Cathedral and Castle in Plock Muons in the

Cathedral and Castle in Plock Muons in the Cosmic Radiation J. Kempa and A. Krawczynska Warsaw University of Technology Off-Campus Płock

A review of measurements of the high muon energy spectra for altitudes close to the sea level and different directions performed with devices placed at various geomagnetic latitudes is presented. The muon spectra and the muon charge ratio, defined as the ratio of positive to negative muon fluxes, are discussed.

MOTIVATION

The sea level average differential muon spectrum at 0 o

Muons in L 3

Measurements of the east - west asymmetry of the cosmic muon flux in Hanoi Pham Ngoc Diep et al. 2004 a) at Θ = 50 o b) at Θ = 65 o

Theoretical Aspect Majority of theoretical calculations of muons and neutrinos in the atmosphere has been done using the following logical schema: Primary Spectrum and Primary Composition High Energy Interaction Model Muon and Neutrino Fluxes Muon charge ratio and electron to muon neutrino ratio

Outline of the talk: 1. Introduction 2. Low energy muons 3. Muon charge ratio 4. High energy muons 5. Conclusions

Introduction

Cosmic-ray muons and neutrinos originate from the decay of pions and kaons produced by the interactions of high-energy primary nuclei Acr with atmospheric ones Aair. Acr + Aair ± , K 0 + + + µ + e+ + e + µ - - + - e - + e + . .

Low energy muons (below 100 Ge. V/c)

Absolute differential muon fluxes at various zenithal angles The absolute differential muon data in the energy region 0. 2 Ge. V/c to 100 Ge. V/c are fitted by parabola on a log – log scale: log I ( ) = a ln 2 p + b ln p + c , where p is the muon momentum in Ge. V/c.

The values of the parameters a, b, c used for vertical and horizontal showers. As an example the values for 20 o are presented. Angle Vertical 0 o Horizontal 88. 5 o 20 o a b c -. 1292 . 0005 -. 266 . 002 -2. 600 0. 002 -. 175 . 002 +. 998 . 002 -8. 60 0. 01 -. 1245 -. 2659 -2. 5621

For other angles the values of the a and b can be found from the following approximation : Y = p 1/(1/ + p 2 ) + p 3 + p 4 exp(-p 5 ) , where Y means a or b respectively and is the zenithal angle in degrees. The coefficients p 1 , p 2 , p 3 , p 4 and p 5 are: pi a b p 1 - 0. 8816 10 p 2 - 0. 111710 -3 - 0. 989110 -4 p 3 - 0. 1096 + 4. 0395 p 4 - 0. 196610 -1 - 4. 3118 p 5 + 0. 204010 -1 - 0. 923510 -3 -4 + 0. 416910 -2

The following approximation for parameter c can be used: c = p 1 2 + p 2 + p 3 + p 4 exp(-p 5 ) , where is the zenithal angle in degrees. The coefficients p 1 , p 2 , p 3 , p 4 and p 5 are: pi c p 1 - 0. 351610 -3 p 2 +0. 886110 -2 p 3 - 2. 5985 p 4 - 0. 874510 -5 p 5 - 0. 1457

The sea level average differential muon spectrum at 0 o

The sea level average differential muon spectrum at 0 o new data

The sea level average differential moun spectrum at 30 o

The sea level differential positive muon spectrum at 0 o assumed that the ratio + / - is equal to 1. 27 J. Kempa, A. Krawczynska Nucl. Phys. B (Proc. Suppl. ) 151 (2006)

The sea level differential negative muon spectrum at 0 o assumed that the ratio + / - is equal to 1. 27 J. Kempa, A. Krawczynska Nucl. Phys. B (Proc. Suppl. ) 151 (2006)

The collected data of the experimental results of the muon charge ratio for four different experiments and four different rigidity cutoff. Data from Allkofer et al. 1968, Sanuki et al. 2002, Kremer et al. 1999.

+ / =f(E ) M. Goodman 2007 HONDA Lipari

Data plots (after Goodman 2007 ) In the formula, +/ - only depends on Esurfacecosq

In theoretical works about muons we find opposite interpretations of muons data: In the paper J. J. Beatty et al. , 2004 the law energy muon data do not agree precisely with calculations. G. Fiorentini et al. , 2001 proves that from different models it is possible to choose one, which gives the good fit for the law energy experimental muon data. J. Wentz et al. , 2003 state that GEISHA and VENUS do not describe + / - ratio for low energies. In the paper V. Plyaskin, 2003 , results of the GEISHA and GEANT + / - ratio calculations fit experimental data.

High energy muons (above 200 Ge. V/c)

The absolute differential muon fluxes are fitted by the function: (following the T. K. Gaisser 1990)

Integral muon energy spectra

CONCLUSION There a lot of new data of muons and neutrinos that has been gathered recently from new experiments such as L 3+C, CAPRICE, BESS, HEAT, Super-Kamiokande, MINOS FD, Cosmo. Aleph. It seams that we are able to understand describe average muon fluxes in the atmosphere for the momentum higher than 10 Ge. V/c (see: Kempa and Krawczynska 2005, Hebbeker and Timmermans 2002)

There is still a lot of confusion about the measuring of the moun fluxes of very low muon energies of different angles and depths in the atmosphere. There are problems with gathering the data for law energy muons because the fluxes are functions of rigidity cutoff and azimuthal angles (East-West effect). The similar problem exists in measuring neutrinos. The constancy of the total high energy muon fluxes shows the main role of the cascading process in the atmosphere. Correlation between + / - values and rigidity cutoff shows that for higher rigidity the + / - is smaller. There are differences between interpretations of the experimental data from different authors.