Acta Polytechnica


doi:10.14311/AP.2013.53.0760
Acta Polytechnica 53(Supplement):760–763, 2013 © Czech Technical University in Prague, 2013

available online at http://ojs.cvut.cz/ojs/index.php/ap

ANALYSIS OF THE MACRO EXPERIMENT DATA TO COMPARE
PARTICLE ARRIVAL TIMES UNDER GRAN SASSO

Francesco Ronga∗

INFN Laboratori Nazionali di Frascati, Frascati Italy
∗ corresponding author: francesco.ronga@lnf.infn.it

Abstract. The claim of a neutrino velocity different from the speed of the light, made in September
2011 by the Opera experiment, suggested the study of the time delays between TeV underground muons
in the Gran Sasso laboratory using the old data of the MACRO experiment, ended in 2000. This study
can also give hints on new physics in the particle cascade produced by the interaction of a cosmic ray
with the atmosphere.

Keywords: neutrino velocity, new massive particles, tachyons, supersymmetry.

1. Introduction
In September 2011 there was a measurement of the
speed of neutrino faster than the speed of light by
(v−c)/c = 2.48±0.28(stat)±0.30(sys)×10−5 [2]. After
many checks, we know now that this result was due to
hardware problems and the Opera 2012 result is that
the speed of the neutrinos traveling from CERN to the
Gran Sasso is (v −c)/c = −0.7 ± 0.5(stat)+2.5−1.5(sys) ×
10−6 [8]. This result is in agreement with the results
of the other Gran Sasso experiments [6].
However the interest in this claim suggested the

possibility to compare neutrino and muon velocity
in a cosmic ray cascade [12]. The interaction of a
primary cosmic ray with the atmosphere produces a
cascade with many kind of particles, and in particular
neutrinos and muons. Muon neutrinos and muons
are produced mainly via the decay of charged pions
and kaons produced in the primary cosmic ray inter-
actions. Above about 10 TeV they can also come from
prompt decays of charmed hadrons. This component
has not yet been observed. In a deep underground
detector only muon and neutrino are detected. If the
neutrino velocity is different from c the neutrinos in
this cascade, should arrive with times different from
the times of the muons from the same parent decay,
or from another decay, with a time delay that should
change according to the neutrino path length which
depends on its zenith angle θ. In underground detec-
tors muon neutrinos are detected looking for induced
muons produced by neutrino charged current interac-
tions in the rock, or in the ice around or inside the
instrumented region. Hence, a time spread should
be observed between the muons produced directly by
the pion or kaon decay and the muons produced by
neutrino interactions.
The path length from the meson decay point is a

few tens of kilometers for vertical neutrinos and up to
∼ 300 km for near horizontal neutrinos. Assuming the
original time difference observed in OPERA, nearly
horizontal neutrinos should arrive up to 28 ns before

the other secondaries. In [10] a table of average pro-
duction heights neutrinos in the atmosphere has been
reported. The typical production height for neutrinos
of energy above 20 GeV can be 17.6 km at the vertical,
94.9 km at cos θ = 0.25 and 335.7 km at cos θ = 0.05,
which would correspond to 1.4, 78 and 27.6 ns.

There are already limits of tachions or anomalous
delayed particles in cosmic rays. The limits are ob-
tained searching for example signals before or after
the main front of the electromagnetic shower. But
of searches of this kind stopped some time ago and
the last particle data book review of those data is
the review of 1994 [11]. The limits obtained are of
small interest in the framework of the OPERA re-
sult. However, if neutrinos were tachions, it is likely
that some other kind of tachions could exist and this
search in very high energy cosmic rays could have a
new interest.

