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Prompt and direct muon production in the atmosphere and very high energy inclined EAS at sea level
Nuclear Physics B (Proc. Suppl.) 151 (2006) 303–306 www.elsevierphysics.com
Prompt and direct muon production in the atmosphere and very high energy inclined EAS at sea level O.G. Ryazhskayaa∗ , L.V. Volkovaa† and G.T. Zatsepina‡ a
Institute for Nuclear Research, Russian Academy of Sciences, 60th October Anniversary pr. 7a, Moscow, 117312 Russia Prompt muons are produced through decays of charmed particles and direct muons are produced through decays of particles with life-time much less than that of charmed particles (for example, resonances). The ratios of the number of particles in showers initiated by bremsstrahlung of these muons to those from decays of π ◦ mesons from primary nucleon interactions in the atmosphere are estimated for the primary nucleon energy 10 19 eV. The calculations are made at θ ∼ 45◦ − 72◦ to the vertical at sea level. At large angles prompt and direct muons could be completely responsible for EAS measured at the sea level.
1. Introduction The GZK effect [1,2] is discussed very widely now in the community of physicists working in the field of cosmic ray physics and astrophysics. But to interpret data [3–5] on EAS in a proper way it is necessary to know very well the nature of nuclear interaction act for nucleon-air nucleus interactions at energies greater than 1019 eV. What is the possible contribution of charmed particles and direct muons to EAS at very high energies? This problem is discussed in this work.
resonances). Muons, electrons or gamma rays are produced in decays or as a result of interactions of these particles with air nuclei (Figure 1). Showers produced by these particles can be measured deep in the atmosphere using an experimental apparatus.
2. A scheme of EAS production in the atmosphere In interactions of primary nucleons (N) with air nuclei (Aair ) in the atmosphere different particles are produced, for example, pions (π), kaons (K), charmed particles (D-mesons, Λc -baryons), particles with a very short life-time (as, for example, ∗ thanks RFBR (grant 03-02-16416-a), Grant of the President of Russian Federation for support of leading scientific schools (grant LSS-1782.2003.2) and RFBR (grant 03-0216436-a) † thanks RFBR (grant 04-02-16757-a), Grant of the President of Russian Federation for support of leading scientific schools (grant LSS-1782.2003.2) and RFBR (grant 03-0216436-a) ‡ thanks Grant of the President of Russian Federation for support of leading scientific schools (grant LSS1782.2003.2) and RFBR (grant 03-02-16436-a)
0920-5632/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2005.07.055
Figure 1. An imaginary scheme of shower production in the atmosphere.
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O.G. Ryazhskaya et al. / Nuclear Physics B (Proc. Suppl.) 151 (2006) 303–306
3. Muon fluxes at sea level The differential energy spectra of muons produced through decays of pions and kaons used in this calculation were obtained in [6]: we recalculate these spectra here using the index γ=1.7 in the primary integral nucleon spectrum instead of γ=1.65 as used in [6]. The kinematical equations for particle propagation through the atmosphere are solved with cross-sections for pion and kaon production found at accelerators and it is assumed that scaling is true in the fragmentation region in the entire considered energy interval. Nuclear interactions, decays and energy losses are taken into account. Many papers have been devoted to the consideration of charm production at high energies (for example, [7–9]). We use here the prompt muon spectra calculated in [10] on the basis of data on charm production inclusive cross-sections obtained in experiments at accelerators, the data on cosmic ray muons from the experiment with roentgen-emulsion camera of MSU [11], on the results of NLO calculations and calculations made in the frame of QGSM-model of QCD (see [10]). Estimates of direct muon fluxes can only be made quite qualitatively: we have no experimental information on very short lived particle production processes at such high energies that are of interest in this work. The 25% uncertainties in prompt muon contributions to muon flux at ∼60 TeV [11] can be considered as a possible maximum direct muon contribution. At higher energies very short lived particles responsible for direct muons begin to give the main contribution to the whole muon flux at sea level [12]. The differential energy spectra of muons Pµ (Eµ , θ) produced in the atmosphere and arriving at sea level at an angle θ to the vertical (multiplied muon energy Eµ cubed) are shown in Figure 2. 4. Ratios of number of particles in showers from muons to those from π ◦ -mesons The cross-section for π ◦ -meson production in a nucleon interaction is much larger than that for charmed particle or very short living parti-
Figure 2. The differential energy fluxes (multiplied by energy cubed) of cosmic ray muons arriving at sea level: the full curves are muons from pion and kaon decays (”conventional”) and the dashed curves are for muons from charmed particle decays (”prompt”) for particles arriving at sea level in the vertical (θ = 0◦ ) and horizontal (θ = 90◦ ) directions; the dashed-pointed curve is for muons from very short living particles (”direct”); the dotted curve is for muons produced by γ-rays from π ◦ -decays [13] .
