# AVASpeech-SMAD: A Strongly Labelled Speech and Music Activity Detection
Dataset with Label Co-Occurrence

###### Abstract

We propose a dataset, AVASpeech-SMAD, to assist speech and music activity
detection research. With frame-level music labels, the proposed dataset
extends the existing AVASpeech dataset, which originally consists of $45$
hours of audio and speech activity labels. To the best of our knowledge, the
proposed AVASpeech-SMAD is the first open-source dataset that features strong
_polyphonic_ labels for both music and speech. The dataset was manually
annotated and verified via an iterative cross-checking process. A simple
automatic examination was also implemented to further improve the quality of
the labels. Evaluation results from two state-of-the-art SMAD systems are also
provided as a benchmark for future reference.

##  1 Introduction

Speech and music activity detection (SMAD) is a long-studied problem and has
been included in the Music Information Retrieval Evaluation eXchange (MIREX)
competition for several years. Like other Music Information Retrieval (MIR)
tasks, the most recent improvements to SMAD rely on data-driven approaches [1,
2, 3, 4, 5, 6]. However, due to copyright issues, many of these systems were
trained on private datasets which impeded the reproducibility of the results
(e.g., the radio datasets used in [2] and [1]). Although several publicly
available datasets have been proposed for training or evaluation of SMAD
systems, as shown in Table 2, they suffer from several drawbacks. GTZAN [7],
MUSAN [8], SSMSC [9] and Muspeak [10] only have non-overlapping speech or
music segments. OpenBMAT [11] and ORF TV [12] only support music labels, while
the original AVASpeech dataset [13] only has speech labels. In the real-world
where speech and music co-occur regularly, these datasets might not be
suitable training sources.

To solve the data limitation problem, we proposed a supplementary dataset,
AVASpeech-SMAD. The dataset is the extension of the AVASpeech dataset proposed
by Chaudhuri et al. [13]. The original AVASpeech dataset only contains speech
activities and we extended it by manually labelling the music activities. We
expect our proposed dataset to be used for training or evaluation of future
SMAD systems. The dataset is open-sourced on the Github repository:
https://github.com/biboamy/AVASpeech_Music_Labels

| Avg (%) | Min (%) | Max (%)
---|---|---|---
Speech | $52.48$ | $14.40$ | $87.02$
Music | $43.40$ | $00.29$ | $100.00$
Both speech and music | $20.73$ | $00.00$ | $77.19$
Table 1: Minimum, maximum, and average percentages of regions with speech only, with music only, and with both speech and music for each audio sample. Dataset | Music Labels | Speech Labels | Overlap | # instances | Duration (hrs)
---|---|---|---|---|---
GTZAN Speech and Music [7] | ✓ | ✓ | No | $128$ | 1.1
MUSAN [8] | ✓ | ✓ | No | $2016$ | 109
Scheirer & Slaney Music Speech (SSMSC) [9] | ✓ | ✓ | No | $245$ | 1
Muspeak [10] | ✓ | ✓ | No | $214$ | 5
OpenBMAT [11] | ✓ | ✗ | Yes | $1647$ | 27.5
ORF TV [12] | ✓ | ✗ | Yes | $13$ | 9
AVASpeech-SMAD (Proposed) | ✓ | ✓ | Yes | $160$ | 45
Table 2: Metadata of the existing datasets compared to our proposed AVASpeech-
SMAD dataset.

##  2 Dataset

The statistics of the dataset are shown in Table 2. Compared to other publicly
available datasets, ours is the only one containing overlapping speech and
music frame labels. The dataset includes a variety of content, languages,
genres and production quality. The audio data, labels, and annotation process
are discussed in the following sections.

###  2.1 Audio & Labels

The original dataset contains $160$ excerpts of $15$-minute clips taken from
YouTube videos with a total duration of $45\text{\,}\mathrm{h}$. Each audio
file is stereo and was sampled at $22\,050\text{\,}\mathrm{Hz}$ with
$16\text{\,}\mathrm{b}\mathrm{i}\mathrm{t}\mathrm{s}$ per sample. Due to
copyright issues, we could not distribute the audio files from this dataset.
Instead, we include the scripts for downloading and preprocessing the audio
files in our GitHub repository.

