Stars as Laboratories for Fundamental Physics - MPP Theory Group

Appendix B
Neutrino Coupling Constants
Neutrinos can interact with other fermions and with each other by
the exchange of W or Z bosons. Because the astrophysical phenomena
relevant for this book take place at very low energies compared with the
W or Z mass, one may always use an effective four-fermion coupling
which is parametrized in terms of the Fermi constant and the weak
mixing angle
G F = 1.166×10 −5 GeV −2 ,
sin 2 Θ W = 0.2325 ± 0.0008.
(B.1)
The tree-level relationship of these quantities with the gauge-boson
masses is
√
2 GF =
(B.2)
πα
m 2 W sin 2 Θ W
=
πα
m 2 Z sin 2 Θ W cos 2 Θ W
,
where m Z = 91.2 GeV and m W = 80.2 GeV.
The effective charged-current interaction between nucleons and leptons
is written in the form
H int = G F
√ ψ p γ µ (C V − C A γ 5 )ψ n ψ l γ µ (1 − γ 5 )ψ νl ,
2
(B.3)
where the ψ j are the proton, neutron, charged-lepton, and the corresponding
neutrino field. The vector-current coupling constant is C V = 1
while the axial-vector coupling for free nucleons is C A = 1.26. However,
in large nuclei this value is suppressed somewhat, and the commonly
used value for nuclear matter is C A = 1.0 (e.g. Castle and Towner 1990).
This quantity would be relevant, for example, for β reactions in supernova
cores and neutron stars.
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