Observation of seasonal variation of atmospheric multiple-muon events in the MINOS Near and Far Detectors
P. Adamson, I. Anghel, A. Aurisano, G. Barr, M. Bishai, A. Blake, G. J. Bock, D. Bogert, S. V. Cao, C. M. Castromonte, S. Childress, J. A. B. Coelho, L. Corwin, . D. Cronin-Hennessy, J. K. de Jong, A. V. Devan, N. E. Devenish, M. V. Diwan, C. O. Escobar, J. J. Evans, E. Falk, G. J. Feldman, M. V. Frohne, H. R. Gallagher, R. A. Gomes, M. C. Goodman, P. Gouffon, N. Graf, R. Gran, K. Grzelak, A. Habig, S. R. Hahn, J. Hartnell, R. Hatcher, A. Holin, J. Huang, J. Hylen, G. M. Irwin, Z. Isvan, C. James, D. Jensen, T. Kafka, S. M. S. Kasahara, G. Koizumi, M. Kordosky, A. Kreymer, K. Lang, J. Ling, P. J. Litchfield, P. Lucas, W. A. Mann, M. L. Marshak, N. Mayer, C. McGivern, M. M. Medeiros, R. Mehdiyev, J. R. Meier, M. D. Messier, W. H. Miller, S. R. Mishra, S. Moed Sher, C. D. Moore, L. Mualem, J. Musser, D. Naples, J. K. Nelson, H. B. Newman, R. J. Nichol, J. A. Nowak, J. O.Connor, M. Orchanian, S. Osprey, R. B. Pahlka, J. Paley, R. B. Patterson, G. Pawloski, A. Perch, S. Phan-Budd, R. K. Plunkett, N. Poonthottathil, X. Qiu, A. Radovic, B. Rebel, C. Rosenfeld, H. A. Rubin, M. C. Sanchez, J. Schneps, A. Schreckenberger, P. Schreiner, R. Sharma, A. Sousa, N. Tagg, R. L. Talaga, J. Thomas, M. A. Thomson, X. Tian, A. Timmons, S. C. Tognini, R. Toner, D. Torretta, et al. (10 additional authors not shown)
aa r X i v : . [ h e p - e x ] M a r FERMILAB-PUB-15-102-ND
Observation of seasonal variation of atmospheric multiple-muon events in the MINOSNear and Far Detectors
P. Adamson, I. Anghel,
14, 1
A. Aurisano, G. Barr, M. Bishai, A. Blake, G. J. Bock, D. Bogert, S. V. Cao, C. M. Castromonte, S. Childress, J. A. B. Coelho, L. Corwin, ∗ D. Cronin-Hennessy, J. K. de Jong, A. V. Devan, N. E. Devenish, M. V. Diwan, C. O. Escobar, J. J. Evans, E. Falk, G. J. Feldman, M. V. Frohne, H. R. Gallagher, R. A. Gomes, M. C. Goodman, P. Gouffon, N. Graf, R. Gran, K. Grzelak, A. Habig, S. R. Hahn, J. Hartnell, R. Hatcher, A. Holin, J. Huang, J. Hylen, G. M. Irwin, Z. Isvan,
2, 21
C. James, D. Jensen, T. Kafka, S. M. S. Kasahara, G. Koizumi, M. Kordosky, A. Kreymer, K. Lang, J. Ling, P. J. Litchfield,
17, 22
P. Lucas, W. A. Mann, M. L. Marshak, N. Mayer,
29, 13
C. McGivern, M. M. Medeiros, R. Mehdiyev, J. R. Meier, M. D. Messier, W. H. Miller, S. R. Mishra, S. Moed Sher, C. D. Moore, L. Mualem, J. Musser, D. Naples, J. K. Nelson, H. B. Newman, R. J. Nichol, J. A. Nowak, J. O’Connor, M. Orchanian, S. Osprey, R. B. Pahlka, J. Paley, R. B. Patterson, G. Pawloski,
A. Perch, S. Phan-Budd, R. K. Plunkett, N. Poonthottathil, X. Qiu, A. Radovic, B. Rebel, C. Rosenfeld, H. A. Rubin, M. C. Sanchez,
14, 1
J. Schneps, A. Schreckenberger,
P. Schreiner, R. Sharma, A. Sousa,
6, 9
N. Tagg, R. L. Talaga, J. Thomas, M. A. Thomson, X. Tian, A. Timmons, S. C. Tognini, R. Toner,
9, 4
D. Torretta, J. Urheim, P. Vahle, B. Viren, A. Weber,
20, 22
R. C. Webb, C. White, L. Whitehead,
