Observation of Seasonal Variations with the MINOS Far Detector
aa r X i v : . [ h e p - e x ] O c t TH I NTERNATIONAL C OSMIC R AY C ONFERENCE
Observation of Seasonal Variations with the MINOS Far Detector
E.W. G
RASHORN , FOR THE
MINOS C
OLLABORATION Univ. of Minnesota School of Physics & Astronomy, 116 Church St., Minneapolis, MN 55455, USA Abstract:
An observation of seasonal variations in underground muon rate, R µ , has been performed atSoudan, MN, by the MINOS Far Detector. The four percent fluctuation seen over three years was highlycorrelated to the temperature variations of the upper atmosphere. The coefficient relating variations intemperature to variations in muon rate was found to be: α T = ( T /R µ )( ∂R µ /∂T ) = 0 . ± . , whichis near the expectation of 0.91. Introduction & Motivation
When cosmic rays interact with molecules in theTroposphere, mesons are produced which eitherinteract again and produce low energy cascadesor decay into muons. While the temperature ofthe Stratosphere varies considerably within the dayin areas far from the equator, the temperature ofthe Troposphere remains nearly constant, slowlychanging over longer timescales such as seasons.Increases in temperature of the Troposphere causeincreases in volume and atmospheric scale height,thus the height of the primary cosmic ray interac-tion. The higher in the atmosphere mesons are pro-duced, the more time they have to decay to muons,thus the rate of muons underground will increaseas temperature increases [1–3]. Though this effecthas been measured by underground experiments,there has been little agreement with the expecta-tion.MINOS is a long baseline neutrino oscillation ex-periment, with a ν µ beam and Near Detector atFermi National Accelerator Laboratory in Batavia,IL. The Far Detector is a 5.4 kt magnetized scintil-lator and steel tracking calorimeter located 720 munderground (2100 mwe) at the Soudan Under-ground Mine State Park in Northern Minnesota. Itsdepth, large acceptance and flat overburden makeit possible to observe cosmic-ray induced muonsof minimum surface energy 0.7 TeV without pref-erence to direction, and thus detect the small sea- sonal fluctuations in arrival rate. The seasonal ef-fect is enhanced as muon energy increases, andthe large size of the Far Detector allows a signif-icant accumulation of statistics with which to per-form this analysis. Additionally, the Far Detectorhas a magnetic field, which allows the separationof particles by charge, so MINOS will be the firstexperiment to measure seasonal variations for µ + separate from µ − . The consistency and availabil-ity of radiosonde temperature measurements fromthe NOAA IGRA (Integrated Global RadiosondeArchive [4]) over the duration of the data set en-sures a high statistics temperature sample as well,increasing the probability of a positive correlation.The data used in this analysis were collected overthree years, from 1 August 2003 - 1 August 2006for three complete cycles, numbering 24 millionmuons. The relationship between the temperatureand intensity can be expressed as [1]: ∆ I µ I µ = Z ∞ dXα ( X ) ∆ T ( X ) T ( X ) (1)where ∆ I µ are the fluctuations about I µ . The shortlived mesons produced in the upper atmosphere in-teract or decay as they descend toward the earth.The meson decay channels result in muons withnearly the same energy as the parent meson, whileinteractions produce lower energy cascades that arefiltered by the rock overburden above the Far De-tector. These outcomes are energy dependent, sep-arated by the “critical energy” [2]. The “Effec- BSERVATION OF S EASONAL V ARIATIONS ... tive Temperature” ( T eff ) approximates the upperatmosphere as an isothermal body, weighting thetemperature of the pressure levels to have a uni-form amount of matter. In the π scaling limit, T eff is [2]: T eff = R dXX T ( X ) (cid:16) e − X Λ π − e − X Λ N (cid:17)R dXX (cid:16) e − X Λ π − e − X Λ N (cid:17) , (2)where X is the scale height of the atmosphere, Λ N = 120 gm / cm and Λ π = 160 gm / cm are the nucleon and pion atmospheric attenua-tion lengths, respectively. For a detector count-ing discrete particles, the intensity is written I µ = R i /ǫA eff Ω , where R i = N i /t i , the number ofmuons observed over time t i , A eff is the effectivearea, ǫ is the efficiency, and Ω is the solid angleobserved. Every term but the rate is constant overtime, so: ∆ I µ I µ = ∆ R µ h R µ i . With these definitions andeq. 1, we can write the experimental determinationof α T : Z ∞ dXα ( X ) ∆ T ( X ) T ( X ) = α T ∆ T eff < T eff > = ∆ R µ < R µ > . (3) The Data
The data for this analysis were accumulated over athree year span, beginning on 1 August, 2003, at atime when the detector was fully operational. Be-ginning with 40.3 million cosmic ray tracks, a se-ries of cuts were performed [5]. Pre-analysis cutsinclude: failure of demultiplexing figure of merit,multiple muon (multiple muons aren’t included inthe Monte Carlo), “bad run” and bad magnet coilstatus. Analysis cuts include: track length less than2 m number of planes less than 20, χ reco > . andeither track vertex or end point outside of the fidu-cial volume of the detector. A total of 24.7 millionevents survived these cuts for the combined sam-ple. T eff was found using weather data from Inter-national Falls, MN weather station. Balloon flightswere usually done twice a day, with the maximumheight reached at noon and midnight, and sampledtemperatures from at least six different heights.Days in which there were not exactly two temper-ature readings or that both measurements did not (s) m t D m N MINOS PRELIMINARY
Figure 1: Time between consecutive µ arrivals inlog y. A Poisson fit gives χ /ndof = 90 . / ; h R µ i (from slope) = . ± . reach a column depth of at least