The speech labels were derived as-is from the original AVASpeech while the new
music labels were manually annotated. The statistics of the labels are shown
in Table 1. The dataset covers a variety of cases. Some samples barely have
any music while some contain mostly music. Some of them do not have any region
with overlapping music and speech, while some have over
$70\text{\,}\mathrm{\char 37\relax}$ of the regions containing both music and
speech. The detailed statistics of each clip can be found in our GitHub
repository.

Figure 1: Overview of the annotation process.

###  2.2 Annotation Process

The annotation process of the proposed dataset is shown in Fig. 1. The
annotation process has four steps, namely music detection, first manual
annotation check, cross-validate and second manual annotation check. Steps
involving human annotators are highlighted in orange. Seven MIR students and
researchers, all of whom are also musicians of varying experience levels, have
volunteered as annotators. An internal algorithm is first used to pseudo-label
the music regions. The annotators are then asked to manually annotate the
regions with music activity, with the pseudo labels acting as a rough guide.
Each annotators were assigned between $12$ to $24$ audio clips to annotate
active music regions. Sonic Visualizer111https://www.sonicvisualiser.org, last
accessed 04/30/2021 was used to mark the active regions and all annotators
used headphones during the annotation process. To ensure the consistency of
the labels and avoid ambiguity, the guideline for determining music versus
speech is listed in GitHub repository.

After the annotations are completed, all the labels were cross-validated with
the speech labels provided by original AVASpeech dataset. Since the original
labels contain “Speech with music” and “Clean speech” classes, we can expect
that the former contains music while the latter do not contains music. Any
discrepancies between our labels and the original labels were algorithmically
detected: the region that was labeled as music in the original labels but not
in our labels, and the region that was labeled no music in the original labels
but labeled as music in our labels. If the discrepancies are less than
$3\text{\,}\mathrm{s}$, we automatically modify the labels based on the
original labels. However, if the discrepancies are greater than three seconds,
we conducted a manual review of the regions. Each region is randomly assigned
to additional two annotators and majority vote is considered to determine the
final labels of the regions.

| Music | Speech
---|---|---
Algo. | F1 | Precision | Recall | F1 | Precision | Recall
[1] | $80.2$ | $69.8$ | $94.3$ | $77.6$ | $82.7$ | $73.1$
[5] | $62.2$ | $85.7$ | $48.8$ | $79.1$ | $83.1$ | $75.4$
Table 3: The segment-level evaluation (%) on our AVASpeech-SMAD dataset by
using two SOTA systems.

##  3 Benchmark

We choose two existing SOTA systems to evaluate on our proposed dataset. First
is the CRNN-based detector proposed by [1]. The method is trained on the
combination of synthetic data and radio broadcast. The second system is the
InaSpeechSegmentor proposed by [5]. The segmentor has a CNN architecture and
can split audio into homogeneous music, speech and noise region. The sed_eval
toolbox is used to perform segment-level evaluation as used in the MIREX 2018
competition222https://www.music-
ir.org/mirex/wiki/2018:Music_and/or_Speech_Detection, last accessed
04/30/2021. The result is shown in Table 3 for future reference.

##  4 Conclusion

In this work, we proposed a supplementary dataset for SMAD. The dataset not
only contains overlapping speech and music frame labels, but also includes a
variety of content. Based on our benchmark experiments, one of the SOTA
systems achieved F1-scores (80% and 77 % for music and speech, respectively)
that are slightly lower than the reported 85% for both music and speech on
MIREX test sets in [1]. This result suggests that our proposed dataset is able
to present new challenges to the model and potentially complement the existing
datasets (e.g., MIREX test sets) with diverse content and frame-level labels.
We expect this dataset to serve as a new resource and reference for future
SMAD research.

##  5 Acknowledgement

K. N. Watcharasupat and J. Lee acknowledge the support from the CN Yang
Scholars Programme, Nanyang Technological University, Singapore. We also
gratefully acknowledge Professor Alexander Lerch and Music Informatics Group
supported this research by providing a Titan X GPU for computing the
experiment.

