20, M. Grabalosa Gándara5, R. Graciani
Diaz36, L.A. Granado Cardoso38, E. Graugés36, E. Graverini40, G. Graziani17,
A. Grecu29, E. Greening55, S. Gregson47, P. Griffith45, L. Grillo11, O.
Grünberg63, B. Gui59, E. Gushchin33, Yu. Guz35,38, T. Gys38, C.
Hadjivasiliou59, G. Haefeli39, C. Haen38, S.C. Haines47, S. Hall53, B.
Hamilton58, T. Hampson46, X. Han11, S. Hansmann-Menzemer11, N. Harnew55, S.T.
Harnew46, J. Harrison54, J. He38, T. Head38, V. Heijne41, K. Hennessy52, P.
Henrard5, L. Henry8, J.A. Hernando Morata37, E. van Herwijnen38, M. Heß63, A.
Hicheur2, D. Hill55, M. Hoballah5, C. Hombach54, W. Hulsbergen41, P. Hunt55,
N. Hussain55, D. Hutchcroft52, D. Hynds51, M. Idzik27, P. Ilten56, R.
Jacobsson38, A. Jaeger11, J. Jalocha55, E. Jans41, P. Jaton39, A. Jawahery58,
F. Jing3, M. John55, D. Johnson38, C.R. Jones47, C. Joram38, B. Jost38, N.
Jurik59, S. Kandybei43, W. Kanso6, M. Karacson38, T.M. Karbach38, S.
Karodia51, M. Kelsey59, I.R. Kenyon45, T. Ketel42, B. Khanji20,38, C.
Khurewathanakul39, S. Klaver54, K. Klimaszewski28, O. Kochebina7, M. Kolpin11,
I. Komarov39, R.F. Koopman42, P. Koppenburg41,38, M. Korolev32, A.
Kozlinskiy41, L. Kravchuk33, K. Kreplin11, M. Kreps48, G. Krocker11, P.
Krokovny34, F. Kruse9, W. Kucewicz26,o, M. Kucharczyk20,26,k, V.
Kudryavtsev34, K. Kurek28, T. Kvaratskheliya31, V.N. La Thi39, D. Lacarrere38,
G. Lafferty54, A. Lai15, D. Lambert50, R.W. Lambert42, G. Lanfranchi18, C.
Langenbruch48, B. Langhans38, T. Latham48, C. Lazzeroni45, R. Le Gac6, J. van
Leerdam41, J.-P. Lees4, R. Lefèvre5, A. Leflat32, J. Lefrançois7, S. Leo23, O.
Leroy6, T. Lesiak26, B. Leverington11, Y. Li3, T. Likhomanenko64, M. Liles52,
R. Lindner38, C. Linn38, F. Lionetto40, B. Liu15, S. Lohn38, I. Longstaff51,
J.H. Lopes2, N. Lopez-March39, P. Lowdon40, D. Lucchesi22,r, H. Luo50, A.
Lupato22, E. Luppi16,f, O. Lupton55, F. Machefert7, I.V. Machikhiliyan31, F.
Maciuc29, O. Maev30, S. Malde55, A. Malinin64, G. Manca15,e, A. Mapelli38, J.
Maratas5, J.F. Marchand4, U. Marconi14, C. Marin Benito36, P. Marino23,t, R.
Märki39, J. Marks11, G. Martellotti25, A. Martín Sánchez7, M. Martinelli39, D.
Martinez Santos42,38, F. Martinez Vidal65, D. Martins Tostes2, A.
Massafferri1, R. Matev38, Z. Mathe38, C. Matteuzzi20, B. Maurin39, A.
Mazurov45, M. McCann53, J. McCarthy45, A. McNab54, R. McNulty12, B.
McSkelly52, B. Meadows57, F. Meier9, M. Meissner11, M. Merk41, D.A. Milanes62,
M.-N. Minard4, N. Moggi14, J. Molina Rodriguez60, S. Monteil5, M. Morandin22,
P. Morawski27, A. Mordà6, M.J. Morello23,t, J. Moron27, A.-B. Morris50, R.
Mountain59, F. Muheim50, K. Müller40, M. Mussini14, B. Muster39, P. Naik46, T.
Nakada39, R. Nandakumar49, I. Nasteva2, M. Needham50, N. Neri21, S. Neubert38,
N. Neufeld38, M. Neuner11, A.D. Nguyen39, T.D. Nguyen39, C. Nguyen-Mau39,q, M.
Nicol7, V. Niess5, R. Niet9, N. Nikitin32, T. Nikodem11, A. Novoselov35, D.P.
