Stars as Laboratories for Fundamental Physics - MPP Theory Group

520 Chapter 13
a charged-current scattering rate of 0.6×10 10 s −1 or an approximate
cooling time-scale by r.h. neutrinos of ϵ −2
CC 2×10 −10 s. The requirement
that this timescale exceeds a few seconds leads to the constraint
ϵ CC ∼ < 10 −5 , (13.18)
in agreement with a result of Barbieri and Mohapatra (1989) while Raffelt
and Seckel (1988) found a somewhat less restrictive limit of ϵ < CC ∼
3×10 −5 . Laboratory experiments yield a limit of order ϵ < CC ∼ 3×10 −2
(e.g. Jodidio et al. 1986) which is much weaker but does not depend
on the assumed existence of r.h. neutrinos. Mohapatra and Nussinov
(1989) extended the SN 1987A bound to the case of r.h. Majorana
neutrinos which mix with ν e .
In order to constrain r.h. neutral currents, equivalent to constraining
the mass of putative r.h. Z ◦ gauge bosons, one considers the emission
of r.h. neutrino pairs ν R ν R . The dominant emission process is by the
nucleons of the medium; in a dilute medium it can be represented as the
bremsstrahlung process NN → NNν R ν R . Apart from a global scaling
factor ϵ 2 NC, the bremsstrahlung energy-loss rate for a nondegenerate
medium was given in Eq. (4.23). However, in a dense medium this
rate probably saturates at around 10% nuclear density as in the case
of axion emission (Sect. 4.6.7). Evaluating Eq. (4.23) at 10% nuclear
density (ρ 15 = 0.03) and at T = 30 MeV, and applying the analytic
criterion Eq. (13.8) one finds
ϵ NC ∼ < 3×10 −3 . (13.19)
This is less restrictive from what was found by Raffelt and Seckel (1988)
or Barbieri and Mohapatra (1989).
The translation of a limit on ϵ NC into one on a r.h. gauge boson mass
depends on details of the couplings to quarks and leptons, and notably
on the mixing angle between the new and the standard Z bosons. Detailed
analyses were presented by Grifols and Massó (1990b), Grifols,
Massó, and Rizzo (1990), and Rizzo (1991). Because these authors did
not consider multiple-scattering effects and the resulting saturation of
the bremsstrahlung process, their bounds on the Z ′ mass are somewhat
too restrictive, perhaps by a factor of 2 or 3. Still, m Z ′ has to exceed
at least 1 TeV, except for special choices of the mixing angle.
The SN 1987A limits on r.h. neutral currents are weaker than those
from big bang nucleosynthesis (ϵ < NC ∼ 10 −3 ) which are based on the
requirement that r.h. neutrinos must not have come to thermal equilibrium
after the QCD phase transition (at T < ∼ 200 MeV) in the early
universe (e.g. Olive, Schramm, and Steigman 1981; Ellis et al. 1986).