## References

  * [1] S. Venkatesh, D. Moffat, and E. R. Miranda, “Investigating the effects of training set synthesis for audio segmentation of radio broadcast,” _Electronics_ , vol. 10, no. 7, p. 827, 2021.
  * [2] Q. Lemaire and A. Holzapfel, “Temporal convolutional networks for speech and music detection in radio broadcast,” in _Proceedings of the 20th International Society for Music Information Retrieval Conference_ , 2019, pp. 229–236.
  * [3] D. de Benito-Gorron, A. Lozano-Diez, D. T. Toledano, and J. Gonzalez-Rodriguez, “Exploring convolutional, recurrent, and hybrid deep neural networks for speech and music detection in a large audio dataset,” _Journal on Audio, Speech, and Music Processing_ , vol. 2019, no. 1, pp. 1–18, 2019.
  * [4] B.-Y. Jang, W.-H. Heo, J.-H. Kim, and O.-W. Kwon, “Music detection from broadcast contents using convolutional neural networks with a mel-scale kernel,” _Journal on Audio, Speech, and Music Processing_ , vol. 2019, no. 1, pp. 1–12, 2019.
  * [5] D. Doukhan, E. Lechapt, M. Evrard, and J. Carrive, “INA’s MIREX 2018 music and speech detection system,” in _14th Music Information Retrieval Evaluation eXchange_ , 2018.
  * [6] M. Papakostas and T. Giannakopoulos, “Speech-music discrimination using deep visual feature extractors,” _Expert Systems with Applications_ , vol. 114, pp. 334–344, 2018.
  * [7] G. Tzanetakis and P. Cook, “Marsyas: A framework for audio analysis,” _Organised Sound_ , vol. 4, no. 3, pp. 169–175, 2000.
  * [8] D. Snyder, G. Chen, and D. Povey, “MUSAN: A music, speech, and noise corpus,” _arXiv preprint arXiv:1510.08484_ , 2015.
  * [9] E. Scheirer and M. Slaney, “Construction and evaluation of a robust multifeature speech/music discriminator,” vol. 2, 1997, pp. 1331–1334.
  * [10] D. Wolff, T. Weyde, E. Benetos, and D. Tidhar, “MIREX muspeak sample dataset,” http://mirg.city.ac.uk/datasets/muspeak/, 2015, accessed: 2020-09-30.
  * [11] B. Meléndez-Catalán, E. Molina, and E. Gómez, “Open broadcast media audio from tv: A dataset of tv broadcast audio with relative music loudness annotations,” _Transactions of the International Society for Music Information Retrieval_ , vol. 2, no. 1, 2019.
  * [12] K. Seyerlehner, T. Pohle, M. Schedl, and G. Widmer, “Automatic music detection in television productions,” in _Proceedings of of the 10th International Conference on Digital Audio Effects (DAFx)_ , 2007.
  * [13] S. Chaudhuri, J. Roth, D. P. Ellis, A. Gallagher, L. Kaver, R. Marvin, C. Pantofaru, N. Reale, L. G. Reid, K. Wilson _et al._ , “AVA-speech: A densely labeled dataset of speech activity in movies,” in _Proceedings of the 19th Annual Conference of the International Speech Communication Association_ , 2018.


# A Simple Setup for the Determination of the Cosmic Muon Magnetic Moment

Damir Bosnar<EMAIL_ADDRESS>Mihael Makek  Department of Physics, Faculty of
Science, University of Zagreb, Croatia  Zoran Matić  Atir d.o.o., Zagreb,
Croatia

###### Abstract

We present a simple setup for the measurement of the magnetic moment of cosmic
muons convenient for a student laboratory experiment. A significant
simplification is made in the detector system compared to previous experiments
of this kind, yet it retains all the necessary functionality of the system.
This simplification additionally allows for the use of low-cost custom-made
electronics for data readout and storage. These improvements considerably
reduce the cost and provide a more accessible setup for a student laboratory
experiment.

##  I Introduction

Measurements of the properties of cosmic muons provide excellent opportunities
for educational experiments in elementary particle physics. A classic and very
popular example is the muon lifetime measurement, an experiment that has been
conducted in numerous variations using standard nuclear physics equipment
(see, for example, a recent review given by Riggi _et al._riggi ) and also
with more accessible low-cost electronics. coan ; bosnar  More complex
measurements of the muon mass have also more recently been performed. mass1 ;
mass2

