Brancus, I M

CERN Document Server

29th International Cosmic Ray Conference Pune (2005) 6, 229232Monte Carlo simulations and semianalytical parameterisations of theatmospheric muon flux controlled by muon charge ratio measurementsperformed with WILLI detectorI.M. Brancus , B. Mitrica , A. Bercuci , G. Toma , J. Wentz, H. Rebeland M.Duma (a) IFIN-HH, RO-76900 Bucharest, POB MG-6, Romania(b) Forschungszentrum Karlsruhe, POB 3640, 76021 Karlsruhe, GermanyPresenter: I.M. Brancus (iliana@muon1.nipne.ro), rom-brancus-IM-abs2-he12-posterThe atmospheric muon flux have been simulated using the CORSIKA code for two different geographicalpositions (Bucharest: 44 deg N, 26 deg E and Hiroshima:34 deg N, 132 deg E). The simulations have beendone for different angles of incidence between 0 deg and 70 deg. The comparison between the simulationsand the experiment have been done using the measurements of the muon charge ratio with the WILLI detectorin Bucharest. The results of the Monte Carlo simulations of the muon flux for the geographical positions ofHiroshima and Bucharest are compared with the semi-analytical formulae of Judge and Nash, and of Gaisserfor different angles of incidence between 0 deg and 70 deg and with experimental results of the Bess experiment(vertical incidence). Various sensitivities of the approach of Judge and Nash, in particular to variations of thepion and kaon production spectra have been studied.1. IntroductionThe muon belongs to the family of elementary particles known as leptons. Like the electron it may be positivelyor negatively charged and has a spin . However its mass is about 100 MeV, more than two orders of magnitudelarger than that of the electron, and about one order of magnitude less than of the proton. It is produced mainlyby the decay of pions and kaons generated by high-energy collisions of cosmic rays with the atoms of the Earthatmosphere. Muons are unstable decaying to electrons and positrons and neutrinos (electron (  ) and muon(  ) neutrinos) with a half - life of 	 .2. The air shower simulation program CORSIKAThe simulation tool CORSIKA has been originally designed for the four dimensional simulation of extensiveair showers with primary energies around eV. The particle transport includes the particle ranges definedby the life time of the particle and its cross-section with air. The density profile of the atmosphere is handledas continuous function, thus not sampled in layers of constant density.Ionization losses, multiple scattering, and the deflection in the local magnetic field are considered. The decayof particles is simulated in exact kinematics, and the muon polarization is taken into account.In contrast to other air shower simulations tools, CORSIKA offers alternatively six different models for thedescription of the high energy hadronic interaction and three different models for the description of the lowenergy hadronic interaction. The threshold between the high and low energy models is set by default to ﬀﬂﬁﬃ ! GeV/n.230 I.M. Brancus et al3. Calculation of atmospheric muon fluxThe calculation of muon flux proceeds by a full 3D-simulation (CORSIKA). The simulations have been doneusing for the primary particle’s spectrum the expresion: "$#&%')(+*,- .0/.The differential particle flux"  1$2143657198:571<;=519>%'?A@,5,5B,5%'CﬀDEGF?7(,( (1)resulting from the simulation was calculated by dividing the number of particles detected by the surface of theparticle collection area ( ?@), solid angle, momentum bin size, and equivalent sampling time of the CR flux.0o≤Θ<10o∆   HIROSHIMAl   BUCHARESTFigure 1. Differential ux of the muons for HIKJMLONQPRHSI4. Semi-analytical approachesThere are several empirical approximations describing the fluxes in by analytical expressions like power-lawdistributions (see P.Grieder[4]). Recent approaches by T.K. Gaisser[1] display explicitly the dependence onprimary energy, but with complicated mathematical procedures and valid only for muon energies above 10GeV. This holds also for the simplification given in Gaisser’s Book:TU&V7W?A@55B5CﬀDE5%'XFCﬀDEY(,7- .