MINOS is the first large magnetic detector deep underground and is the first to measure the muon charge ratio with high statistics in the region near 1 TeV.[1] An approximate formula for the muon charge ratio can be expressed in terms of {eta}{sub {pi}} = 115 GeV, {eta}{sub K} = 850 GeV and E{sub {mu}}{sup surface}The implications for K production in the atmosphere will be discussed

/Argonne

Goodman, Maury

Schreiner, Philip

U., /Argonne /Benedictine

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30TH INTERNATIONAL COSMIC RAY CONFERENCEInterpretation of the atmospheric muon charge ratio in MINOSPHILIP SCHREINER  AND MAURY GOODMAN FOR THE MINOS COLLABORATION Argonne National Lab,Benedictine Universitymaury.goodman@anl.govAbstract: MINOS is the rst large magnetic detector deep underground and is the rst to measurethe muon charge ratio with high statistics in the region near 1 TeV.[1] An approximate formula for themuon charge ratio can be expressed in terms of  = 115 GeV,  = 850 GeV and 	 ﬁﬀ . Theimplications for K production in the atmosphere will be discussed.IntroductionDefining Aﬂﬃ  "!$#%'&)(+* ,-.+/10203547698 (1)the muon energy spectrum underground can be ex-pressed as [2]:: ;=<?>: ;&->A@ﬂCB##ED *  FHGJILKNMOPRQD "!  =ST%#ED *  FUGVILKMWOPX Y(2)where the two terms give the contributions ofcharged pions and kaons; the values of Z @[]\^`_TaWb are close to the energies where the prob-ability of meson interaction and decay are equal:Zc = 115 GeV and Zd = 850 GeV. The zenith an-gle is e and in experiments with a flat overburden,the largest muon intensity comes at .9f0e@#. Itis possible to generalize this equation to separatelyconsider gVh and g(by introducing constants i cand i d :: ;=<h>: ;&->@ﬂBic#ED *  jFG+kILKMTO  lnmJopD `!  'Sq%)rid#ED *  jFG+kILKMTOsl_mJopY: ;=<(>: ;&->t@ﬂCB#vuiTc#ED *  FGwILKNMO N jlnmJopD "!  =ST%xrzy#vuiqd|{#ED *  jFGwILKNMOsl_mJopYThe measured charge ratio in a bin of surface muonenergy and zenith angle can then be expressed as<-k<-w@BiTc#ED *  FGkILKMTO N jlnmJopD "!  =ST%)riqd#ED *  FGkILKNMOsNl_mJopYaB#vuic#ED *  FGwILKNMO N jlnmJopD "!  =ST%)r}yj#vuid{#ED *  jFGwILKNMWOsl_mJopY(3)An interesting feature of Equation 3 is that it de-pends only on the product&~LWW+L-.+f0e and nototherwise on E or e . This combination of termscontrols the relative portions of interaction and de-cay for both  ’s and K’s. Thus at a fixed value of&~LWW+L-.+f0e the ratio of g ’s from  ’s and K’sis constant. Equation 3 postulates an energy in-dependent h a (ratio related to iqc , an energyindependent Łh a (ratio related to iqd and anenergy independent  a  ratio embodied in the0.054. These are all reasonable as a consequenceof Feynman scaling. (At energies above 10 TeV,charm and the changing cosmic ray chemical com-position could also affect the muon charge ratio.)In this simple but powerful parameterization, thecharge ratio depends only on the relative number of ’s and K’s that contribute to muons measured un-derground. The relative contribution to the muonintensity from  ’s and K’s is affected by the rel-ative probability of hadron interaction and decay,which vary with both energy and angle. It variesas a function of energy because of the hadron life-times, and it varies as a function of angle becauseof the interaction probability in the atmosphere.FERMILAB-CONF-07-174CHARGE RATIO INTERPRETATIONBut as can be seen from inspection of Equation 3,at any xed value of&~LWNW+L-.9f0e , the ratio ofmuons from  and K decay is also fixed, even if Eor e is varied.Measurement of zq+T9 =H under-groundThe energy of a muon underground can be re-lated to the energy at the surface by&~LWNW+L@&WLNWD&vN~j~The energy loss for muons inMINOS has been calculated using the energy lossequation,;&a;@ y¡&{D£¢qy¡&{r)&. Many highenergy muons which do reach the detector do notbend enough in MINOS’ magnetic field to measurethe curvature and hence charge. This can be quan-tified in terms of the maximum detectable momen-tum, which depends on the geometry of the trackthrough the detector [3]. A magnetic detector un-derground can measure the charge of muons thathave the lowest energies&WLNWwhen theyreach the detector.MINOS has made measurements of the charge ra-tio in the far detector [1] which is 710 meters un-derground or 2070 m.w.e., and also has yielded apreliminary result using its near detector [4] whichis 100 m underground or 225 m.w.e. (Note that thefar detector is under a small ridge.)As a crude approximation, we can consider thecase when: 1) the parameter a is constant, 2) theparameter b is zero. 3) the rock density is con-stant in all directions, 4) the surface is flat and5) the maximum detectable momentum is negligi-ble compared to the energy loss from the surface.The first four assumptions are equivalent to sayingthat the energy loss is proportional to the overbur-den which only depends on zenith angle. In thatcase&N~j~@&¤A¥a.9f0e where&¤A¥is the min-imum energy loss for a vertical cosmic ray muon.The fifth assumption implies that the undergroundenergy of muons used for the charge ratio mea-surement in MINOS was much smaller than theirsurface momentum. The MINOS maximum de-tectable momentum, defined at one sigma, is dis-cussed in these proceedings [3] and a cut was cho-sen at 2.2 sigma.In the limit corresponding to these assumptions,the frequency distribution in&~LWW+L-.