cle production. Prompt muons and direct muons give photons in bremsstrahlung. These photons are produced much lower in the atmosphere than photons from the decays of π ◦ -mesons. Thus showers from them are attenuated down to sea level in the atmosphere much less than those from π ◦ -mesons. These photons from muons transfer the energy of a primary particle deeper in the atmosphere. The ratio, R, of the number of particles in showers arriving at sea level at an angle, θ, to the vertical from photons produced by the bremsstrahlung of muons to that from π ◦ -meson decays estimated in this paper is shown in Figure 3 (the curve is marked ”γ”). In our calculations we suppose that spectra of produced secondary particles have scaling character in the entire considered energy interval. But if scaling violation is similar for pions (no big change takes place at x = E secondary /E primary ∼
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0.05 ÷ 0.15 which gives the main contribution in cosmic ray calculations because of very quickly falling fluxes with energy increase) and other secondary particles then this braking can not noticeably change the ratios discussed above.
5. Ratios of particles in showers initiated by electrons from charmed particle decays to those from π ◦ -mesons The ratio, R, of the number of particles in showers from electrons produced in charmed particle decays and arriving at sea level at an angle θ to the vertical to those from π ◦ -meson decays estimated in this work is given in Figure 3 (the curve is marked ”e”).
6. Conclusion Figure 3 shows that the contribution of prompt and direct muons in showers at sea level begins to be remarkable (∼10%) at zenith angle ∼ 70◦ and increases very quickly with increasing zenith angle: at 71◦ this contribution is ∼50% and becomes dominant very soon (≥ 72◦ ). We made all the above estimates for a primary nucleon energy of 1019 eV. The ratio of the number of particles in showers from prompt electrons arriving at sea level to those in showers from π ◦ meson decays is larger than that of particles in showers from direct and prompt muons at zenith angles < 65◦ but this ratio is only ∼ 0.2%. Thus, it is clear that it is important to take carefully into account the mechanisms of charmed particle production and direct muon production when we deal with calculations of the characteristics of EAS at sea level at inclined angles at high energies. It is to be noticed that the results discussed above have a character of an arbitrary estimation: for such high energies as considered here, we have no experimental information on the mechanisms of very short lived particle production. We suggest that at least the scaling behaviour of differential cross-sections has the same characteristics for pion, charmed particle and processes of direct muon production.
Figure 3. The ratios of the number of particles in showers from prompt and direct muon bremsstrahlung (the curve marked ”γ”) and of particles in showers from electrons produced in charmed particle decays (the curve marked ”e”) arriving at sea level at different angles θ to the vertical to those in showers from π ◦ -decays
REFERENCES 1. K.Greisen, Phys. Rev. Lett. 16 (1966) 748. 2. G.T. Zatsepin and V.A. Kuzmin, JETP Lett. 4 (1966) 99, (Pis’ma Zh. Eksp. Teor. Fiz. 4, (1966) 144). 3. M. Takeda et al., Phys. Rev. Lett. 81 (1998) 1163. 4. M.A. Lawrence, R.J.O. Reid and A.A. Watson, J. Phys.G: Nucl. Part. Phys.17 (1991) 733. 5. B.A. Afanasiev et al., Proc. Int. Symp. on Extremely HE Cosmic Rays: Astrophysics and Future Observatories, 1996, Ed. by Nagano,
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p. 32. 6. L.V. Volkova, G.T. Zatsepin and L.A. Kuz’michev, Sov. J. Nucl. Phys. 29 (1979) 645. 7. E. Zas, F. Halzen and R.A. Vazquez, Astropart. Phys. 1 (1993) 297. 8. V.A. Naumov, T.S. Sinegovskaya and S.I. Sinegovsky, Nuov. Cim. A 111 (1998) 129. 9. M. Thunman, G. Ingelman and P. Gondolo, Astroparticle Physics 5 (1996) 309. 10. L.V. Volkova and G.T. Zatsepin, Phys. of Atomic Nuclei 64 (2001) 266. 11. G.T. Zatsepin, N.P. Il’ina, N.N. Kalmykov et al., Izvestiya RAS, ser. Fiz. 61 (1997) 559. 12. L.V. Volkova, Physics of Atomic Nuclei 67 (2004) 2062. 13. V.A.Kudryavtsev, O.G. Ryazhskaya and O. Saavedra, Nuov. Cim. 21C (1998) 119.