It is important to note that the Gran Sasso moun-
tain minimum depth ∼ 2700 g/cm2 corresponds to a
minimum muon energy of 1.4 TeV. It easy to compute
that, requiring a minimum threshold of 50 MeV in the
detector, the time difference between two muons un-
derground should be � 0.2 ns. Therefore anomalous
time differences should be a signal of “new physics”,
for example a signal of supersymmetric massive parti-
cles produced in a cosmic ray cascade. For example,
let us assume a hypothetical hadron of mass 100 GeV,
produced by an interaction of a proton with center of
mass energy 7 TeV (the LHC energy). If this hypothet-
ical hadron interacts or decays after 10 km producing
at the end muons, the delay between the underground
muon from the massive particle and the muon pro-
duced in the primary vertex is of the order of 13 ns.
LHC experiments have put limits for new hadron-like
massive particles [1, 7], but it is important to remem-
ber that the cosmic ray energy could be larger than
the LHC energy. Under Gran Sasso the fraction of
multiple muons produced by cosmic rays with center
of mass energy ≥ 7 TeV is estimated of the order of
10−3 in MACRO, corresponding to several thousand

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vol. 53 supplement/2013 Analysis of the MACRO Experiment Data

Figure 1. Event with six parallel muons in 3 MACRO
“supermodules”. At the top there is the full MACRO
display, on the bottom the zoom of the 3 supermodules
interested by the event. The 12 steamer tube hori-
zontal planes are shown as horizontal lines, the back
points are the streamer tubes fired; the scintillator
boxes fired are shown as rectangles.

multiple muon events in the MACRO data set. One
should also consider the possibility that new mas-
sive relic particles are directly in the primary cosmic
radiations.

The MACRO experiment has made several searches
for possible anomalies of the time differences between
muons [3]. The search was made mainly to study time
differences of the order of a few ms or more, but this
paper contains also a study of time differences at the
ns-level. The statistics was limited to 35 832 tracks
in events with two or more tracks. In 1992 noone
was thinking about tachionic neutrinos, and therefore
there was no estimate of the number of tracks due
to down-going neutrino together with the primary
muons. In [13], this study was extended to about
140 000 tracks of multi muon events, corresponding to
about 4 % of the total MACRO statistics. The time
distribution was in agreement with the predictions.
In this paper, I present an analysis of the full

MACRO statistics. This was not an easy job.
The main reason is that MACRO ended in 2000,
and most of the analysis software was designed for
VAX/AlphaVAX computers and data formats around
1990 (a geological era for computers!). A lot of time
was needed to convert programs and to find data files,
sometimes stored on data tape cassette of old formats,
obsolete and not supported by modern computers.

2. The MACRO experiment and
the timing system

The MACRO experiment [5] was located in Hall B of
the Gran Sasso underground laboratory. The modu-
larity allowed data-taking also with partial configura-
tions of the apparatus, starting from March 1989. The
full detector was operative in the period April 1994–
December 2000.
MACRO was a large rectangular box (76.6 × 12 ×

9.3 m3) divided longitudinally in 6 supermodules and
vertically in a lower and an upper part (called attico).

The active elements were liquid scintillator counters
for time measurement and streamer tubes for tracking,
with 27° stereo strip readouts. The lower half of the
detector was filled with trays of crushed rock absorber
alternating with streamer tube planes, while the attico
was hollow and contained the electronics racks and
work areas. The rock absorber sets a minimum energy
threshold for vertical muons of 1 GeV.
The tracking system was designed to reconstruct

the particle trajectory in different views (x–z for hori-
zontal streamer tubes, d–z for horizontal strips, y–z
for vertical streamer tubes combined with central hits).
To perform this analysis the standard MACRO track-
ing software was improved to have greater efficiency
for near horizontal tracks.

The intrinsic angular resolution for muons typically
ranges from 0.2° to 1° depending on track length.
This resolution is lower than the angular spread due
to multiple scattering of downward-going muons in
the rock.

The scintillator system consisted of horizontal and
vertical layers of counters filled with a mixture of
mineral oil (96.4 %), pseudocumene (3.6 %) and wave-
length shifters (2.88 g/l). The counters had an active
volume of 11.2×0.73×0.19 m3 in the horizontal planes
and 11.1 × 0.22 × 0.46 m3 in the vertical planes.