11, 2
L. H. Whitehead, S. G. Wojcicki, and R. Zwaska (The MINOS Collaboration) Argonne National Laboratory, Argonne, Illinois 60439, USA Brookhaven National Laboratory, Upton, New York 11973, USA Lauritsen Laboratory, California Institute of Technology, Pasadena, California 91125, USA Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, United Kingdom Universidade Estadual de Campinas, IFGW-UNICAMP, CP 6165, 13083-970, Campinas, SP, Brazil Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221, USA Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA Instituto de F´ısica, Universidade Federal de Goi´as, CP 131, 74001-970, Goiˆania, GO, Brazil Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA Holy Cross College, Notre Dame, Indiana 46556, USA Department of Physics, University of Houston, Houston, Texas 77204, USA Department of Physics, Illinois Institute of Technology, Chicago, Illinois 60616, USA Indiana University, Bloomington, Indiana 47405, USA Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 USA Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom University of Minnesota, Minneapolis, Minnesota 55455, USA Department of Physics, University of Minnesota Duluth, Duluth, Minnesota 55812, USA Otterbein College, Westerville, Ohio 43081, USA Subdepartment of Particle Physics, University of Oxford, Oxford OX1 3RH, United Kingdom Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA Rutherford Appleton Laboratory, Science and TechnologiesFacilities Council, Didcot, OX11 0QX, United Kingdom Instituto de F´ısica, Universidade de S˜ao Paulo, CP 66318, 05315-970, S˜ao Paulo, SP, Brazil Department of Physics and Astronomy, University of South Carolina, Columbia, South Carolina 29208, USA Department of Physics, Stanford University, Stanford, California 94305, USA Department of Physics and Astronomy, University of Sussex, Falmer, Brighton BN1 9QH, United Kingdom Physics Department, Texas A&M University, College Station, Texas 77843, USA Department of Physics, University of Texas at Austin, 1 University Station C1600, Austin, Texas 78712, USA Physics Department, Tufts University, Medford, Massachusetts 02155, USA Department of Physics, University of Warsaw, Pasteura 5, PL-02-093 Warsaw, Poland Department of Physics, College of William & Mary, Williamsburg, Virginia 23187, USA (Dated: April 1, 2015)We report the first observation of seasonal modulations in the rates of cosmic ray multiple-muonevents at two underground sites, the MINOS Near Detector with an overburden of 225 mwe,and the MINOS Far Detector site at 2100 mwe. At the deeper site, multiple-muon events withmuons separated by more than 8 m exhibit a seasonal rate that peaks during the summer,similar to that of single-muon events. In contrast and unexpectedly, the rate of multiple-muon events with muons separated by less than 5-8 m, and the rate of multiple-muon eventsin the smaller, shallower Near Detector, exhibit a seasonal rate modulation that peaks in the winter.