Prompt and direct muon production in the atmosphere and very high energy inclined EAS at sea level O.G. Ryazhskayaa∗ , L.V. Volkovaa† and G.T. Zatsepina‡ a
Institute for Nuclear Research, Russian Academy of Sciences, 60th October Anniversary pr. 7a, Moscow, 117312 Russia Prompt muons are produced through decays of charmed particles and direct muons are produced through decays of particles with life-time much less than that of charmed particles (for example, resonances). The ratios of the number of particles in showers initiated by bremsstrahlung of these muons to those from decays of π ◦ mesons from primary nucleon interactions in the atmosphere are estimated for the primary nucleon energy 10 19 eV. The calculations are made at θ ∼ 45◦ − 72◦ to the vertical at sea level. At large angles prompt and direct muons could be completely responsible for EAS measured at the sea level.
1. Introduction The GZK effect [1,2] is discussed very widely now in the community of physicists working in the field of cosmic ray physics and astrophysics. But to interpret data [3–5] on EAS in a proper way it is necessary to know very well the nature of nuclear interaction act for nucleon-air nucleus interactions at energies greater than 1019 eV. What is the possible contribution of charmed particles and direct muons to EAS at very high energies? This problem is discussed in this work.
resonances). Muons, electrons or gamma rays are produced in decays or as a result of interactions of these particles with air nuclei (Figure 1). Showers produced by these particles can be measured deep in the atmosphere using an experimental apparatus.
2. A scheme of EAS production in the atmosphere In interactions of primary nucleons (N) with air nuclei (Aair ) in the atmosphere different particles are produced, for example, pions (π), kaons (K), charmed particles (D-mesons, Λc -baryons), particles with a very short life-time (as, for example, ∗ thanks RFBR (grant 03-02-16416-a), Grant of the President of Russian Federation for support of leading scientific schools (grant LSS-1782.2003.2) and RFBR (grant 03-0216436-a) † thanks RFBR (grant 04-02-16757-a), Grant of the President of Russian Federation for support of leading scientific schools (grant LSS-1782.2003.2) and RFBR (grant 03-0216436-a) ‡ thanks Grant of the President of Russian Federation for support of leading scientific schools (grant LSS1782.2003.2) and RFBR (grant 03-02-16436-a)
0920-5632/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2005.07.055
Figure 1. An imaginary scheme of shower production in the atmosphere.
304
O.G. Ryazhskaya et al. / Nuclear Physics B (Proc. Suppl.) 151 (2006) 303–306
3. Muon fluxes at sea level The differential energy spectra of muons produced through decays of pions and kaons used in this calculation were obtained in [6]: we recalculate these spectra here using the index γ=1.7 in the primary integral nucleon spectrum instead of γ=1.65 as used in [6]. The kinematical equations for particle propagation through the atmosphere are solved with cross-sections for pion and kaon production found at accelerators and it is assumed that scaling is true in the fragmentation region in the entire considered energy interval. Nuclear interactions, decays and energy losses are taken into account. Many papers have been devoted to the consideration of charm production at high energies (for example, [7–9]). We use here the prompt muon spectra calculated in [10] on the basis of data on charm production inclusive cross-sections obtained in experiments at accelerators, the data on cosmic ray muons from the experiment with roentgen-emulsion camera of MSU [11], on the results of NLO calculations and calculations made in the frame of QGSM-model of QCD (see [10]). Estimates of direct muon fluxes can only be made quite qualitatively: we have no experimental information on very short lived particle production processes at such high energies that are of interest in this work. The 25% uncertainties in prompt muon contributions to muon flux at ∼60 TeV [11] can be considered as a possible maximum direct muon contribution. At higher energies very short lived particles responsible for direct muons begin to give the main contribution to the whole muon flux at sea level [12]. The differential energy spectra of muons Pµ (Eµ , θ) produced in the atmosphere and arriving at sea level at an angle θ to the vertical (multiplied muon energy Eµ cubed) are shown in Figure 2. 4. Ratios of number of particles in showers from muons to those from π ◦ -mesons The cross-section for π ◦ -meson production in a nucleon interaction is much larger than that for charmed particle or very short living parti-
Figure 2. The differential energy fluxes (multiplied by energy cubed) of cosmic ray muons arriving at sea level: the full curves are muons from pion and kaon decays (”conventional”) and the dashed curves are for muons from charmed particle decays (”prompt”) for particles arriving at sea level in the vertical (θ = 0◦ ) and horizontal (θ = 90◦ ) directions; the dashed-pointed curve is for muons from very short living particles (”direct”); the dotted curve is for muons produced by γ-rays from π ◦ -decays [13] .
