Stars as Laboratories for Fundamental Physics - MPP Theory Group

Nonstandard Neutrinos 267
The quantity τ |U e3 | 2 is shown as a dotted line in Fig. 7.2. Even
without nonstandard physics the decay rate is fast on cosmological
scales if m 3 ∼ > 2m e . Because experimentally m 3 may be as large as
24 MeV the cosmological mass bound of 30 eV does not automatically
apply. Experimental limits on U e3 together with the BBN mass bound,
however, exclude a heavy standard ν 3 . Even without reference to BBN
it can be excluded on the basis of the SN 1987A neutrino radiative
lifetime limits (Sect. 12.5.2).
7.3 Neutrino Electromagnetic Form Factors
7.3.1 Overview
When Wolfgang Pauli in 1930 first postulated the existence of neutrinos
he speculated that they might interact like a magnetic dipole of a
certain moment µ ν . If that were the case they could be measured by
their ionizing power when they move through a medium; this ionizing
power was first calculated by Bethe (1935). Nahmias (1935) measured
the event rates in a Geiger-Müller counter in the presence and absence
of a radioactive source and interpreted his null result as a limit
µ < ν ∼ 2×10 −4 µ B (Bohr magneton µ B = e/2m e ) on the neutrino dipole
moment. He concluded that “since this limit is already smaller than a
nuclear magneton, it seems probable that the neutrino has no moment
at all.” Subsequent attempts to measure ever smaller neutrino dipole
moments have consistently failed.
The main difference between then and now is the advanced theoretical
understanding of neutrino interactions in the context of the
standard model of electroweak gauge interactions. A magnetic dipole
interaction couples l.h. with r.h. states so that the latter would not
be strictly sterile. This would be in conflict with the standard model
where neutrinos interact only by their l.h. coupling to W and Z gauge
bosons. Thus neutrino dipole moments must vanish identically because
weak interactions violate parity maximally.
This picture changes when neutrinos have masses because even the
r.h. components of a Dirac neutrino are then not strictly sterile as
they couple to the Higgs field—or else they would not have a mass.
Indeed, an explicit calculation in the standard model with neutrino
masses gave a magnetic dipole moment µ ν = 3.20×10 −19 µ B (m ν /eV)
(Eq. 7.16). If neutrinos mix, they also obtain transition magnetic and
electric moments. However, they are even smaller because of the GIM
suppression effect—see Eq. (7.15).