Conceptually and instrumentally much more demanding is the measurement of the
muon magnetic moment. Being a point-like charged lepton that carries a unit
electrical charge, either positive or negative, and with a spin of 1/2 and a
mass of about 207 masses of the electron, the muon possesses a magnetic
moment. PDG  One of the most effective and successful measurements of the
magnetic moment of cosmic muons as an educational experiment using standard
nuclear physics equipment was performed by C. Amsler. amsler  This measurement
exploits the non-conservation of parity in the production and decay chain of
muons, first observed in the experiment of Garwin _et al._ , garwin  which was
also the incentive for Amsler’s experiment. In particular, as a consequence of
parity violation, there is a net polarization of cosmic muons that have been
stopped in a material at Earth’s surface. By putting this material in a known
magnetic field, the spins of the stopped muons precess in the field. The spins
of the muons are correlated to the direction of the positrons (electrons)
emitted in the muon decays. By measuring the distribution of positrons
(electrons) in a certain direction as a function of time, it is possible to
determine the precession frequency of the muons and from this the magnetic
moment of the muon.

Our measurement is based on the same idea, but the detector system is
simplified to the bare minimum of only one scintillation detector. Instead of
using standard nuclear and particle physics equipment, low-cost electronics is
used for the processing and recording of the signals from the scintillation
detector developed for a simple system for muon lifetime measurement. bosnar

In Sec. II, we briefly describe the origin of cosmic muons and their
properties relevant for this measurement. In Sec. III, we introduce the muon
magnetic moment and elucidate the principle of the measurement. Our
experimental setup and measurements are described in Sec. IV. Section V
presents the analysis of our acquired data and the obtained results, which are
then discussed in Sec. VI.

##  II Cosmic muons: origin, polarization, and decay

By the term _cosmic muons_ we mean muons which are produced in the decays of
pions and kaons originating from the interactions of primary cosmic rays
(mainly protons and light nuclei) with the nuclei in the Earth’s atmosphere;
see, for example, the textbook of D. Perkins.perkins  Cosmic muons from pion
decay are much more common because, in the primary interactions pions (
$\pi^{+}$, $\pi^{0}$, $\pi^{-}$) are created with a much greater probability
than kaons ( $K^{+}$, $K^{0}$, $K^{-}$). While focused on pion decay, the
subsequent discussion is also valid for muons from kaon decay.

Charged pions decay by weak interaction according to:

$\pi^{+}\rightarrow\mu^{+}+\nu_{\mu}\quad\textrm{and}\quad\pi^{-}\rightarrow\mu^{-}+\bar{\nu}_{\mu}.$
(1)

In the pion rest frame, decays are isotropic in the full solid angle of
4$\pi$. However, since created pions have given momenta toward Earth,
determined by the initial directions of primary cosmic rays, most of the
produced muons also have momenta directed toward the Earth. On Earth’s
surface, the mean muon energy is approximately 4 GeV and the total downward-
directed flux of muons with energies higher than 1 GeV/c is approximately 1
cm-2 min-1. Due to the positive charge of the primary cosmic rays, the ratio
of the number of positive-to-negative cosmic muons is about 1.25 in the GeV
range. PDG

In pion decay, there is maximal violation of parity and, in the rest frame of
a positive pion, the produced positive muon is always left-handed (meaning its
spin is in the opposite direction of its momentum). This property is the
consequence of the conservation of the total angular momentum and the fact
that pions have spin zero and neutrinos can only be left-handed. On the other
hand, since antineutrinos can only be right-handed (i.e., their spin is in the
direction of their momentum), negative muons can only be right-handed when
produced in the rest frame of the negative pions; see, for example, the
textbook of D. Griffiths.griffiths

Polarization of the cosmic muons is the property resulting from a preferred
orientation of their spin, see, for example, articles of S. Hayakawa haya  and
S. J. Johnson. john  At ground level it is caused by parity violation in the
processes of pion decay and by the energy spectra of pions from which the
muons are produced. To explain this point, let us consider two extreme cases,
one in which the muon is emitted in the direction of the pion boost ( i.e.,
toward Earth’s surface) in the rest frame of the decaying pion, _forward muon_
, and the other in which the muon is emitted in the opposite direction of the
pion boost (i.e., away from Earth’s surface) in the rest frame of the decaying
pion, _backward muon_.

Figure 1: a) A positive muon emitted in the pion boost direction in the rest
frame of decaying pion. b) A positive muon emitted in the opposite direction
of the pion boost in the rest frame of a decaying pion.