I. INTRODUCTION
Muons observed in underground particle detectorsoriginate from the interactions of cosmic rays with nu-clei in the upper atmosphere. These interactions producepions ( π ) and kaons ( K ) which can either interact, gen-erating hadronic cascades, or decay, producing muons.The probability that these mesons will decay rather thaninteract is dependent on their energy and the densityof the atmosphere near their point of production. Thetemperature of the upper atmosphere varies slowly overthe year, causing a seasonal effect on underground muonrates. Increases in the temperature of the atmospheredecrease the local density and thus reduce the probabil-ity that a secondary meson will interact. Consequently,the muon flux should increase in the summer. A numberof experiments have observed this variation in the singlemuon rate [1–11], including MINOS in both Far Detector(FD) data [12, 13] and Near Detector (ND) data [14].Seasonal variations for single muons have been studiedwith a correlation coefficient α T defined by:∆ R µ < R µ > = α T ∆ T eff < T eff > (1)where < R µ > is the mean muon rate, and is equivalent tothe rate for an effective atmospheric temperature equalto < T eff > . The magnitude of the temperature coeffi-cient α T is dependent on the muon energy at productionand hence the depth of the detector. The effective tem-perature T eff is a weighted average over the region of theatmosphere where the muons originate.By the same reasoning as above a variation should alsobe present in the rate of multiple-muon events. No suchstudies of multiple-muon seasonal rates are reported inthe literature. The formulae used to calculate T eff forsingle muons assume a single leading hadron from thefirst interaction is the parent, an assumption that is notapplicable for multiple-muon events.The probability that a cosmic ray shower will give amultiple-muon event observed in the MINOS Near or Fardetectors is enhanced whenever any of the following con-ditions are true: 1) The primary interaction occurs highin the atmosphere where the density is lower and a largerfraction of produced hadrons decay; 2) The energy ofthe primary is large so a higher multiplicity of hadronsis produced; 3) The cosmic ray primary is a heavy nu-cleus which breaks up and makes more hadrons; and 4)A leading hadron decays to dimuons. Assuming the rel-ative probability of interaction and decay for each mesonin a shower is independent, for multiple muons that comefrom the same energy and altitude as a single muon event,one might expect an increase in rate during the summerthat is roughly proportional to the muon multiplicity, N, ∗ Now at South Dakota School of Mines and Technology, RapidCity, South Dakota 57701, USA. such that α T,N = N × α T, . The result presented herediffers greatly from this. This paper presents the firstmeasurement of the multiple-muon modulation parame-ters.Note that most extensive air showers have many muonsin them, but that the highest energy muons which canreach an underground detector are produced in the firstfew interactions. Observed single-muon events are mostlikely multiple muons in which any other muons range outbefore reaching the detector or missed the detector later-ally. A single muon observed in a detector undergroundis most likely the highest energy muon from the showerdue to the steeply falling cosmic ray energy spectrum.The MINOS detectors and the event selection are de-scribed in Sec. II. In Sec. III the measurement and com-parison of the modulation parameters for the MINOS NDand FD multiple-muon and single-muon event rates arepresented. In Sec. IV and Sec. V some possible explana-tions of the seasonal behavior of the multiple-muon ratesare considered. II. THE MINOS DETECTORS AND MUONDATA
The MINOS detectors are planar magnetizedsteel/scintillator tracking calorimeters [15]. Thevertically oriented detector planes are composed of2.54 cm thick steel and 1 cm thick plastic scintillator.A scintillator layer is composed of 4.1 cm wide strips.The MINOS ND has a total mass of 0.98 kton, and lies104 m (225 mwe) underground at Fermilab at 42 ◦ Northlatitude. The detector is made from 3.8 m × ◦ Northlatitude. It is composed of 484 steel-scintillator 8.0 moctagonal planes and is 31 m long. The detectors areoriented to face the NuMI beam, but through-goingcosmic muons are well reconstructed over wide geometricangular regions.Six years of MINOS ND data collected betweenJune 1, 2006 and April 30, 2012 and 9 years of MINOS FDdata collected between August 1, 2003 and April 30, 2012are analyzed for this paper. The cosmic muon trigger cri-teria are similar at both detectors requiring that a signalis registered in either 4 strips in 5 sequential planes orthat strips from any 20 planes register a total signal abovethreshold within a given time window. The raw cosmictrigger rate at the ND and FD are approximately 27 Hzand 0.5 Hz respectively.The single-muon event selection requires there to be asingle reconstructed track in an event. The multiple-muon event selection requires there to be more thanone reconstructed track in an event. However, since thesingle-muon event rate is much larger than the multiple-muon event rate, the multiple-muon sample contains abackground of single-muon events that have been mis-reconstructed to contain two tracks This background isgreatly reduced by requiring that, for multi-track events,the track separation, ∆ S , defined as the minimum pointof closest approach between any two tracks, be greaterthan 0.6 m. Observed excesses due to this backgroundat small ∆ S in both the ND and FD were removed bythis selection, reducing the background from 1.3% to lessthan 200 events out of 11 million in the FD. Figure 1shows the time between sequential multiple-muon events.The multiple-muon event rates at the ND and FD are19.6 mHz and 14.1 mHz respectively. In total the MI-NOS ND and FD have collected 2.45 × and 3.36 × good multiple-muon events respectively.The rate of multiple muons in the MINOS detectors isdominated by m µ = 2 and m µ = 3, where m µ is the muonmultiplicity. For the FD, the reconstruction works wellfor these small multiplicities, identifying all tracks in 84%(67%) of events for m µ = 2 (3). From a multiple-muonMonte Carlo [16], the efficiency for identifying an eventas a multiple muon is 84% (94%) for m µ = 2 (3), risingto above 97% for m µ >
3. However, the reconstructedmultiplicity is frequently too low for high multiplicityevents. No event with m µ >
13 is recorded in eitherof the MINOS detectors. Similar measurements with thefiner-grained Soudan 2 detector at the same depth as theMINOS FD recorded multiplicities up to 20 [17]. In thecoarser-grained MINOS detectors, the individual tracksclosest in distance from such high-multiplicity events willbe resolved as a single track or not pass the track qualitycriteria used in the MINOS reconstruction algorithms.Figure 2 shows the reconstructed multiplicity distribu-tion in the MINOS FD.
