The magnetized MINOS near detector can accurately determine the charge sign
of atmospheric muons, this facilitates a measurement of the atmospheric muon
charge ratio. To reduce the systematic error associated with geometric bias and
acceptance we have combined equal periods of data obtained with opposite
magnetic field polarities. We report a charge ratio of
$1.2666\pm0.0015(stat.)^{+0.0096}_{-0.0088}(syst.)$ at a mean
E$_{\mu,0}cos(\theta)$=\unit[63]{GeV}. This measurement is consistent with the
world average\cite{Hebbeker}\cite{Haino}\cite{Achard} but significantly lower
than the earlier observation at the MINOS far detector\cite{Adamson}. This
increase is shown to be consistent with the hypothesis that a greater fraction
of the observed muons arise from kaon decay within the cosmic ray shower.Comment: Proceedings for the 2009, 31st International Cosmic Ray Conference in
  Lodz Polan

/IIT, Chicago /Oxford U.

de Jong, J.K.

English

arXiv

The magnetized MINOS near detector can accurately determine the charge sign of atmospheric muons, this facilitates a measurement of the atmospheric muon charge ratio. To reduce the systematic error associated with geometric bias and acceptance we have combined equal periods of data obtained with opposite magnetic field polarities. We report a charge ratio of 1.2666 {+-} 0.0015(stat.){sub -0.0088}{sup +0.0096}(syst.) at a mean E{sub {mu},0{sup cos}}({theta}) = 63 GeV. This measurement is consistent with the world average but significantly lower than the earlier observation at the MINOS far detector. This increase is shown to be consistent with the hypothesis that a greater fraction of the observed muons arise from kaon decay within the cosmic ray shower

de Jong, J. K.