cle production. Prompt muons and direct muons give photons in bremsstrahlung. These photons are produced much lower in the atmosphere than photons from the decays of π ◦ -mesons. Thus showers from them are attenuated down to sea level in the atmosphere much less than those from π ◦ -mesons. These photons from muons transfer the energy of a primary particle deeper in the atmosphere. The ratio, R, of the number of particles in showers arriving at sea level at an angle, θ, to the vertical from photons produced by the bremsstrahlung of muons to that from π ◦ -meson decays estimated in this paper is shown in Figure 3 (the curve is marked ”γ”). In our calculations we suppose that spectra of produced secondary particles have scaling character in the entire considered energy interval. But if scaling violation is similar for pions (no big change takes place at x = E secondary /E primary ∼
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0.05 ÷ 0.15 which gives the main contribution in cosmic ray calculations because of very quickly falling fluxes with energy increase) and other secondary particles then this braking can not noticeably change the ratios discussed above.
5. Ratios of particles in showers initiated by electrons from charmed particle decays to those from π ◦ -mesons The ratio, R, of the number of particles in showers from electrons produced in charmed particle decays and arriving at sea level at an angle θ to the vertical to those from π ◦ -meson decays estimated in this work is given in Figure 3 (the curve is marked ”e”).
6. Conclusion Figure 3 shows that the contribution of prompt and direct muons in showers at sea level begins to be remarkable (∼10%) at zenith angle ∼ 70◦ and increases very quickly with increasing zenith angle: at 71◦ this contribution is ∼50% and becomes dominant very soon (≥ 72◦ ). We made all the above estimates for a primary nucleon energy of 1019 eV. The ratio of the number of particles in showers from prompt electrons arriving at sea level to those in showers from π ◦ meson decays is larger than that of particles in showers from direct and prompt muons at zenith angles < 65◦ but this ratio is only ∼ 0.2%. Thus, it is clear that it is important to take carefully into account the mechanisms of charmed particle production and direct muon production when we deal with calculations of the characteristics of EAS at sea level at inclined angles at high energies. It is to be noticed that the results discussed above have a character of an arbitrary estimation: for such high energies as considered here, we have no experimental information on the mechanisms of very short lived particle production. We suggest that at least the scaling behaviour of differential cross-sections has the same characteristics for pion, charmed particle and processes of direct muon production.
Figure 3. The ratios of the number of particles in showers from prompt and direct muon bremsstrahlung (the curve marked ”γ”) and of particles in showers from electrons produced in charmed particle decays (the curve marked ”e”) arriving at sea level at different angles θ to the vertical to those in showers from π ◦ -decays
REFERENCES 1. K.Greisen, Phys. Rev. Lett. 16 (1966) 748. 2. G.T. Zatsepin and V.A. Kuzmin, JETP Lett. 4 (1966) 99, (Pis’ma Zh. Eksp. Teor. Fiz. 4, (1966) 144). 3. M. Takeda et al., Phys. Rev. Lett. 81 (1998) 1163. 4. M.A. Lawrence, R.J.O. Reid and A.A. Watson, J. Phys.G: Nucl. Part. Phys.17 (1991) 733. 5. B.A. Afanasiev et al., Proc. Int. Symp. on Extremely HE Cosmic Rays: Astrophysics and Future Observatories, 1996, Ed. by Nagano,
306
O.G. Ryazhskaya et al. / Nuclear Physics B (Proc. Suppl.) 151 (2006) 303–306
p. 32. 6. L.V. Volkova, G.T. Zatsepin and L.A. Kuz’michev, Sov. J. Nucl. Phys. 29 (1979) 645. 7. E. Zas, F. Halzen and R.A. Vazquez, Astropart. Phys. 1 (1993) 297. 8. V.A. Naumov, T.S. Sinegovskaya and S.I. Sinegovsky, Nuov. Cim. A 111 (1998) 129. 9. M. Thunman, G. Ingelman and P. Gondolo, Astroparticle Physics 5 (1996) 309. 10. L.V. Volkova and G.T. Zatsepin, Phys. of Atomic Nuclei 64 (2001) 266. 11. G.T. Zatsepin, N.P. Il’ina, N.N. Kalmykov et al., Izvestiya RAS, ser. Fiz. 61 (1997) 559. 12. L.V. Volkova, Physics of Atomic Nuclei 67 (2004) 2062. 13. V.A.Kudryavtsev, O.G. Ryazhskaya and O. Saavedra, Nuov. Cim. 21C (1998) 119.