Compton-like interaction of massive neutrinos with virtual photons

Abstract

The amplitude of a Compton-like process nu_i gamma^* -> nu_j gamma^* with virtual photons is calculated in the standard GWS theory with lepton mixing. The contribution of this process to the high energy neutrino scattering on the nucleus with single photon radiation nu N -> nu N gamma is discussed. The bremsspectrum and the total cross-section are estimated in the leading log approximation.Comment: 6 pages, LATEX, 2 PS figure

Radiative decay of the massive neutrino in external electromagnetic fields

“…It is most easily seen, if ∆M (F ) is expanded into a series in terms of the external field, as is shown in Fig 2, where the dotted lines designate the external electromagnetic field A ex . We note that the first seven diagrams in Fig 2 coincide with the diagrams describing Compton-like process ν i γ * → ν j γ * and, as was pointed out in [19], this process amplitude is reduced to the contribution of the first two diagrams in the local limit. With the orthogonality of the mixing matrix K ij taken into account, this is due to the fact, that the main contribution to the integral over momentum in the loop gives from the region of the virtual momenta p ∼ m ℓ ≪ m W .…”

“…The comparison demonstrates the catalyzing effect of the external crossed field on the decay probabilities, as there is no suppression ∼ (m 2 ℓ /m 2 W ) in Eqs. ( 18) and (19). Actually, the enhancement influence of the external field takes place in the weak field limit (F ≪ F e ) under the condition: F > 2 • 10 −3 F e .…”

“…Actually, the enhancement influence of the external field takes place in the weak field limit (F ≪ F e ) under the condition: F > 2 • 10 −3 F e . Besides, the decay in the strong crossed field (19) is catalyzed by an additional factor of the form ∼ (F/F e ) 6 ≫ 1.…”

“…Such an enhancing influence of an external field can be illustrated with the straightforward example of a neutrino radiative decay in a weak (as compared with the Schwinger value F e = m 2 e /e ≃ 4.41 • 10 13 G) electromagnetic field. To this end we use the amplitude of the Compton-like process ν i γ * → ν j γ * with virtual photons [19], which, in particular, allows obtaining the first term of the expansion of the radiative decay ν i → ν j γ amplitude in a weak external field. In the expression for the amplitude of the process ν i (p 1 )+γ * (q 1 ) → ν j (p 2 )+γ * (q 2 ) it is sufficient to consider γ(q 2 ) as a real photon, and to replace the field tensor of the virtual photon γ * (q 1 ) by the Fourier image of the external electromagnetic field tensor.…”

Neutrino scattering in a magnetic field

“…Dicus and collaborators [3][4][5][6] have given cross sections for both massless and massive neutrino photon scattering. Neutrino scattering in a magnetic field has been considered in detail by Mikheev and collaborators [7][8][9][10], as well as by other authors [11,12]. For high energy neutrinos, the radiated photons are energetic and the distribution is peaked in the forward direction.…”