Stars as Laboratories for Fundamental Physics - MPP Theory Group

268 Chapter 7
Much larger values would obtain with direct r.h. neutrino interactions.
For example, in left-right symmetric models there exist heavier
gauge bosons which mediate r.h. interactions; parity violation would
occur because of the mass difference between the l.h. and r.h. gauge
bosons. For a neutrino ν l (flavor l = e, µ or τ) the dipole moment in
such models is (Kim 1976; Marciano and Sanda 1977; Bég, Marciano,
and Ruderman 1978)
µ ν = eG [
)
)]
F
2 √ m
2 π 2 l
(1 − m2 W 1
sin 2ζ + 3
m m 2 4 ν l
(1 + m2 W 1
,
W 2
m 2 W 2
(7.18)
where ζ is the left-right mixing angle between the gauge bosons W L
and W R ; W 1,2 are their mass eigenstates.
Because of the smallness of the mass-induced standard dipole moments
any evidence for neutrino electromagnetic interactions would represent
evidence for interactions beyond the standard model. Therefore,
the quest for neutrino electromagnetic interactions is more radical than
that for masses and mixings.
In a dense medium even standard massless neutrinos interact with
photons by an effective coupling which is mediated by the ambient electrons.
This coupling can be expressed in terms of an effective neutrino
charge radius. Presently I focus on neutrino interactions in vacuum,
leaving a discussion of their properties in media to Sect. 6.6.
7.3.2 Single-Photon Coupling
There are many possible extensions of the standard model which would
give sizeable neutrino dipole and transition moments by some novel r.h.
interaction. For the purposes of this book the underlying new physics
is of no concern; all we need is a generic representation of its observable
effects in terms of neutrino electromagnetic form factors.
The most general interaction structure of a fermion field ψ with the
electromagnetic field can be expressed as an effective Lagrangian
L int = −F 1 ψγ µ ψA µ − G 1 ψγ µ γ 5 ψ ∂ µ F µν
− 1 2 ψσ µν(F 2 + G 2 γ 5 )ψF µν , (7.19)
where A µ is the electromagnetic vector potential and F µν the field
strength tensor. The interpretation of the coupling constants is that
of an electric charge for F 1 , an anapole moment for G 1 , a magnetic