UNT Digital Library

PROCEEDINGS OF THE 31st ICRC, ŁÓDŹ 2009 1The Atmospheric Muon Charge Ratio at the MINOS NearDetector.J.K. de Jong ∗†for the MINOS collaboration.∗Illinois Institute of Technology,Chicago Illinois 60616 USA†now at University of Oxford, Oxford OX1 3RH United KingdomAbstract. The magnetized MINOS near detectorcan accurately determine the charge sign of at-mospheric muons, this facilitates a measurementof the atmospheric muon charge ratio. To re-duce the systematic error associated with geo-metric bias and acceptance we have combinedequal periods of data obtained with opposite mag-netic field polarities. We report a charge ratioof 1.2666 ± 0.0015(stat.)+0.0096−0.0088(syst.) at a meanEµ,0cos(θ)=63 GeV. This measurement is consistentwith the world average[1][2][3] but significantlylower than the earlier observation at the MINOS fardetector[4]. This increase is shown to be consistentwith the hypothesis that a greater fraction of theobserved muons arise from kaon decay within thecosmic ray shower.Keywords: MINOS, muon charge ratioI. INTRODUCTIONThe MINOS experiment consists of two steel-scintillating sampling calorimeter detectors. The 980 tonnear detector is used to characterize the spectrum ofthe neutrino beam and is located at Fermilab in acavern 94.3 m underground at the end of the NuMIbeam facility (approximately 1 km from the primaryproton target). The 5.4 kton far detector is located732 km further downstream and is 710 m below thesurface. MINOS looks for neutrino oscillations byidentifying changes to the neutrino spectrum. BothMINOS detectors utilize toroidally magnetized steelplanes as the passive absorber material. This magneticfield, which varies between 1 and 2 Tesla, allows themto distinguish between positive and negative muons.When high energy cosmic rays interact with nuclei inthe upper atmosphere the subsequent shower produceskaons (K) and pions (π). These secondary mesons caneither interact, or decay to produce muons. Since themajority of cosmic rays are positively charged therewill be an excess of positively charged mesons in theshower and consequently an asymmetry in the measuredmuon charge ratio Nµ+/Nµ− . The magnitude of thisasymmetry is also influenced by the π/K productionratio and the fraction of the mesons which decayversus interact. The latter process will be shown to beresponsible for the increase in the charge ratio observedby the MINOS far detector[4]II. THE MINOS NEAR DETECTORThe MINOS near detector[6], located at 88 ◦16’14” west longitude and 41◦ 50’ 26” north latitudeon the Fermilab campus, is a steel-scintillatorsampling calorimeter with tracking, energy andtopology measurement capabilities. It is located94.3 m underground with a flat overburden of224.6 meters of water equivalent(mwe). It measures3.8 m x 4.8 m x 16.6 m. The detector contains 282vertical steel planes, each 2.5 cm thick. Betweeneach plane there is either a 1.0 cm thick scintillatorplane and a 2.4 cm air gap, or a 3.6 cm air gap(thescintillator is encased in a 0.1 cm thick aluminumskin). Each scintillator plane is comprised of eithera full or partial plane which consists of 64 or 96scintillator strips respectively. The scintillator stripsare 4.1 cm wide(transverse direction) and between2.5 to 4 m in length(longitudinal direction). The first120 planes located on the upstream portion of thedetector comprise the calorimeter. In the calorimeterevery 5th plane is fully instrumented covering thecross-sectional area defined by the steel planes. Thefollowing 4 planes are partially instrumented. Thelast 162 planes located on the downstream side ofthe detector make up the spectrometer. In this regiononly every 5th plane is instrumented, but instrumentedwith full scintillator coverage. This region aids in themomentum determination of long tracks. The stripsin each scintillator layer are rotated by 90◦ withrespect to the previous layer to allow for 3 dimensionaltrack reconstruction. The curvature induced in thetrack by the magnetic field, which has a strengthbetween 1 and 2 Tesla, coupled with the 3 dimensionaltrack reconstruction allows the determination of thecharge sign of the muon track. The detector has twodistinct magnetic field polarities. The “forward” fieldfocuses µ−’s coming from the south, toward thecenter of the detector. The “reverse” field focuses µ+’scoming from the south, toward the center of the detector.FERMILAB-CONF-09-838-EOperated by Fermi Research Alliance, LLC under Contract No. De-AC02-07CH11359 with the United States Department of Energy.  