If we consider positive pions, in the forward muon case, the $\mu^{+}$ is
emitted toward Earth and the $\nu_{\mu}$ is emitted in the opposite direction,
as in Fig. 1(a). Thus, forward muons, which are initially left-handed, remain
left-handed when they arrive at Earth’s surface. In the backward muon case,
the momentum of the produced $\mu^{+}$ in the rest frame of the decaying pion
is in the opposite direction of the pion boost, but since it is left-handed,
its spin is in the boost direction, that is, in the direction toward Earth, as
in Fig. 1(b). Positive backward muons that reach Earth’s surface (i.e., the
muons for which the boosts of the decaying pions were sufficiently large to
reverse the initial direction of the backward muons) will be right-handed at
Earth’s surface. Since the number of pions decreases with the pion energy, an
excess number of forward muons will reach Earth’s surface, producing a net
upward polarization of positive muons at Earth’s surface.

The analogous consideration is also valid for negative muons and, keeping in
mind that they are produced as right-handed particles, their net polarization
at Earth’s surface will be downward.

Muon polarization has been measured at Earth’s surface as a function of energy
and zenith angle. For example, for positive muons from the zenith, the
polarization has been determined to be $-0.38\pm 0.04$ and $-0.33\pm 0.04$ for
energies near 3.5 Ge and 1.0 GeV, respectively; the polarization falls off at
lower muon energies. turner  The negative sign indicates that the spin is
antiparallel to the direction of the flight of the positive muons. The
observed polarization of the muons at Earth’s surface indeed proves the parity
violation in the pion decay.

Muons decay via the weak interaction with a mean lifetime of
$\tau=2.1969811\pm 0.0000022\,\mu$s.PDG  Parity violation is also present in
these decay processes, which proceed as follows:

$\mu^{+}\rightarrow
e^{+}+\nu_{e}+\bar{\nu}_{\mu}\quad\textrm{and}\quad\mu^{-}\rightarrow
e^{-}+\bar{\nu}_{e}+\nu_{\mu}.$ (2)

The directions of the emitted positrons (electrons) in these decays are
correlated with the above described net polarization of the muons at Earth’s
surface, producing an asymmetric angular distribution. This fact can be
qualitatively understood if, in the decay of a muon at rest, we consider the
extreme case where the most energetic positron (electron) is emitted. okun  In
this case, both the neutrino and antineutrino must be emitted in the direction
opposite that of the positron (electron), as in Fig. 2. Since neutrinos and
antineutrinos have an opposite handedness, the total angular momentum carried
by them is zero, and a positron (electron) must be emitted with the spin
parallel to that of the decaying muon. To meet this requirement, and since
positrons (electrons) are right-handed (left-handed), their momenta should be
directed in (opposite to) the directions of the muon spin. So, for the decays
of positive muons, positrons are favorably emitted in the direction of the
muon spin, and for the decays of negative muons, electrons are favorably
emitted in the opposite direction of the muon spin.

Figure 2: Decay at the rest of a positive (a) and a negative (b) muon with the
emission of the most energetic positron and electron, respectively.

##  III Muon magnetic moment and principle of measurement

A charged particle with a spin carries a magnetic moment. For the muon, which
is a point-like lepton and has charge $e$, mass $m_{\mu}$, and spin $\vec{s}$,
the magnetic moment is given by

$\vec{\mu}_{\mu}=g_{\mu}\,\mu_{\mu}^{\rm{Bohr}}\,\vec{s}$ (3)

where $g_{\mu}$ is the proportionality factor called the gyromagnetic ratio
and $\mu_{B}$ is the Bohr magneton of the muon given by
$\mu_{\mu}^{\rm{Bohr}}=\frac{e\hbar}{2m_{\mu}}$. The gyromagnetic ratio is
predicted by the Dirac equation to be exactly 2 for leptons, but the
experimentally determined $g_{\mu}$-value differs slightly from this
theoretical expectation, an inconsistency termed the _magnetic moment anomaly_
,PDG  a subject of great interest in particle physics both experimentally
mion-mag-exp  and theoretically. mion-mag-th

If a muon is in an external magnetic field $\vec{B}$, its spin will precess
with the frequency

$\omega=g_{\mu}\,\frac{eB}{2m_{\mu}}.$ (4)

If cosmic muons are stopped in a suitable non-magnetic material that is
immersed in a horizontal magnetic field (with respect to Earth’s surface),
there will be a precession of spins of the stopped muons. Copper is one such
suitable material because it effectively stops cosmic muons due to its
relatively high density and atomic number. Most of the negative muons are
quickly caught by nuclei in the stopping material (the lifetime of negative
muons in copper is 0.163 $\mu$s eck ) and since our apparatus is not sensitive
enough to determine their influence, in the following discussion we restrict
ourselves to the positive muons, which stop in the material and decay as free
particles.