III. MODULATION ANALYSIS
To compare the variation in the event rates formultiple-muon and single-muon events, the rates are fitto a sinusoidally-varying function of time. There is noa-priori reason to believe that the rates vary sinusoidallythrough the year, but this fit gives a qualitatively use-ful amplitude and phase. The following function, whichcontains four free parameters, is used for the fit: R ( t ) = R (1 − f t .
25 )(1 + A cos[ 2 πT ( t − t )]) (2)where t is the number of days since Jan. 1, 2010 and t is the phase; R is the mean rate on Jan. 1, 2010; A Time to Previous Event (s)0 200 400 600 800 1000 N u m be r o f M uon s -1 MINOS Near Detector DataMINOS Near Detector FitMINOS Far Detector DataMINOS Far Detector Fit
FIG. 1: Time between neighboring atmospheric multiple-muon events in the MINOS detectors. The data are welldescribed by an exponential over six orders of magnitude ininstantaneous rate.
Reconstructed tracks in an event N u m be r o f r e c on s t r u c t ed m uon s pe r e v en t FIG. 2: The reconstructed muon multiplicity, for events con-taining more than one reconstructed track, in the Far Detec-tor. is the modulation amplitude and T is the period (ap-proximately 1 year). The parameter f is the loss rate(described in Reference [14]) that accounts for an ob-served linear decrease in the event rate in both the FDand ND over the lifetime of the experiment. The sourceof this small but apparently steady decrease has not beenconclusively identified and is under study. The best-fitparameters are given in Table I. Data Set Amplitude Loss Rate (f) Period (T) Phase (t )(%) (%/year) (days) (days)MINOS FD∆S > ± ± ± ± < ∆S < ± ± ± ± < ∆S < ± ± ± ± > ± ± ± ± ± ± ± ± > ± ± ± ± < ∆S < ± ± ± ± < ∆S < ± ± ± ± > ± ± ± ± ± ± ± ± A. Modulations in the Far Detector
The fit for seasonal variations in the FD multiple-muonsample shows a much smaller amplitude than for singlemuons, and a poorly defined phase. Since the MINOSFD is larger than the ND and is fully instrumented, themodulation is studied as a function of track separation.Figure 3 shows the track separation ∆ S . The multiple-muon data are grouped into three bins of roughly equalstatistics with track separations from 0.6-4.5 m (FD re-gion A), 4.5-8.0 m (FD region B) and greater than 8 m(FD region C). Region A most closely resembles the dis-tribution in the ND.Figure 4 presents the multiple-muon rate in the MI-NOS FD as a function of time for differing track separa-tions. The FD multiple-muon data set with the largesttrack separation, > t = 184.8 ± t = 27.6 ± B. Modulations in the Near Detector
The ND multiple-muon data, shown in Fig. 6, and thesingle-muon data (shown in Reference [14]) were fit toEq. 2 using one month time interval bins. The multiple-
Track Separation (m)0 10 20 30 F r a c t i on o f E v en t s MINOS Far DetectorAll EventsSelected Events
A B C
FIG. 3: The minimum track separation ∆ S between anytwo tracks in multiple-muon events recorded in the FD. Thegray (black) histogram is the distribution before (after) theselection to remove misreconstructed single-muon events. Re-gions of track separation ∆ S are defined as A: 0.6-4.5 m, B:4.5-8.0 m and C: > muon event rate data show a clear modulation signature.However, unlike the single muon rate which reaches itsmaximum in the summer [14], the multiple-muon ratereaches its maximum in the winter. This also matchesthe modulation for the region-A multiple muons in theFD. Both the single-muon and multiple-muon data setshave periods consistent with one year but their phases,198.6 ± ± (cid:9) Calendar Date (m/yyyy) 1/2003 1/2005 1/2007 1/2009 1/2011 R a t e ( m H z ) ∆ C: R a t e ( m H z ) ∆ B: 4.5m < R a t e ( m H z ) ∆ A: 0.6m < S < 4.5m ∆ A: 0.6m <
