Photon-neutrino interactions Page: 1 of 7
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Duane A. Dicus
Center for Particle Physics and Department of Physics
University of Texas, Austin, Texas 78712
Wayne W. Repko
Department of Physics and Astronomy
Michigan State University, East Lansing, Michigan 48824
Draft(February 15, 1997)
The cross sections for the processes yv -* yyv and yy -* 7y1 are calculated with the
aid of an effective Lagrangian derived from the Standard model. These cross sections
are shown to be much larger than the elastic cross section -a-yv -* yv) for photon
energies w > 1 keV. Possible astrophysical implications are discussed.
1. Elastic processes
Photon-neutrino scattering is of potential interest in astrophysical processes. The various
yv reaction cross sections, which are expected to be small due to the weak interaction, are
further suppressed because of the vector-axial vector nature of the weak coupling [1, 2]. For
the channel vv -- yy, Yang's theorem  implies a vanishing decay amplitude to order GF
when the neutrinos are massless. This means that the amplitude in any channel contains
additional factors of w/mw, where w is the photon energy and mw is the W mass. If the
neutrinos have a mass m,,, the amplitude is reduced by factors of m,/mw .
In the case of massless neutrinos, the amplitude for yv -4 yv in the Standard model is
, to leading order in m-,
1 2 a 4 M2wt
Mas = 2M4[1+-in ( 2 a ) cos(9/2) s2(1+ AA') + -(1 + A)(1 + A') , (1)
where A and A' are the photon helicities, s = 4w2, t = -2w2(1 - cos 0) and 0 is the scattering
angle. Notice that there are no inverse powers of me in this expression and hence the scale
is set by mw. As a consequence, all 2 -* 2 yv channels can be calculated using the effective
Ge 4 2w [1 + 3 In (t) [rnJ(1 +ys)(8a') - (8, )-(1 +-xY)7p] F,aF , , (2)
47 m 3 m
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Dicus, D.A. & Repko, W.W. Photon-neutrino interactions, report, December 1, 1997; United States. (digital.library.unt.edu/ark:/67531/metadc694914/m1/1/: accessed January 21, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.