The muon spin precession is determined as follows. We detect positrons from
the decays of stopped muons only in the upward direction. Above, we described
the net polarization of the cosmic muons at Earth’s surface, the precession of
their spins in the magnetic field, and the correlations of the directions of
emitted positrons with muon spins. Based on these facts, there will be an
oscillation in time of the number of detected positrons from the decays about
the usual exponential decay curve. When there is no magnetic field present,
the data from our experiment should follow a simple exponential dependence

$I(t)=I_{0}e^{-\frac{t}{\tau}}+C$ (5)

where $I(t)$ is the number of muon decays in a unit of time at time $t$,
$I_{0}$ is the decay rate at $t=0$, $\tau$ is the muon mean lifetime, and a
constant $C$ due to the background. With an applied magnetic field, with good
accuracy, we expect the above relation to becomeamsler

$I(t)=I_{0}e^{-\frac{t}{\tau}}[1+\alpha\cos(\omega t+\delta)]+C,$ (6)

where $\alpha$ is the experimental asymmetry (that depends on the asymmetry of
the positrons emitted in the muon decays, the polarization of the stopped
muons, and the geometry of the setup), $\omega$ is the muon precession
frequency, and $\delta$ is the angle of initial muon polarization.

By fitting function Eq. (6) to the measured time distribution, which is
obtained by detecting upward emitted positrons from the decays of muons that
are stopped in the material in the horizontal magnetic field, we can determine
the frequency of the muon precession $\omega$, and hence $g_{\mu}$ from Eq.
(4).

##  IV Experimental setup and measurements

We used one scintillation detector for the detection of the incoming cosmic
muons and the same detector for the detection of the positrons from the
decays. The scintillation detector consisted of an NE 102A scintillator plate
of 50 cm $\times$ 50 cm $\times$ 1 cm, coupled to a twisted light guide of 60
cm in length on which a Philips XP5312/SN 3-inch photomultiplier tube was
attached. The scintillator and the light guide were glued with optical cement
and wrapped with thin aluminum foil and with black scotch tape. The PMT was
mounted in an aluminum tube with holders that enabled tight coupling to the
light guide; the coupling was enhanced by optical grease. A box with a custom-
made high-voltage supply with variable output voltage was attached to the
aluminum tube that housed the PMT. The voltage applied in the measurement was
$-1060$ V.

A block of copper measuring 50 cm $\times$ 50 cm $\times$ 2.5 cm was placed
beneath the scintillator plate. The copper block consisted of 40 pieces of 2.5
cm $\times$ 2.5 cm $\times$ 25 cm copper bars. The distance between the middle
of the copper block and the middle of the scintillator plate was 6.3 cm. The
role of the copper block was to stop some of the incoming cosmic muons.

The copper block was positioned centrally inside a rectangular copper coil of
one layer with 355 windings, a length of 60 cm, a width of 57.5 cm and a
height of 7.5 cm, and whose purpose was to produce the necessary magnetic
field. The wire in the coil had a cross section of 1.5 mm2. The copper coil
was mounted on an aluminum frame, which also held the copper bars and the
scintillation detector. During the measurements with the currents, the coil
was cooled by a fan.

The experimental setup is schematically shown in Fig. 3.

Figure 3: Schematic representation of the experimental setup (not to scale,
dimensions are given in the text).

With a current of 5 A through the coil, we obtained a magnetic field of
approximately 3.7 mT at the center of the coil. The field fell to
approximately 3.4 mT at 25 cm from the coil’s center (i.e., at a position
toward the open edges of the coil and the end of the copper target). With a
current of 6 A, the magnetic fields were $\sim$4.3 mT and $\sim$3.9 mT at the
coil’s center and at 25 cm from the coil’s center (towards the open edges of
the coil), respectively. No significant variation was observed in the measured
field (measured approximately every 10 cm) on the lines transverse to the
longitudinal axis of the coil. These measurement were made at at several
distances along the longitudinal axis from the center of the coil.