The total charge and the time of occurrence of the
signals were measured at the two ends of each counter
with two independent systems, the Energy Response
Processor (ERP) and the Pulse Height Recorder and
Synchronous Encoder (PHRASE). The analysis de-
scribed in this paper is based on ERP data. The time
and longitudinal position resolution for a single muon
in a counter were about 0.6 ns and 12 cm, respectively.
The photomultiplier signal is split into a direct out-
put and one attenuated by a factor of 10, in order
to be on-scale also for very large pulses. Two differ-
ent thresholds are used for the timing of these two
outputs. The redundancy of the time measurement
helps to eliminate spurious effects. Each MACRO
supermodule is connected to a dedicated independent
ERP system. The timing between the ERP systems
is insured by standard CAMAC TDC. Due to the ran-
dom noise the possibility to have wrong times in the
inter ERP TDCs is quite high, and this is the main
source of non-Gaussian tails in the time distributions
for events interesting different supermodules.

3. Time differences in the
MACRO muon bundles

Thanks to its large area and fine tracking granularity
the MACRO detector was a proper tool for the study
of multiple parallel muons. Many papers were pub-
lished by MACRO on this topic to study the muon
multiplicity, the distance between muons and the im-
pact on cosmic ray composition from the multiple
muon measurement. The last MACRO paper on this
argument is in [4]. One important number to consider
is that the average distance between muon pairs is

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Francesco Ronga Acta Polytechnica

Figure 2. Difference between track time and average
time for multiple parallel muons with 2 or 3 tracks
as function of cos(θ). The dot size is proportional
to the logarithm of the bin content. If the original
OPERA claim had been correct, a few tracks would
be expected inside the dashed region (see text).

〈r〉 ∼ 9.4 m. For vertical tracks and average depth
3800 g/cm2. The value of 〈r〉 changes slowly with
depth and zenith angle. Figure 1 shows a typical
multiple muon event. From this picture is easy to
understand one of the problems of this analysis: the
large dimension of the scintillator boxes compared to
the average value of 〈r〉. The probability of having
more than one track intercepting the same counters is
high. In this case, the time could be wrong. This is
because the analysis software could fail to compute the
light propagation time from the intercept of the track
to the photomultipliers. This is the second source of
non-Gaussian tails in the time distributions (the first
is the timing between different supermodules).
For each track the analysis program computes the

β = v/c and the “track time” (average between the
scintillator times along the track). To remove noise,
the analysis program uses only the scintillators in
which the position along the scintillator computed by
the time differences between the PM at the ends is in
agreement with the position given from the streamer
chambers. Therefore the analysis program computes
the differences between the “track times” and the
average time of all the tracks in the bundle. This
is done including a correction due to the incidence
angle. A 5° angular cut is applied to require parallel
tracks. To have a valid track time a single scintillator
is sufficient, but in the case of events between different
supermodules there is the requirement that at least
one track between two different supermodules has two
scintillators and that the beta value is consistent with
one. This is to reduce the noise due to the inter ERP
TDCs.

Figure 3. Difference between track time and average
time for multiple muons with 2 or 3 tracks (continuos
line) compared with a “simulation” using the data
(dashed line).

The calculation of the expected number of events,
if the original OPERA claim was correct, is done
considering the probability to have a neutrino and
a muon from the same decay, computed in [12] and
the probability to have a neutrino and a muon from
different decays, computed using the approximated
Elbert formulas [9]. The detector and analysis efficien-
cies were evaluated using the standard multiple muon
MACRO simulation software, with a modification to
allow a delay in one of the muons. This calculation
gives 2 delayed tracks with time delay |δt| ≥ 10 ns
expected in MACRO the data set.
In the case of events with a muon from a neutrino

interaction there is unlikely more than one muon di-
rectly from the hadronic cascade, so the analysis is
limited to events with less than 3 tracks (one track
could be a spurious track). The results are in Fig. 2.
Figure 2 also shows the times expected if the original
Opera result would have been correct. Considering
the region with cos(θ) ≤ 0.2 and |δt| ≥ 10 ns there is
one event with two tracks with a time track – average
time ∼ 22 ns (the dot of Fig. 2 near the dashed arrow).
However this time is outside the Opera region. In the
Opera region there are no tracks. This result should
be compared with the 2 tracks expected.
To understand if the distribution tails in the full