[Z \^]`_ acb0dfe0cgRhji\& k9l \^]`_ acb0dfe.0mgRhjin(2)used for example by Unger[5]. In Fig.2 this formula is compared with the the results of the Monte Carlosimulations , displaying the disaggreement in particular at lower energies.Mone Carlo Simulations....WILLI 231The approach by Judge and Nash[2] uses as input the production spectra of parent pions and kaons and calcu-lates the flux resulting from pion and kaon decay by:op%q srt (+8p5Su5U,ﬂvwp5xpp 5?yz t \x p (3)oU{%' srt ([8{5u5,|v7}{5x{{5?yz t \x{ (4)Therexp<~ {andx are parameters accounting for tte propagation of the particles in the atmosphere. Theparameters8p<~ {are the normalisations of the pion and kaon production spectra. There are several otherparameters entering in the approximation: the absorption lengths of the primary particle  # , of the pions pand kaons {. There is clearly some influence, but in the present investigation the values have fixed along theoriginal proposal. Only the8p~ {values have been changed in order to adjust the calculated fluxes to the theresults of the Monte Carlo simulations and to experimental data from the BESS[3] experiment.0o≤Θ<10o∆   HIROSHIMAl   BUCHARESTH   GAISSERq   NASHP   BESS0o≤Θ<10o∆   HIROSHIMAl   BUCHARESTH   GAISSERq   NASHP   BESSFigure 2. Comparison of the results of Monte Carlo simulations and BESS data with predictions of simplied semi-analytical formulae. In the approach of Jugde and Nash  = 0.373 and G = 1.0 ( Fig. 1.a) and G = 0.373 and G =0,373 ( Fig. 1.b) is used.5. Test of the simulation program by experimental resultsThe Monte Carlo program outlined in chapt. 2 and to be used for calculations of the muon fluxes at variouslocations has been checked by experimental results of accurate muon charge ratio measurements[6]. Fig.3displays the comparison between measured results of the East -West effect performed with WILLI and withCORSIKA simulations. The values are compiled in tab.1.232 I.M. Brancus et alpµ [GeV/c]N(µ+) / N(µ-)WestEastpreliminary0.60.811.21.41.61.80.3 0.4 0.5 0.6 0.7 0.8 0.9 1Figure 3. Comparison of the muon charge ratio and the East -West effect with the CORSIKA predictionsTable 1. Compilation of the numerical values displayed in g.3Azimuth Momentum(GeV/c)  t # ﬀ &  Ł9RK0.36 35 0.89 0.680.50 35 0.95 0.88EAST 0.65 35 0.85 0.910.87 35 0.84 0.950.36 35 1.50 1.40.50 35 1.43 1.46WEST 0.65 35 1.06 1.320.87 35 1.23 1.366. Concluding remarksSemi-analytical approaches[7] are able to reproduce globally the results of Monte Carlo simulations and ex-perimental data, and in particular the approach of Judge and Nash does account for muon energies 4CﬀDE .However, these approaches can be hardly modified in order to take into account also finer effect like the influ-ence of the geomagnetic field. For that detailed Monte Carlo simulations have to be invoked.References[1] T.K. Gaisser, Astropart. Phys. 16(2002)285[2] R.J.R.Judge and W.F.Nash, Il Nuovo Cimento, XXXV-4(1965)999[3] M. Motoki et al, Astropart. Phys. 19(2003)113-126[4] P.K.Grieder, Cosmic Rays at Earth, Researcher’s Reference Manual and Data Book, Elsiver (2001)354-454[5] M.Unger, PhD thesis, Humboldt-Universitat zu Berlin, (2003)[6] I.M.Brancus et al, Nucl. Phys. A721(2003)1044c[7] B.Mitrica, Master Thesis, University Bucharest (2004)

Monte Carlo simulations and semianalytical parameterisations of the atmospheric muon flux controlled by muon charge ratio measurements performed with WILLI detector

Monte Carlo simulations and semianalytical parameterisations of the atmospheric muon flux controlled by muon charge ratio measurements performed with WILLI detector

Abstract

Similar works

Full text

Available Versions

CERN Document Server