FIG. 4: The multiple-muon rate in the FD as a function oftime for different track separations. Each data point corre-sponds to one calendar month of data. The solid red lines arethe best fit to Eq. 2. The top graph is for the smallest trackseparation, the middle graph for mid-range and the bottomgraph for the largest. The vertical lines are year boundariesand the solid horizontal line represents the fit without thecosine term.
Figure 8 shows the track separation in ND multiple-muon events. To qualitatively match the procedure in theFD, the data have been grouped into three bins of roughlyequal statistics with track separations of 0.6-1.8 m (NDregion A), 1.8-3.0 m (ND region B) and greater than 3 m(ND region C). As before, the data are fit to Eq. (2)and the best fit parameters are given in Table I. Thereis no apparent difference in the fit parameters for thethree ND regions, which all peak in the winter. There isconsistency between ND regions ABC and FD region Ain both ∆ S and a winter maximum. IV. DISCUSSION OF RESULTS AND POSSIBLEEXPLANATIONS
We have previously observed seasonal variations insingle-muon rates in the MINOS ND and FD that corre-late at expected levels with the temperature changes andthe season. Those muon rates rose in the summer as didthe calculated values of T eff , and the measured correla-tions were α NDT = 0.428 ± α F DT = 0.873 ± Day In Year0 100 200 300 R a t e ( m H z ) ∆ R a t e ( m H z ) ∆ MINOS Far Detector 0.6m <
FIG. 5: The multiple-muon rate in the FD for events with∆ S range A from 0.6 m to 4.5 m (top graph) and for eventswith ∆ S range C larger than 8 m (bottom) binned accordingto calendar month. The top figure shows a winter maximum.The bottom figure shows a summer maximum. Calendar Year (m/yyyy) M uon R a t e ( m H z ) MINOS Near Detector Data
FIG. 6: The multiple-muon rate in the ND as a function oftime. Each data point corresponds to one calendar month. Aclear modulation in the data is observed with the maximumoccurring towards the start of the year. The vertical lines areyear boundaries. considered. They involve: A) a source of dimuons fromprompt hadron decays (such as η and ρ ) that may havethe opposite seasonal variation, since in the winter thesecondary pions are more likely to interact than decayand produce more of such hadrons; B) a geometric effectin which different altitude distributions affect the trackseparation underground; C) a different altitude distribu-tion for multimuon events that may come from regions Day In Year 0 100 200 300 M uon R a t e ( m H z ) MINOS Near Detector Multiple MuonsBest Fit
Day In Year0 100 200 300 M uon R a t e ( H z ) MINOS Near Detector Single MuonsBest Fit
FIG. 7: The top figure is the multiple-muon rate in theND, binned according to calendar month, which each pointshowing the average rate for all years of data-taking. Thefigure also shows a cosine fit to the data. The single-muonrate is shown in the bottom figure, showing a clearly differentseasonal modulation. of the atmosphere with different seasonal temperatureprofiles; and D) leading secondary hadrons being morelikely to decay than interact in the summer, and thusless likely to make multiple hadrons which make multi-ple muons. We discuss each of these possibilities in thecurrent section.