+f0e thatwe would measure is a delta function at&¦¤A¥. Atlarge zenith angles, the surface energy increasesdue to the .+f0e dependence of the slant depth, but&~LWW+L-.+f0e is constant.This can be compared with the measured E and& ~LWW+L-.+f0e distributions from MINOS for thefar detector in Figure 1 and for a preliminary re-sult from the near detector in Figure 2. Both&~LWW+L-.+f0e distributions are much narrowerthan the corresponding&~LW9Ldistributions. Thelargest contribution to the width of the measured&~LWW+L-.+f0e distribution for the far detector isthe b(E) term in the energy loss, while the largestcontribution to the much narrower near detectordistribution is the larger ratio of maximum de-tectable momentum to energy loss in the overbur-den.Implication for KaonsThe charge ratio of muons that we measure from decay is § c = Q (HQand from kaon decay i d= X (HX. The value 0.054 is related to the relativekaon/pion intensity in Gaisser’s model.[2]A fit was made to MINOS data and the publishedL3+C ratio data [5] to this parameterization for r.A chi-square fit was done in 178 bins of&x~LWNW+L-vs. .9f0e . The fit gave iqc @ `!¨SS'S|© `!   =ªandid@ `! ««ﬁ¬1©­ "!  ' =¬. The errors in i c and i d arecorrelated. [1] Using these numbers, the chargeratio versus&~LW9L-.+f0e is plotted in Figure 3.These values for i c and i d imply that the muoncharge ratio from pion decay is § @#!¨ªSand thatthe muon charge ratio from kaon decay is about§@ª`!  .As noted above, there is some&x~LWNW+L-.9f0e vari-ation in the MINOS far detector data at a value of&~LWW+L-.+f0e where the curve in Figure 3 is vary-ing. We have performed a fit solely to the MINOSfar detector data, and obtain i c = `!¨ST%=®©¯ `!  `#Wªand i d = `!°¬T =ª¦©± "!  %'®, which imply § c @#!¨ªªand § d @ª²! ³«. The errors on i c and i d in thisfit are almost completely correlated and are shownin Figure 4. A fit which also incorporates the pre-liminary MINOS near detector charge ratio will bepresented at the 30th ICRC.Equation 3 has asymptotic values at both lowenergy and high energy. Note that both val-30TH INTERNATIONAL COSMIC RAY CONFERENCEues have contributions from both  and K de-cays. For the above MINOS-only fit, the low&~LW9L-.+f0e charge ratio is § @#!¨ª'¬and thehigh&~jW+L-.+f0e charge ratio is § @#'! %ﬁS. Theparameterization does contain enough physics to(so far) satisfactorily represent the world’s under-ground muon charge ratio data. Furthermore, it is areasonable way to parameterize the energy depen-dency of the charge ratio, and seems preferable toa linear fit in E or ´ fµ&. We suggest that the newMINOS data, equation 3, and the fitted values forthe model parameters near 1 TeV will be useful inthe next round of atmospheric neutrino modelingin this energy range. It is also now apparent thatfuture precise muon charge ratio data in the 0.2-0.6 TeV energy range will be useful for verifyingthe&~LWNW+L-.+f0e dependency of the charge ratio.Our fits to §c give values near expectation [6]. Ourfit to the §d @ Łh a (charge ratio in atmo-spheric showers yield values just above 2. It isclearly difficult to directly measure this ratio. Eq. 3provides a direction for future study of this subject.AcknowledgmentsThis work is supported by US Department of En-ergy and National Science Foundation, the UK Par-ticle Physics and Astronomy Research Council,and the University of Minnesota. Operations of theFermilab beam are possible only through the largeamount of work of many collaborators and Fermi-lab employees. We wish to thank the MinnesotaDepartment of Natural Resources for use of thefacilities of the Soudan Underground State Park,and also the large crews of workers who helpedconstruct the detector and its components, and themine crew for help in operating the detector.References[1] P. Adamson et al., “Measurement of the At-mospheric Muon Charge Ratio at TeV Ener-gies with MINOS,” to be published; S. Muf-son for MINOS, “Measurement of the Atmo-spheric Muon Charge Ratio with the MINOSFar Detector”, these proceedings.[2] T. Gaisser, “Cosmic Rays and ParticlePhysics”, Cambridge University Press, 1990.Energy E (GeV)500 1000 1500 2000 2500 3000 3500 4000 4500 5000Events / 8 GeV Bin020004000600080001000012000Surface Energy)θEcos(Figure 1: Distribution of E and&x~LWNW+L-.9f0e forMINOS data muons in the far detector, after cuts.Figure 2: Preliminary distribution of E and&~LWW+L-.+f0e for MINOS data muons in the neardetector, after cuts.[3] M. Goodman for MINOS, “Maximum De-tectable Momentum in MINOS”, these pro-ceedings.[4] J.K. de Jong for MINOS, “Measurement ofthe Atmospheric Muon Charge Ratio with theMINOS Near Detector”, these proceedings.[5] P. Achard et al., Phys. Lett. B 598, 15 (2004).[6] V. Naumov, private communication.CHARGE RATIO INTERPRETATIONFigure 3: Behavior of Equation 3 for&x~LW9L-.+f0e from 1 GeV to 10 TeV. The critical energies of  ’sand  ’s are shown. The regions where the MINOS near and far detectors are sensitive are also indicated.Values of iTc and iqd from the MINOS/L3+C fit were used.Figure 4: Distribution of ¶surface in the i c - i d plane, showing the error of the MINOS only fit and thecorrelation between i c and i d .

Interpretation of the atmospheric muon charge ratio in MINOS

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Interpretation of the atmospheric muon charge ratio in MINOS

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