O’Hanlon48, A. Oblakowska-Mucha27,38, V. Obraztsov35, S. Oggero41, S.
Ogilvy51, O. Okhrimenko44, R. Oldeman15,e, C.J.G. Onderwater66, M. Orlandea29,
J.M. Otalora Goicochea2, A. Otto38, P. Owen53, A. Oyanguren65, B.K. Pal59, A.
Palano13,c, F. Palombo21,u, M. Palutan18, J. Panman38, A. Papanestis49,38, M.
Pappagallo51, L.L. Pappalardo16,f, C. Parkes54, C.J. Parkinson9,45, G.
Passaleva17, G.D. Patel52, M. Patel53, C. Patrignani19,j, A. Pearce54, A.
Pellegrino41, M. Pepe Altarelli38, S. Perazzini14,d, P. Perret5, M. Perrin-
Terrin6, L. Pescatore45, E. Pesen67, K. Petridis53, A. Petrolini19,j, E.
Picatoste Olloqui36, B. Pietrzyk4, T. Pilař48, D. Pinci25, A. Pistone19, S.
Playfer50, M. Plo Casasus37, F. Polci8, A. Poluektov48,34, E. Polycarpo2, A.
Popov35, D. Popov10, B. Popovici29, C. Potterat2, E. Price46, J.D. Price52, J.
Prisciandaro39, A. Pritchard52, C. Prouve46, V. Pugatch44, A. Puig Navarro39,
G. Punzi23,s, W. Qian4, B. Rachwal26, J.H. Rademacker46, B.
Rakotomiaramanana39, M. Rama18, M.S. Rangel2, I. Raniuk43, N. Rauschmayr38, G.
Raven42, F. Redi53, S. Reichert54, M.M. Reid48, A.C. dos Reis1, S.
Ricciardi49, S. Richards46, M. Rihl38, K. Rinnert52, V. Rives Molina36, P.
Robbe7, A.B. Rodrigues1, E. Rodrigues54, P. Rodriguez Perez54, S. Roiser38, V.
Romanovsky35, A. Romero Vidal37, M. Rotondo22, J. Rouvinet39, T. Ruf38, H.
Ruiz36, P. Ruiz Valls65, J.J. Saborido Silva37, N. Sagidova30, P. Sail51, B.
Saitta15,e, V. Salustino Guimaraes2, C. Sanchez Mayordomo65, B. Sanmartin
Sedes37, R. Santacesaria25, C. Santamarina Rios37, E. Santovetti24,l, A.
Sarti18,m, C. Satriano25,n, A. Satta24, D.M. Saunders46, D. Savrina31,32, M.
Schiller42, H. Schindler38, M. Schlupp9, M. Schmelling10, B. Schmidt38, O.
Schneider39, A. Schopper38, M. Schubiger39, M.-H. Schune7, R. Schwemmer38, B.
Sciascia18, A. Sciubba25, A. Semennikov31, I. Sepp53, N. Serra40, J. Serrano6,
L. Sestini22, P. Seyfert11, M. Shapkin35, I. Shapoval16,43,f, Y. Shcheglov30,
T. Shears52, L. Shekhtman34, V. Shevchenko64, A. Shires9, R. Silva Coutinho48,
G. Simi22, M. Sirendi47, N. Skidmore46, I. Skillicorn51, T. Skwarnicki59, N.A.
Smith52, E. Smith55,49, E. Smith53, J. Smith47, M. Smith54, H. Snoek41, M.D.
Sokoloff57, F.J.P. Soler51, F. Soomro39, D. Souza46, B. Souza De Paula2, B.
Spaan9, P. Spradlin51, S. Sridharan38, F. Stagni38, M. Stahl11, S. Stahl11, O.
Steinkamp40, O. Stenyakin35, S. Stevenson55, S. Stoica29, S. Stone59, B.
Storaci40, S. Stracka23, M. Straticiuc29, U. Straumann40, R. Stroili22, V.K.
Subbiah38, L. Sun57, W. Sutcliffe53, K. Swientek27, S. Swientek9, V.
Syropoulos42, M. Szczekowski28, P. Szczypka39,38, T. Szumlak27, S. T’Jampens4,
M. Teklishyn7, G. Tellarini16,f, F. Teubert38, C. Thomas55, E. Thomas38, J.
van Tilburg41, V. Tisserand4, M. Tobin39, J. Todd57, S. Tolk42, L.
Tomassetti16,f, D. Tonelli38, S. Topp-Joergensen55, N. Torr55, E. Tournefier4,
S. Tourneur39, M.T. Tran39, M. Tresch40, A. Trisovic38, A. Tsaregorodtsev6, P.
Tsopelas41, N. Tuning41, M. Ubeda Garcia38, A. Ukleja28, A. Ustyuzhanin64, U.