2 J.K. DE JONG et al. MINOS CHARGE RATIOIII. THEORYThe differential muon production spectrum which hasbeen parameterized [7] asdNµdEµ,0≈0.14 · E−2.7µ,0cm2srGeV× (1)(1.01 +1.1·Eµ,0cos(θ)επ+0.0541 +1.1Eµ,0cos(θ)εK),where Eµ,0 and θ are the muons surface energy andzenith angle respectively. The values επ =115 GeV andεK=850 GeV are the critical energies above which thepions and kaons would prefer to interact more oftenthan decay. The 0.054 value is related to the π/K ratioin the showers and the branching fraction of the Kaonto a muon. The first term in the brackets is the muoncontribution from pion decay, and the second term isthe muon contribution from kaon decay. As a functionof Eµ,0cos(θ) the denominator of the Kaon contributionterm drops slower (επ < εK) than the pion term meaningthat at large values more of the observed muons arecoming from Kaon decays. Since strong interactionproduction channels lead to a muon charge ratio thatis greater for kaon decays than that from pion decaysthe observed charge ratio should increase[4]. Followingthe prescription in [4] and defining fπ+ and fK+ as thefraction of all decaying pions and kaons which decaywith a detected µ+, the atmospheric muon charge ratioNµ+/Nµ− is given in eq. (2):Nµ+Nµ−=(fπ+1 +1.1Eµ,0cos(θ)επ+0.054fK+1 +1.1Eµ,0cos(θ)εK)(2)((1 − fπ+)1 +1.1Eµ,0cos(θ)επ+0.054(1− fK+)1 +1.1Eµ,0cos(θ)εK).IV. THE ANALYSISThe desired data sample for this analysis consistsof atmospheric muons with well reconstructed energyand charge sign. A series of pre-analysis selectionsare made to reject events which are not consistentwith atmospheric muons and to reject events whoseorigin and kinematics can not be determined. Furtherselections are applied to ensure track reconstructionquality and that the charge sign of the candidatemuon track is accurately determined. This analysis isperformed on 190.2 days of data, roughly 450 milliontriggers, collected between 2006 and 2008.This analysis has been constructed with the intentionof reducing the two dominant systematic errors forthe charge ratio measurement: geometric bias andrandomization. Geometric bias refers to a preferentialselection of one charge sign over another, whereasrandomization refers to an inability to determine thecharge which results in a random charge being assignedto the track. The variables discussed in the followingsections were derived using monte-carlo and validatedusing the data sample.A. Geometric BiasDue to east-west asymmetry of the detector (the mag-netic coil hole is off-center), as well as the north-southasymmetry introduced by the spectrometer, the detectorpreferentially reconstructs northerly going muons whichoccur on the east side of the detector. The forward fieldfocuses northerly going µ− and defocuses µ+, thereforethe forward field charge ratio will be less than the truecharge ratio; similarly, the reversed field charge ratioshould be greater for northerly going muons(and vice-versa for southerly going). This is the trend that isobserved in figure 1.Azimuthal Angle0 100 200 300- µ/N + µN0.811.21.41.61.8Forward B-FieldReverse B-FieldCombined B-FieldE S W NFig. 1. The charge ratio, after all the analysis cuts, varies considerablydue to acceptance effects in either field configuration as a function ofazimuth angle: Closed circles are the ratios observed during forwardfield running, and open circles during reversed field running. Thecombined field has been determined using the geometric mean. Theerror bars are statistical only.Cancelling the biases due to geometric acceptanceshas been previously discussed in [4]. If ε1 is the ac-ceptance for µ+ and ε2 is the acceptance for µ− inthe forward field direction(FF) then the acceptance forµ+ and µ− in the reverse field direction(RF) are ε2and ε1 respectively. Two independent equations for thecharge ratio, ra and rb, can be constructed where theacceptance effects cancel. These ratios, corrected fordetector lifetime, are:ra = (Nµ+/t)FF /(Nµ−/t)RF , (3)andrb = (Nµ+/t)RF /(Nµ−/t)FF , (4)By combining equations (3) and (4) we obtain a chargeratio in which the geometric acceptance and life-timebiases cancel.Nµ+Nµ−=√rarb =√(Nµ+Nµ−)FF (Nµ+Nµ−)RF (5)PROCEEDINGS OF THE 31st ICRC, ŁÓDŹ 2009 3The charge ratio in equation (5) is also independentof any changes in the muon flux due to