60 gm / cm wereexcluded from the data set. Analysis
Upon examination of the data, it was found that onfour days there were fluctuations that deviated inan erratic manner. The great stability of the detec-tor over the 1096 days of data and the fact that theywere documented by the Control Room Logbookmade these days stand out and diagnose as hard-ware issues. To find the rate for each day, the num-ber of muons counted was divided by that day’slivetime. T eff was calculated for two times eachday using the IGRA temperature data and 2, andthe error was found by σ = D T eff E − h T eff i added in quadrature with . ◦ . The fit resultsfrom Fig. 1 was used to find h R µ i over three years,0.287 Hz. Histograms of the deviations from themean for both R µ and T eff are shown in Fig. 2,binned by day. The expected periodic fluctuationin T eff , with maxima in July, minima in January,is very clearly shown, as is a very similar (nearlyindistinguishable) fluctuation in R µ . An indepen-dent analysis used a smoothed time series, andtheir results were highly consistent with what isshown here. To quantify the correlation betweenrate and temperature, a plot of R µ ( T eff ) was pro-duced (Fig. 3) and a linear regression was fit usingROOT’s MINUIT fitting package. This packageaccounts for error bars on both the x and y axisusing a numerical minimization method. This fitgives α T = 0 . ± . from the slope. In order TH I NTERNATIONAL C OSMIC R AY C ONFERENCE depth (mwe)0 1000 2000 3000 T a Hobart Torino Poatina Utah Sherman Baksan Barrett 2 Barrett 1 AMANDA MINOS MACRO
MINOS PRELIMINARY
Figure 4: The theoretical α T ( X ) (solid curve) for slant depths up to 4000 mwe. The MINOS point is fromthis analysis, Barrett 1,2 [1], AMANDA [3]; all other points from [2] (%) m R D -505 MINOS PRELIMINARY (%) eff T D -505 MINOS PRELIMINARY
Figure 2: ∆ R µ , (top), and ∆ T eff (bottom) from8/03-8/06, binned by day.to compare our experimental α T to the theoreticalexpectation, a simple numerical program was writ-ten to find the expected value given by [1]: h α T i π = D γ ( γ + 1) × ǫ π . E th cosθ E (4)Note that this expression is only valid for pions.Future work will involve this kaon contribution,which should lower the expected α T since kaonsare short lived and always decay. A muon energyand cos θ were chosen out of the differential muonintensity [6], dI µ dE µ = 0 . E − ( γ +1) µ h
11 + 1 . E µ cos θ/ǫ π i (5) (%) eff T D -6 -4 -2 0 2 4 (%) m R D -10-50510 MINOS PRELIMINARY
Figure 3: A plot of ∆ R µ / h R µ i vs. ∆ T eff / h T eff i for single muons. The fit χ /ndof = 1420 / , and correlation coefficientR = 0.79.where γ = 1 . is the muons spectral index [5]. arandom azimuthal angle, φ was chosen and com-bined with cos θ and Soudan rock overburden map[7] to find the slant depth. The threshold surfaceenergy required for a muon to survive this columndepth is found from E th ( θ, φ ) = a ( e bX − , wherea = 0.45 TeV and b = 0 .
44 [kmwe] − for Soudanrock [5], column depth X = X ( θ, φ ) , and if thechosen E µ > E th , it was used in the calculationof the theoretical h α T i π . This was repeated for10,000 successful E µ to find h α T i π = 0 . forMINOS, which is very near to the experimentalvalue, . ± . . To compare the MINOS re- BSERVATION OF S EASONAL V ARIATIONS ... sult with other underground experiments, this pro-cess was repeated for standard rock ( a = 0 .
50 TeV and b = 0 . − ), flat overburden, and X = H/ cos θ , where H is the detector depth in mwe,using 10,000 successful muons at depths from 0 to4,000 mwe. The result of this calculation, alongwith data from other experiments, can be seen inFig. 4. The MINOS result matches the expectationand has tighter error bars than both recent results,AMANDA ( ± . [3]) and MACRO ( ± . [2]).The curvature of the track is used to determinethe momentum and charge of the particle, so acharge sign confidence cut was required. This cutwas charge over momentum divided by the errorin the determination of charge over momentum( q/pσ q/p > . ), determined from previous investiga-tions of the muon charge ratio. That left 8.8 million (%) m R D -1001020 MINOS PRELIMINARY (%) m R D -10-50510 MINOS PRELIMINARY
Figure 5: ∆ R µ / h R µ i for µ + (open triangles, top)and µ − (open circles, bottom), binned by day.events; 5.1 million positive, 3.7 million negative,which is consistent with the published MINOScharge ratio. Fig. 5(t) shows ∆ R µ + (open trian-gles) and Fig. 5(b) shows ∆ R µ + (open circles) overthe same time period, binned by day. The sampleof muons is smaller than for the µ tot sample, thusthe error bars on R µ are larger, but the trade offis that the error bars on the temperature are muchsmaller since the small fluctuations over severaldays are not washed out. Performing the same fitof R µ ( T eff ) as for the µ tot sample on µ + sepa-rate from µ − resulted in a slope of . ± . and . ± . respectively. These correspondhighly to each other, and are within one sigma of α T found from the µ tot sample. Conclusions
A three year sample of 42 million cosmic ray in-duced muons has been collected by the MINOSFar Detector and daily rate fluctuations have beencompared to daily fluctuations in atmospheric tem-perature, and these distributions were shown to behighly correlated, with a correlation coefficient of0.79. The constant of proportionality relating thetwo distributions, α T , was found to be . ± . ,which, within the error band, is in good agreementwith the theoretical expectation in the pion-onlyapproximation of h α T i π = 0 . . This suggeststhat the majority of muons seen in the Far Detectorwere generated by pion parents. Acknowledgments
This work was supported by the U.S. Departmentof Energy and the University of Minnesota.
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