Uwer11, C. Vacca15, V. Vagnoni14, G. Valenti14, A. Vallier7, R. Vazquez
Gomez18, P. Vazquez Regueiro37, C. Vázquez Sierra37, S. Vecchi16, J.J.
Velthuis46, M. Veltri17,h, G. Veneziano39, M. Vesterinen11, B. Viaud7, D.
Vieira2, M. Vieites Diaz37, X. Vilasis-Cardona36,p, A. Vollhardt40, D.
Volyanskyy10, D. Voong46, A. Vorobyev30, V. Vorobyev34, C. Voß63, J.A. de
Vries41, R. Waldi63, C. Wallace48, R. Wallace12, J. Walsh23, S. Wandernoth11,
J. Wang59, D.R. Ward47, N.K. Watson45, D. Websdale53, M. Whitehead48, J.
Wicht38, D. Wiedner11, G. Wilkinson55,38, M.P. Williams45, M. Williams56, H.W.
Wilschut66, F.F. Wilson49, J. Wimberley58, J. Wishahi9, W. Wislicki28, M.
Witek26, G. Wormser7, S.A. Wotton47, S. Wright47, K. Wyllie38, Y. Xie61, Z.
Xing59, Z. Xu39, Z. Yang3, X. Yuan3, O. Yushchenko35, M. Zangoli14, M.
Zavertyaev10,b, L. Zhang59, W.C. Zhang12, Y. Zhang3, A. Zhelezov11, A.
Zhokhov31, L. Zhong3.

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
10Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
12School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy
14Sezione INFN di Bologna, Bologna, Italy
15Sezione INFN di Cagliari, Cagliari, Italy
16Sezione INFN di Ferrara, Ferrara, Italy
17Sezione INFN di Firenze, Firenze, Italy
18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
19Sezione INFN di Genova, Genova, Italy
20Sezione INFN di Milano Bicocca, Milano, Italy
21Sezione INFN di Milano, Milano, Italy
22Sezione INFN di Padova, Padova, Italy
23Sezione INFN di Pisa, Pisa, Italy
24Sezione INFN di Roma Tor Vergata, Roma, Italy
25Sezione INFN di Roma La Sapienza, Roma, Italy
26Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
27AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
28National Center for Nuclear Research (NCBJ), Warsaw, Poland
29Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
30Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
31Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
32Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
33Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
34Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
35Institute for High Energy Physics (IHEP), Protvino, Russia
36Universitat de Barcelona, Barcelona, Spain
37Universidad de Santiago de Compostela, Santiago de Compostela, Spain
38European Organization for Nuclear Research (CERN), Geneva, Switzerland
39Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
40Physik-Institut, Universität Zürich, Zürich, Switzerland
41Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
42Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
43NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
44Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
45University of Birmingham, Birmingham, United Kingdom
46H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
47Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
48Department of Physics, University of Warwick, Coventry, United Kingdom
49STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
50School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
51School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
52Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
53Imperial College London, London, United Kingdom
54School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
55Department of Physics, University of Oxford, Oxford, United Kingdom
56Massachusetts Institute of Technology, Cambridge, MA, United States
57University of Cincinnati, Cincinnati, OH, United States
58University of Maryland, College Park, MD, United States
59Syracuse University, Syracuse, NY, United States
60Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
61Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
62Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
63Institut für Physik, Universität Rostock, Rostock, Germany, associated to 11
64National Research Centre Kurchatov Institute, Moscow, Russia, associated to
31
65Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC,
Valencia, Spain, associated to 36
66Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 41
67Celal Bayar University, Manisa, Turkey, associated to 38

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
cUniversità di Bari, Bari, Italy
dUniversità di Bologna, Bologna, Italy
eUniversità di Cagliari, Cagliari, Italy
fUniversità di Ferrara, Ferrara, Italy
gUniversità di Firenze, Firenze, Italy
hUniversità di Urbino, Urbino, Italy
iUniversità di Modena e Reggio Emilia, Modena, Italy
jUniversità di Genova, Genova, Italy
kUniversità di Milano Bicocca, Milano, Italy
lUniversità di Roma Tor Vergata, Roma, Italy
mUniversità di Roma La Sapienza, Roma, Italy
nUniversità della Basilicata, Potenza, Italy
oAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
pLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
qHanoi University of Science, Hanoi, Viet Nam
rUniversità di Padova, Padova, Italy
sUniversità di Pisa, Pisa, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità degli Studi di Milano, Milano, Italy
vPolitecnico di Milano, Milano, Italy