angular region are real or due to detector effects I
made a comparison, computing for each track with two
scintillator counters the time difference between times
(instead of the average). This is shown in Fig. 3 as a
dashed line. This plot shows that there is agreement
between the two distributions and therefore we can
conclude that most of the tails are indeed due to effect
of the detector.
Finally Fig. 4 shows the time difference, including

all the multiple muon multiplicity. Since a possible sig-
nal due to massive particles or exotic relics is expected
at high path length, I have divided the angular region

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vol. 53 supplement/2013 Analysis of the MACRO Experiment Data

Figure 4. Difference between track time and aver-
age time for multiple muons with all multiplicities:
continuous line cos(θ) ≥ 0.5, dashed line cos(θ) ≤ 0.5
(histograms normalized to 1).

in two parts: cos(θ) ≥ 0.5, and cos(θ) ≤ 0.5. The two
distributions are comparable. But the cos(θ) ≤ 0.5
distribution has two tracks with time differences
≥ 15 ns, compared with 0.4 tracks expected from the
cos(θ) ≥ 0.5 distribution (Poisson probability 0.06).

4. Conclusions
This work ended some time after the solution of the
superluminal neutrino puzzle, but I think that has
been very useful to remember that cosmic rays are
still important tools in particle physics. For the super-
luminal neutrino, 2 tracks were expected but 0 were
found. Considering the different mean-lives of the
pion and the kaon, an “exotic” limit can be derived
from the horizontal tracks of Fig. 2 on the equality
of the pion and kaon speed in a cascade produced by
a primary with E ≥ 3 TeV: |βπ − βk| � 1.5 × 10−4.
This result at the moment is of very low interest but
the superluminal neutrino saga has shown that noth-
ing can be given as guaranteed. More investigations

are necessary on the delayed tracks in events with
multiplicity bigger than 3 and on massive particles in
cosmic rays.
This work has shown once again the importance

of saving past experiment data for further analysis.
I must thank the MACRO collaboration which built
and run the detector and many MACRO people who
helped me to recover data and programs and particu-
larly Nazareno Taborgna of the Gran Sasso laboratory,
who was able to save a working alphaVAX with sev-
eral MACRO original disks. Particular thanks go to
Teresa Montaruli for useful and deep discussions.

References
[1] Aad G. et al. [ATLAS Collaboration], Eur. Phys. J. C

72, 1965 (2012)
[2] Adam T. et al. [OPERA Collaboration],
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[3] Ahlen S. P.et al. [MACRO Collaboration], Nucl. Phys.
B 370, 432 (1992)

[4] Ambrosio M. et al. [MACRO Collaboration], Phys.
Rev. D 60, 032001 (1999)

[5] Ambrosio M. et al. [MACRO Collaboration], Nucl.
Instrum. Meth. A 486, 663 (2002)

[6] Bertolucci S., Kyoto Neutrino 2012 conference
[7] Chatrchyan S.et al. [CMS Collaboration], Phys. Lett.
B 713, 408 (2012)

[8] Dracos M. (OPERA Collaboration), Kyoto Neutrino
2012 conference

[9] Gaisser T.K., Cosmic rays and particle physics,
Cambridge, UK: Univ. Pr. (1990)

[10] Gaisser T. K. and Stanev T., Phys. Rev. D 57
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[11] Montanet L. et al. pag 1811, Phys. Rev. D50,
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[12] Montaruli T. and Ronga F., arXiv:1109.6238 [hep-ex]
[13] Scapparone E. Ph. Thesis Bologna Univ. 1995

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	Acta Polytechnica 53(Supplement):760–763, 2013
	1 Introduction
	2 The MACRO experiment and the timing system
	3 Time differences in the MACRO muon bundles
	4 Conclusions
	References