seasonalvariations that may have occurred between the forwardand reversed field running[5].B. Reducing RandomizationRandomization refers to any process which resultsin the track charge being assigned randomly. Infact any process which degrades “track quality”introduces randomization into the data sample. Awell reconstructed track is defined as a track whosereconstructed points correspond to strips where a signalwas detected. If a “noise” hit were to be included asa hit on the track, the reconstruction algorithm willattempt to include this hit in the track and pull the bestfit curve away from the true signal hits. Since noise hitsare distributed randomly around a track, the curvatureinduced by this noise hit will result in a random chargebeing assigned. A well reconstructed track is requiredto have a maximum deviation from the center of eachstrip no more than 3 cm in the transverse direction andno more than 1/2 the strip length plus 1 cm in thelongitudinal direction. It is required that at least 60%of the hits recorded in the detector be part of the trackin order to eliminate particularly noisy events. Finally,it’s required that the track be reconstructed with a goodχ2 per degree of freedom.Track quality ensures that the track is wellreconstructed, however when determining theatmospheric muon charge ratio the charge sign ofthe track needs to be identified accurately as well. TheKalman filter [8] assigns for each track a quantity of(q/p) ± σ(q/p), where q = ±1 is the track chargeand p the track momentum. A track with a large valueof (q/p)/σ(q/p) is a track for which the fitter has ahigh confidence in the assigned charge and momentum.Secondly, a long track occurring in a region of highmagnetic field would have a high degree of curvature,and the more hits that occurred along this track thegreater the confidence in that curvature. This selectionvariable will be referred to as the “BdL”. The BdL cutwas originally constructed in the far detector analysis[4]to ensure that the magnitude of the bending due tocurvature was larger than apparent bending due tomultiple scattering. These two selection criteria havebeen optimized in data, and validated in Monte-Carlo,to maximize selection efficiency and minimize chargesign mis-identification.Figure 2 plots the charge ratio as a function ofboth (q/p)/σ(q/p) (after the curvature cuts and in-cluding BdL >1.8) and the minimum plane cut(curvature+(q/p)/σ(q/p) >2.8). In both cases wesee that the charge ratio flattens off indicating thatthe systematics due to randomization have been re-duced. After all the analysis cuts have been applied m]⋅BdL [T0 1 2 3 4- µ/N + µN11.11.21.31.4Forward FieldReverse FieldCombined Field(q/p)σ(q/p)/0 2 4 6 8 10 12- µ/N + µN1.151.21.251.31.351.4Forward FieldReverse FieldCombined FieldFig. 2. The charge ratio as a function of (t) of BdL, after all thetrack quality cuts and a (q/p)/σ(q/p) >2.8 and (b) as a function of(q/p)/σ(q/p) after all cuts and a BdL cut of 1.8. The vertical linesindicate the values used for the analysis cuts. Error bars are statisticalonly.we retain 2,739,349 events(0.608% acceptance), with1,530,719 µ+ and 1,208,530 µ− for a charge ratio of1.2666±0.0015(stat.)V. DISCUSSION OF ERRORSWe consider three specific systematic errors, theseare: non-perfect magnetic field inversion, cut-basederrors and remnant randomization.We have made the assumption that the systematicerror associated with geometric acceptance cancelswhen determining ra and rb (equations 3 and 4respectively). Had these cancellations been exact wewould expect ra=rb, instead we measure ra=1.2625and rb=1.2706. Half the difference between these twovalues, ±0.0041 is taken as the systematic uncertaintyassociated with the magnetic field inversion.The largest systematic uncertainty comes fromthe structure observed in the plot of charge ratioversus (q/p)/σ(q/p) in Fig. 2. Increasing the strengthof the applied (q/p)/σ(q/p) cut increases the charge4 J.K. DE JONG et al. MINOS CHARGE RATIOratio(decreases the randomization) and reaches amaximum value at (q/p)/σ(q/p) ≈3.5, it then fallsslightly and flattens off for (q/p)/σ(q/p) > 5.0.Classifying this bump as a randomization errorwould imply, counter-intuitively, that the chargeidentification is worse at large values(low momentum) of(q/p)/σ(q/p) than at smaller values(high momentum).The charge ratio was calculated for the peak region2.8< (q/p)/σ(q/p) <5.0 as 1.27444, and for