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82 for µe = 200 MeV and � � �eB Γ � � (1) URCA Γ (0) � � � � � URCA ≃ 1.0×10−5 B14 , � � � � eB Γ � � (1) ν−e Γ (0) � � � � � ν−e � ≃ 7.3×10−6 B14 , (8) for µe = 50 MeV. These relative asymetries are as large as the ones calculated in [3] and one can expect the nucleon polarization to give a comparabel contribution. I therefore conclude, based on the results in [8], that neutrino absorption is an important process for the neutrino opacity (see Fig. 4 in [8]) and that the asymmetry in URCA processes needs to be taken into account in any reliable estimate of the total neutrino propagation asymmetry in a neutron star. However, it is also my impression that the final word has not yet been said about the influence from collective behavior of nucleons on the neutrino propagation. Acknowledgements I would like to thank D. Grasso and P. Ullio for collaboration and the organizers for the invitation to Ringberg. References [1] N.N. Chugai, Sov. Astron. Lett. 10 (1984) 87. [2] V.G. Bezchastnov and P. Haensel, Phys. Rev D 54 (1996) 3706. E. Roulet, hepph/9711206. L.B. Leinson and A. Pérez, astro-ph/9711216. [3] C.J. Benesh and C.J. Horowitz, astro-ph/9708033. D. Lai and Y-Z. Qian, astroph/9712043. [4] C.J. Horowitz and G. Li, astro-ph/9705126. [5] G. Raffelt and D. Seckel, Phys. Rev. Lett.67 (1991) 2605. [6] H.A. Weldon, Phys. Rev. D 28 (1983) 2007. [7] R. Kobes and G. Semenoff, Nucl. Phys. B260 (1985) 714. [8] S. Reddy, M. Prakash and J.M. Lattimer, astro-ph/9710115.
Cherenkov Radiation by Massless <strong>Neutrino</strong>s in a Magnetic Field Ara N. Ioannisian 1,2 and Georg G. Raffelt 2 1 Yerevan Physics Institute, Yerevan 375036, Armenia 2 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut) Föhringer Ring 6, 80805 München, Germany Abstract We discuss the Cherenkov process ν → νγ in the presence of a homogeneous magnetic field. The neutrinos are taken to be massless with only standard-model couplings. The magnetic field fulfills the dual purpose of inducing an effective neutrino-photon vertex and of modifying the photon dispersion relation such that the Cherenkov condition ω < |k| is fulfilled. For a field strength Bcrit = m 2 e /e = 4.41 ×1013 Gauss and for E = 2me the Cherenkov rate is about 6 × 10 −11 s −1 . In many astrophysical environments the absorption, emission, or scattering of neutrinos occurs in dense media or in the presence of strong magnetic fields [1]. Of particular conceptual interest are those reactions which have no counterpart in vacuum, notably the decay γ → ¯νν and the Cherenkov process ν → νγ. These reactions do not occur in vacuum because they are kinematically forbidden and because neutrinos do not couple to photons. In the presence of a medium or B-field, neutrinos acquire an effective coupling to photons by virtue of intermediate charged particles. In addition, media or external fields modify the dispersion relations of all particles so that phase space is opened for neutrino-photon reactions of the type 1 → 2 + 3. If neutrinos are exactly massless as we will always assume, and if medium-induced modifications of their dispersion relation can be neglected, the Cherenkov decay ν → νγ is kinematically possible whenever the photon four momentum k = (ω,k) is space-like, i.e. k 2 − ω 2 > 0. Often the dispersion relation is expressed by |k| = nω in terms of the refractive index n. In this language the Cherenkov decay is kinematically possible whenever n > 1. Around pulsars field strengths around the critical value Bcrit = m 2 e/e = 4.41 ×10 13 Gauss are encountered. The Cherenkov condition is satisfied for significant ranges of photon frequencies. In addition, the magnetic field itself causes an effective ν-γ-vertex by standard-model neutrino couplings to virtual electrons and positrons. Therefore, we study the Cherenkov effect entirely within the particle-physics standard model. This process has been calculated earlier in [2], but we do not agree with their results. Our work is closely related to a recent series of papers [3] who studied the neutrino radiative decay ν → ν ′ γ in the presence of magnetic fields. Our work is also related to the process of photon splitting that may occur in magnetic fields as discussed, for example, in Refs. [4, 5]. Photons couple to neutrinos by the amplitudes shown in Figs. 1(a) and (b). We limit our discussion to field strengths not very much larger than Bcrit = m 2 e/e. Therefore, we keep only electrons in the loop. Moreover, we are interested in neutrino energies very much smaller than the W- and Z-boson masses, allowing us to use the limit of infinitely heavy gauge bosons and 83
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arXiv:astro-ph/9801320v1 30 Jan 199
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Preface This was the fourth worksho
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vi S.J. Hardy Quasilinear Diffusion
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viii
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History of Neutrino Physics: Pauli
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Brief an Oskar Klein, Stockholm, vo
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Recent observations with the Hubble
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MACHO sample of ∼100,000 light cu
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Solar Neutrinos
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14 In the depth range where an abun
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16 as follows: (1) All the detector
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18 [3] J.N. Bahcall and H.A. Bethe,
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20 the opacity has a very slowly ch