A. Hadronic dimuon decays
One idea is that the winter maximum may be due tohadronic decays into dimuons. In the winter, while pionsare less likely to decay in the atmosphere, the decay prob-
Track Separation (m)0 2 4 6 8 F r a c t i on o f E v en t s MINOS Near DetectorAll EventsSelected Events
A B C
FIG. 8: The minimum track separation ∆ S between anytwo tracks in multiple-muon events recorded in the ND. Thegray (black) histogram is the distribution before(after) the se-lection to remove misreconstructed single-muon events. Re-gions of track separation ∆ S are defined as A: 0.6-1.8 m, B:1.8-3.0 m and C: > ability of other hadrons which have dimuon decays, suchas η and ρ mesons, changes negligibly. The 2% more pi-ons [13] which interact will increase the number of theseother hadrons. This increase, which is at most 2%, mustthen be folded in with the small dimuon branching ra-tios, such as 4.6 × − for ρ → µ + µ − and 3.1 × − for η → µ + µ − γ [35]. Observed dimuon rates are 1% ofthe single muon rates in the FD, and 0.16% in the ND,so even if ρ and η production were comparable to π , thiscontribution is at most 6 × − , too small to accountfor the observed effect. B. A geometry effect
A possibility is that the muons generated higher in theatmosphere in the summer spread out farther so thatthere are fewer of them in region A. This would be solelya geometric effect, in that it would not affect the num-ber of multimuons in each season but only the track-separation distribution. This is further complicated bymultiple scattering, but an effect due to the opening an-gle at production can be estimated. For a fixed-size de-tector, a difference in the track separation distributionwould affect the measured rate. The altitude of the firstinteraction in an isothermal atmosphere is related to theabsolute temperature. A ±
2% seasonal change in theeffective temperature would cause a ±
2% change in thealtitude, and hence less than a 4% change in the averagemuon track separation underground. This would moveevents to the right in Fig. 3. Due to the shape of thedistribution, more events would move from region A toregion B than from region B to region C, which is in
Modulation Phase (days)0 100 200 300 P r e ss u r e ( h P a ) A l t i t ude ( k m ) ECMWF Data
Near Detector SiteFar Detector Site
Modulation Amplitude (%)0 2 4 6 8 10 P r e ss u r e ( h P a )
10 1020304050 A l t i t ude ( k m ) ECMWF Data
Near Detector SiteFar Detector Site
FIG. 9: The (top) modulation phase and (bottom) ampli-tude in the ECMWF temperature data based on a cosine fitare shown as a function of altitude and detector site. Thesedistributions were used to study both the geometry effect (B)and the temperature effect (C). contradiction to our fits. Also, one would expect a sim-ilar effect in the ND as shown in Fig. 8, but no trackseparation dependence is seen in the ND.
C. A temperature effect
To determine whether there may be an altitude-dependent seasonal variation that differs for single andmultiple muons, meteorological data is used to deter-mine the atmospheric temperature profile. Figure 9 givesthe phase and amplitude of the modulation of the atmo-spheric temperature, based on a cosine fit to data takenfrom the European Center for Medium-Range WeatherForecasts (ECMWF) model [29], as a function of at-mospheric pressure. Indeed, there is a small region ofthe atmosphere, between 70 hPa and 175 hPa, where thetemperature reaches a maximum in the winter. Note,however, the small amplitude of the annual temperature variation at those altitudes.In order to study the possible altitude dependenceof multiple muons we simulated cosmic ray air showerswhich could make multiple muons in the MINOS FD. TheMonte Carlo sample was produced by CORSIKA [30, 31]using version 7.4. We have run CORSIKA with threedifferent hadronic models, QGSJET-01C, QGSJET II-04[32] and EPOS [33] which gave consistent results. Wenote that CORSIKA uses an isothermal atmosphere andcannot be used per se to study seasonal variations. Thegoal here is to roughly calculate the altitude dependencefor the three regions of track separation. CORSIKA out-puts muon energies and positions at the earth’s surface.To reach the MINOS FD, energy loss through the rockwas calculated using [34]: E loss ( X ) = ab T ( e b T X − , (3)where X is the rock overburden, a is a parameter for theionization energy loss and b T = b brem + b pair + b DIS rep-resents the energy loss due to bremsstrahlung, electron-positron pair production and photo-nuclear interactions.Simulated events were selected for which two or moremuons reached