1. Muon Monte Carlo: a versatile tool for lepton propagation through matter Dmitry Chirkin, LBNL, Berkeley, USA October 31, 2006, Dortmund University

2. Introduction Muon propagation: why do we need it? Muon/neutrino detectors?

3. Particles observed by neutrino detectors

4. Muon Monte Carlo A tool for muon propagation simulation

5. Structure of the program

6. Simulation of muon propagation Starting with E i Ending with E f f(E)dx P(E)dx Continuous losses Stochastic losses 1.0 v cut =0.05 E cut =500 MeV

7. Method of propagation Distribution of the final energy of the muons that crossed 300 m of Frejus rock starting with 100 TeV 0.05 10 -4 0.05 0.01 10 -3 10 -4

8. Method of propagation Distribution of the final energy of the muons that crossed 300 m of Frejus rock starting with 100 TeV 0.05 10 -4 0.05 0.01 10 -3 10 -4 0.05 0.01 10 -3 10 -4

9. Muon cross sections Ionization losses + knock-on electrons Bremsstrahlung Photonuclear Electron pair production Decay 10 TeV muon

10. Bremsstrahlung muons electrons

11. Photonuclear interaction Photon-nucleonPhotonuclear

12. Q2Q2 1 GeV 2 softhard photoproductionDIS GVDMCKMTALLM Bezrukov-BugaevButkevich-Mikheyev Abramowicz Levin Levy Maor 19911997 2002BB 1981 BB + Hard 03 Bugaev Shlepin ZEUS 94 Kokoulin 99 Nuclear effects DuttaSmirnov Muon propagator (MMC) settings: ph-nu settings

13. Mass effects Delta-correction to ionization (included into the ionization cross section) LPM suppression of the bremsstrahlung and direct electron pair production Dialectric suppression of the bremsstrahlung cross section

14. Moliere scattering

15. Electron, tau, and monopole muonelectron taumonopole

16. Neutrino propagation Neutrino cross sections Also:       oscillations Earth density profile is implemented

17. Interpolation errors Distribution of the final energy of the muons that crossed 300 m of Frejus rock starting with 100 TeV Comparison: parameterized vs. non-parameterized Interpolation precision: (e pa -e np )/e pa Interpolation order: g=2,…6 v cut =0.01v cut =10 -4 E low =10 TeV

18. Algorithm errors: average propagation Deviation from average energy loss (with v cut =1) Propagating 4 10 6 muons through 100 m of Frejus rock

19. Algorithm errors: survival probability 10 6 muons with energy 9 TeV propagated through 10 km of water

20. Comparison with other codes: MUM (MUons + Medium) MUM code by E. Bugaev, I. Sokalski, S. Klimushin

21. Spectra of the secondaries MMC MUMLOH LIP

22. Number and energy of secondaries

23. Implementation for muon/neutrino detector 3 propagation regions: before the detector: propagation with fixed v cut inside the detector: propagation with fixed v cut or E cut after the detector: fast propagation with v cut =1.0

24. Parameterization of atmospheric lepton fluxes withCORSIKA Primaries with Z=1,…,26:Poli-gonato composition model Run CORSIKA Parameterize simultated fluxes with With corrections for zenith angle, muon energy loss and decay

25. Parameterization of the atmosphere

26. Muon energy losses

27. Atmospheric lepton fluxes muonsmuon neutrinoselectron neutrinos

28. Integrated fluxes

29. Quality of the fits fit qualitystability of the result

30. Things to remember mmc was written in 2000 and has been updated a few times with new cross sections and features mmc has been used by AMANDA and now IceCube, also in data analysis of Frejus mmc is available at http://icecube.berkeley.edu/~dima/work/MUONPR mmc stands for Muon Monte Carlo and propagates muons perhaps more appropriate name is ALMC: All Lepton Monte Carlo, since it propagates muons, taus, electrons, all neutrinos mmc can also stand for monopole monte carlo

31. Applet demonstration