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22 Status of the Radiochemical Gall
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24 known true source activity. The
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26 Solar Neutrino Observation with
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28 Events/day/kton/bin 0.3 0.25 0.2
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30 log(Δm 2 (eV 2 log(Δm )) 2 (eV
Page 40 and 41: 32 Table 1: Neutrino event rates in
Page 42 and 43: 34 tank and sphere high purity wate
Page 44 and 45: 36 Measurements of Low Energy Nucle
Page 46 and 47: 38 Figure 1: The S(E) factor of 3 H
Page 48 and 49: 40 Solar Neutrinos: Where We Are an
Page 50 and 51: 42 [9] B. Pontecorvo, Chalk River R
Page 52 and 53: 44 Figure 2: The difference between
Page 55 and 56: Phenomenology of Supernova Explosio
Page 57 and 58: Figure 2: Theoretical classificatio
Page 59 and 60: Supernova Rates Bruno Leibundgut Eu
Page 61 and 62: galaxies, however, and the statisti
Page 63 and 64: Figure 1: The motions of pulsars re
Page 65 and 66: Convection in Newly Born Neutron St
Page 67 and 68: a b Figure 2: Panel a shows the rec
Page 69 and 70: ference). The angular variations of
Page 71 and 72: Figure 1: Neutrino luminosity and e
Page 73 and 74: [9] G.S. Bisnovatyi-Kogan, Astron.
Page 75 and 76: and the mass-to-luminosity ratio of
Page 77 and 78: Figure 1: Time variation of superno
Page 79 and 80: Figure 3: Energy spectra of the sup
Page 81 and 82: Supernova Neutrino Opacities G.G. R
Page 83 and 84: Quasilinear Diffusion of Neutrinos
Page 85 and 86: Assuming a saturated thermal distri
Page 87 and 88: Anisotropic Neutrino Propagation in
Page 89: So far the damping rate corresponds
Page 93 and 94: on ω so that they are well approxi
Page 95: 2 2 / meff,e m eff 1.0 0.5 0.0 elec
Page 99 and 100: Gamma-Ray Burst Observations D.H. H
Page 101 and 102: Figure 1: The cumulative distributi
Page 103 and 104: [7] Lilly, S., in Critical Dialogue
Page 105 and 106: ) Phase Transitions in Neutron Star
Page 107 and 108: after the collapse began (nb., no e
Page 109 and 110: Models of Coalescing Neutron Stars
Page 111 and 112: Figure 2: Contour plots of the mass
Page 113 and 114: From our torus models we find that
Page 115: High-Energy Neutrinos
Page 118 and 119: 110 in gamma-rays. However, the acc
Page 120 and 121: 112 Atmospheric Muons and Neutrinos
Page 122 and 123: 114 Today, however, charm productio
Page 124 and 125: 116 Atmospheric Neutrinos in Super-
Page 126 and 127: 118 number of events 300 200 100 (a
Page 128 and 129: 120 Acknowledgements D.K. is suppor
Page 130 and 131: 122 Key signatures for νµ nucleon
Page 132 and 133: 124 (a.u) 0.5 0.4 0.3 0.2 0.1 0 0 1
Page 134 and 135: 126 However, in order to operate th
Page 136 and 137: 128 could be gravitationally captur
Page 138 and 139: 130 Ground-Based Observation of Gam
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132 Figure 2: Sensitivities in unit
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134 Crab flux Figure 4: Gamma-ray f
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136
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Helium Absorption and Cosmic Reioni
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Non-Standard Big Bang Nucleosynthes
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) Non-standard Neutrino Properties
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some heating of the plasma. In cont
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Big Bang Nucleosynthesis With Small
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Neutrinos and Structure Formation i
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Photon and Neutrino Backgrounds The
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The (photon) temperature at aeq is
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spectrum has therefore changed to 1
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Figure 4: Growth of structure in CD
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Future Prospects
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162 Figure 1: Calorimetric β − s
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164 References [1] F. Gatti: Procee
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166 The frequency of Galactic super
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168 Table 1: Comparison of proposed
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170 Neutrinos in Astrophysics José
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172 N eq 7 6.5 6 5.5 5 4.5 4 3.5 3
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174 Figure 4: SN 1987A bounds on FC
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176 [5] A. Joshipura and J. W. F. V
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178 Some Neutrino Events of the 21s
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180 2099: Relic Neutrinos And last
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182
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184 Tuesday, Oct. 21: Supernova Neu
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186 Michael Altmann Technische Univ
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188 Paolo Gondolo Max-Planck-Instit
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190 Patrizia Meunier Max-Planck-Ins
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192 Torsten Soldner Technische Univ
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194 A Experimental Particle Physics
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196 C Astrophysics and Cosmology C1
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