the flatregion of the graph (q/p)/σ(q/p) >5.0 as 1.260. Themaximum deviation from the average charge ratio is0.0078, which is taken as an uncertainty.Monte Carlo studies suggest that the analysis miss-identifies the charge on 0.2555% of the events, whichimplies the true charge ratio should be 1.2682 (a changeof +0.0016). However, given the complexity of thedetector it is expected that the true miss-identificationrate will be larger in the data than in the Monte Carlosimulation. Further data to monte-carlo comparisonstudies indicate that the charge miss-identification indata is 2.3 times higher than in monte-carlo. The resultis a one-sided systematic of +0.0037.After all analytical selections the charge ratio mea-sured at the MINOS near detector is:R = 1.2666± 0.0015(stat.)+0.0096−0.0088(syst.). (6)VI. ATMOSPHERIC MUON CHARGE RATIOUsing the technique outlined in [9] the energy lostEloss by muons traversing the near detector overburdenhas been calculated as a function of reconstructed trackmomentum Eµ,det and zenith angle θ . For this analysiswe take the Near Detector cavern floor to be situatedat 123.8 meters above sea level(msl), and the roof at133.5 msl. Directly above the cavern hall lies 72.1 m ofDolomite/Shale bedrock ( CaMg(C03)2 w/ 8.0% H2Oby weight) at a density of 2.41 g/cm3, followed by 22.2meters of Glaciel till with a density of 2.29 g/cm3. Thisgives a flat vertical overburden of 224.6 meters of waterequivalent(mwe). The energy lost by muons traversingthe overburden increases with both detected momentumand zenith angle. The muon energy at the surface issimply:Eµ,0 = Eµ,det + Eloss(Eµ,det, θ). (7)The requirement that the muon track possesses acharge confidence value (q/p)/σ(q/p)>2.8, is a statementthat the track must bend significantly in the magneticfield. The detector’s magnetic field and spatial resolutionlimits the maximum detectable momentum for a muonin this analysis. Since MINOS is a shallow undergrounddetector with a low maximum detectable momentum, theEµ,0cos(θZ) distribution is narrow only about 30 GeV.The MINOS near detector measurement is observed tobe consistent with previous experiments and lower thanthe TeV scale measurement from the Far Detector. Aχ2/ndof fit test to the πK model, equation (2), wasperformed over fK /fπ space using the L3+C, MINOSnear and far detector charge ratio results. A χ2/ndofminimum of 0.474 is found at fπ=0.5488±0.0016 andfK=0.7021±0.011. The best fit curve to the data isplotted in Fig. 3.) [GeV]Zθcos(,0µE210 310− µ/N+ µN1.21.31.41.5K modelπFit to MINOS Near DetectorMINOS Far DetectorL3_CBESS−TeVFig. 3. Charge ratio as a function of Eµ,0cos(θ). The MINOS neardetector agrees very well with the L3+C measurements. The dashedline is the best fit value to the πK model.VII. CONCLUSIONThe atmospheric muon charge ratio has been mea-sured using 190.2 days of data at the MINOS neardetector to be 1.2666 ± 0.0015(stat.)+0.0096−0.0088 (syst.).The πK model was shown to fit both the near andfar detector data implying that the observed increasein charge ratio at the far detector is dominated by theincreased fraction of observed muons arising from kaondecay. The MINOS collaboration has collected 120 moredays of data which will be added to this dataset andpublished at a later date.VIII. ACKNOWLEDGEMENTSThis work was supported by the US DOE, the UKSTFC, the US NSF, the State and University of Min-nesota, the University of Athens, Greece and Brazil’sFAPESP and CNPq. We are grateful to the MinnesotaDepartment of Natural Resources, the crew of SoudanUnderground Laboratory, and the staff of Fermilab fortheir contributions to this effort.REFERENCES[1] T. Hebbeker C. Timmermans, Astropart. Phys 18, 107(2002)[2] S. Haino et al.(BESS-TeV), Phys. Lett. B594,35(2004)[3] P. Achard et al.(L3), Phys. Lett. B598,15(2004)[4] P. Adamson et al.(MINOS), Phys. Rev. D76,052003(2007)[5] J.K. de Jong et al.(MINOS) Seasonal Variations in the MINOSDetectors, These Proceedings[6] D.G. Michael et al.(MINOS),Nucl. Instrum. Meth.A596,190(2008)[7] T.K. Gaisser(1990), cambridge UK:Univ Pr. (1990) 279 p.[8] R. Fruhwirth, Nucl. Instrum. Meth/ A262 444(1987)[9] J. Reichenbacher J.K. de Jong,Calculation of the UndergroundMuon Intensity Crouch Curve from a Parameterization of theFlux at Surface Proceedings of the 30th ICRC(2007)

The Atmospheric Muon Charge Ratio at the MINOS Near Detector

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