In the calculation of $g_{\mu}$ from Eq. (4) and for its uncertainty
estimation we used the average of the fields measured in the center of the
coil and at 25 cm from the coil’s center (towards the open edges of the coil)
and the corresponding uncertainties.

Most of the cosmic muons come from above and the scintillation detector
registered the muons that pass through or stop and decay in the copper block
beneath it. The same scintillation detector also registered the positrons that
were emitted in the upward direction in the decays of the stopped muons in the
copper block.

For signal processing and data acquisition, we used custom-made low-cost
electronics developed for the simple setup for the measurement of the cosmic
muon lifetime.bosnar  Negative analog signals from the PMT of the
scintillation detector were input to the fast TTL comparator (Analog Devices
AD8561) with a variable threshold in the range of 0 to $-500$ mV. To secure a
constant width of the output pulse, regardless of the input pulse width, a
Texas Instruments 74121 chip was used. Positive logic signals, produced by the
signals from the scintillation detector above the set threshold, were input to
the 32-bit microcontroller (MikroElektronika PIC32 module, model MINI-32
BOARD). The PIC32 module recorded time stamps of the events with a time
resolution of 12.5 ns, which were then stored on a PC disk. A schematic
representation of the electronics is given in Fig. 4.

Figure 4: Schematic representation of the electronics for signal processing
and data acquisition.

When started, the time span of the measurement by the PIC32 module was
approximately 54 seconds ($2^{32}$ $\times$12.5 ns) and after this time it was
reset automatically to zero, and the measurement continued automatically until
it was stopped by the user. The module was programmed to transfer the recorded
data in a block of 16 events to a computer via serial/USB connection and to
perform simple operational tasks on the data. It counted the total number of
registered events during the measurement and the number of events for which
the time difference was less than 10 $\mu$s, and these numbers were shown on a
display. The last number indicates the number of registered muon decays in the
selected time window, as explained in the following sections.

With this setup we performed one measurement of approximately 5 days without
the magnetic field, one measurement of 20 days with a current of 5 A through
the copper wire, and one measurement of 21 days with a current of 6 A.

##  V Data analysis and results

Extractions of the time distributions of the muon decays were performed in an
identical way as for the muon lifetime measurement. bosnar  We first
calculated the time differences between every pair of subsequently registered
events. By selecting the time differences smaller than some selected time
window, e.g., 10 $\mu$s, we can extract events that, with high probability,
correspond to the decays of the stopped muons. Since the time resolution of
the PIC32 unit is pretty high, 12.5 ns per channel, even with the measurements
of several weeks, the number of events registered in each channel will be
small. To obtain a statistically significant number of counts we selected time
intervals in which we counted the number of muons that decay.

We used time intervals $\Delta T=0.2\,\mu$s and fitted Eqs. (5) or (6) on the
obtained distributions for the measurement without a magnetic field or with a
magnetic field, respectively.

For the measurement without a magnetic field, we obtained 5981 events within
the time window of 10 $\mu$s (a total of 2,942,766 events was registered with
the scintillation detector). The obtained time distribution and fit are shown
in Fig. 5. We obtained a muon mean life of $\tau$ = 2.12 $\pm$ 0.04 $\mu$s.

Figure 5: Measurement without a magnetic field and the fit to Eq. (5).

For the measurements with a magnetic field, within the time window of 10
$\mu$s we obtained 20,936 events (total 10,246,368 registered events), and
22,882 events (total 11,077,886 registered events) with a current of 5 A and 6
A, respectively. The time distributions and fits with the Eq. (6) for these
measurements are shown in Fig. 6.

Figure 6: Measurements with the magnetic fields and fits to Eq. (6), left
current of 5 A and right current of 6 A.

All the fits were performed by using Minuit in the CERN Root software package
v6.20. The fit region was from 0.2 $\mu$s – 8.8 $\mu$s, which corresponds to
approximately four mean muon lifetimes. The constant $C$, which represents the
background in the measurement, was not left as a free parameter in the fit but
was determined from the data at the large values of $t$. For the measurement
of 5 days without the magnetic field, $C$ was approximately 3.5 and for the
measurements with the magnetic field, it was approximately 13 for our binning.