the top of the FD with a total remainingenergy of at least 0.9 GeV. The distribution of track sep-aration obtained with this simulation was similar to, butnot identical to, the distribution seen in data (Fig. 3).We then extracted from CORSIKA the altitude at whicheach muon was created in each track-separation region.Those three distributions are shown in Fig. 10. There is ashift in the mean altitude for each region of track separa-tion from 17 km in region A to 21 km in region C, thoughall three distributions are quite broad. We then combinedthe altitude dependence with the temperature phase andamplitude fits shown in Fig. 9, assuming the rate and T eff were completely correlated, to compare the over-all variation of T eff averaged over each track-separationregion. The result was a variation that peaked in thesummer in all three regions, with an amplitude of 1.9% inregion C and 1.6% in regions A and B. This study was re-peated using QGSJET-01C, QGSJET II and EPOS andall three results were similar. It does not appear that thetemperature variations noted in Fig. 9 can account forthe observed reverse seasonal effect in region A. D. Anticorrelation of primary and secondarydecays
As a last hypothesis, while most single-muon eventscome from secondary pions and kaons produced in theprimary cosmic ray interaction, multiple muons may bemore likely to come from higher energy primaries wherethere are further hadronic interactions deeper in theshower. In that case, if the secondary hadron is morelikely to decay in the summer, it is less likely to interactand make additional pions and kaons which contribute tomultiple muons. This may be the best explanation for the
Muon Production Altitude (km) N u m be r o f E v en t s Region ARegion BRegion C
QGSJET 01CMultiplicity: 2 Mean values (km):Region A: 17.03Region B: 18.66Region C: 20.61
FIG. 10: To study a possible temperature effect with altitude,(Sec. IV C in the text), the altitude distribution from COR-SIKA for MINOS FD multiple muons are shown for each ofthe three regions of track separation in Fig. 3. winter maximum measured in the MINOS ND multiple-muon data set. A quantitative test of this hypothesiswill require a detailed study of air shower developmentthat is beyond the scope of this analysis. This hypoth-esis accounts for the stronger effect in the MINOS ND,where the muons come from pions and kaons below theircritical energies ( ǫ π = 115 GeV and ǫ K = 850 GeV, de-fined as those energies for which meson decay and inter-action rates in the atmosphere where muons originate areequal) [1] and for the more complex effect in the MINOSFD where the energies are above ǫ π and comparable to ǫ K . Mesons which are much below their critical energiesmostly decay, so the temperature effect that does exist toincrease the decay rate in the summer has a large effecton decreasing the interaction rate in the summer. Thisis the situation for muons in the ND where the thresholdfrom the overburden is near 50 GeV. At the FD, wherethe threshold is almost a TeV, a change in the decay ratehas a smaller impact on the interaction rate, since a largefraction of the hadrons are interacting before they decay.As pointed out in the introduction, single muons comepredominantly from the decay of a leading hadron, and multiple muons from a more complicated process. It isclear that if a leading hadron is more likely to decay inone season, it is less likely to interact. V. CONCLUSION
We have shown evidence of an annual modulation inthe MINOS ND multiple-muon data set in which themaximum rate occurs in the winter. This phase is incon-sistent with the summer maximum observed in the NDand FD single-muon data. Data collected by the MINOSFD were used to show that there is a transition from asummer maximum in multiple-muon events with a largetrack separation to a winter maximum in multiple-muonevents with a small track separation. This transition oc-curs at track separations of about 5-8 m.Four possible explanations for this observed character-istic in seasonal variations were considered. One expla-nation is favored: this is a hypothesis in which multiplemuons come preferentially from higher energy pions andkaons which, in the summer, are less likely to interact andproduce the secondary pions and kaons that give rise tothe multiple muons. However, a full explanation of ourobservations including the dependence in the FD on trackseparation must come from a more detailed study of ex-tensive air-shower properties and the properties of theatmosphere.
VI. ACKNOWLEDGMENTS
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