Stars as Laboratories for Fundamental Physics - MPP Theory Group

416 Chapter 11
The relevant neutrino interaction processes in water are elastic scattering
on electrons (Sect. 10.3.4), and the charged-current reactions
ν e p → n e + and ν e 16 O → 16 F e − (Arafune and Fukugita 1987; Haxton
1987). The cross section for the ν e p reaction is given by
σ = G2 F
π
cos2 θ C
(
C
2
V + 3C 2 A
)
pe E e (1 + δ)
= 9.4×10 −44 cm 2 (1 + δ) p e E e /MeV 2 , (11.6)
where G F is the Fermi constant and cos 2 θ C ≈ 0.95 refers to the Cabibbo
angle. The charged-current vector and axial-vector weak coupling constants
are C V = 1 and C A = 1.26, and δ incorporates small corrections
from recoil, Coulomb, radiative and weak magnetism corrections (Vogel
1984). Further, p e and E e refers to the positron momentum and
energy. Ignoring recoil effects, the latter is E e = E ν − m n + m p ≈
E ν −1.3 MeV; the threshold is 1.8 MeV because the minimum E e is m e .
A general expression for the ν e 16 O cross section is much more complicated.
A simple approximation, taking only the 2 − state of the 16 F
nucleus, is
σ ≈ 1.1×10 −44 cm 2 (E ν /MeV − 13) 2 (11.7)
(Arafune and Fukugita 1987).
Fig. 11.10. Total cross sections for the measurement of neutrinos in a water
Cherenkov detector according to Eqs. (10.17), (11.6), and (11.7). The curves
refer to the total cross section per water molecule so that a factor of 2 for
protons and 10 for electrons is already included.