The fitting results for the measurements with the magnetic fields and the
determination of $g_{\mu}$ by using Eq. (4) are presented in Table 1.

Table 1:  The results of the fits on the measurements with the magnetic fields and the determination of $g_{\mu}$. The uncertainties of the fitted parameters are obtained only by the fitting procedure. The uncertainty of $g_{\mu}$ is calculated by the error propagation using Eq. (4) and solved for $g_{\mu}$. B [mT] | (I[A]) |  $\tau$ [$\mu$s] | $\alpha$ |  $\omega$ [MHz] | $\delta$ |  $\chi^{2}$/$ndf$ | $g_{\mu}$
---|---|---|---|---|---|---|---
3.55 $\pm$ 0.15 | (5) | 2.16 $\pm$ 0.02 | 0.05 $\pm$ 0.01 | 3.36 $\pm$ 0.10 | -1.0 $\pm$ 0.3 | 69.01/38 | 2.22 $\pm$ 0.11
4.1 $\pm$ 0.2 | (6) | 2.07 $\pm$ 0.02 | 0.06 $\pm$ 0.01 | 3.76 $\pm$ 0.12 | -0.60 $\pm$ 0.25 | 49.83/38 | 2.12 $\pm$ 0.12

##  VI Summary and Discussion

We have presented a simple setup for the measurement of the muon magnetic
moment suitable for a student laboratory experiment. We exploited the idea of
the very effective experiment presented by C. Amsler, amsler  but we made two
significant modifications and improvements.

First, we reduced the detection system to only one scintillation detector
compared to three scintillation detectors used in a
coincidence/anticoincidence mode in the Amsler experiment. To the best of our
knowledge, there are always several scintillation detectors used in various
realizations of this experiment as a student laboratory exercise. However,
this reduction does not significantly affect the functionality of our system.
As also argued in the discussion of the muon lifetime system based on only one
scintillation detector, bosnar  the main source of the background in our
approach (if there are no other radioactive sources present) is a second
cosmic muon that comes in the selected time window (in our case 10 $\mu$s)
after the first registered muon and which is then wrongly interpreted as a
positron from the muon decay. The rate of these accidentals, which can be
removed by veto in the multiple-detector case, is a decisive factor for the
proper functioning of a measuring system comprised of only one scintillation
detector.

Using the statistics of random events for the case of cosmic muons (see, for
example, A.C. Melissinos _et al._melissinos ) and the rate of all incoming
cosmic muons that pass through our size of scintillator, it can be shown that
the rate of these accidentals in the time window of 10 $\mu$s is indeed not
insignificant. However, the overall efficiency of our scintillation detector
for the settings used in the measurement was about 12 % for the detection of
cosmic muons (assuming that there are in total about 200
muons/m${}^{2}\cdot$s). This detection efficiency level also reduces the rate
of accidentals, resulting in an expected rate of slightly less than 1 per
hour. This estimate is confirmed by the measured total background rate of
around 1.5 per hour, which compares favorably to the average of approximately
45 registered events in the time window of 10 $\mu$s per hour.

We conclude that the rate of muon accidentals is acceptable for the execution
of the measurements with our setup. Their contribution is taken into account
in the off-line analysis by supposing a flat background in the decay spectra.
The apparatus is not sensitive enough to quantify the influence of the decays
of negative muons, which are caught by nuclei, and this limits the accuracy of
the measurements. One of the main sources of the systematic errors also comes
from the inhomogeneity in the magnetic field of approx. 5%.

Second, the maximal simplification in the detector setup enables our other
important improvement, that is, the usage of basic and low-cost electronics
for the signal processing and data acquisition. Compared to the classical
nuclear physics equipment used for such measurements, typically including
discriminators, coincidence units, time-to-amplitude converters, and
appropriate power crates, our electronics system is more than an order of
magnitude lower in cost, and also simpler and more compact, making this
experiment readily accessible as a student laboratory experiment.

###### Acknowledgements.

We would like to thank Ines Mance and Dražen Paunović for their help in the
preparation of the cooper coil used in this measurement. This work was
supported in part by the Project for the Popularization of Science of the
Ministry of Science and Education of Republic of Croatia.

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