Subatomic Physics

11.15. References 381
11.41. For nucleons composed of point quarks,
(a) show that the total cross section for high-energy neutrino scattering
varies linearly with the laboratory energy E.
(b) How is the total cross section modified as the center-of-mass energy
approaches mW c 2 ?
(c) What is the laboratory energy of neutrinos for which the center-of-mass
energy is equal to mW c 2 ?
11.42. Verify Eq. (11.97).
11.43. Electron neutrinos can interact with electrons via charged and neutral weal
currents.
(a) Draw Feynman diagrams showing these possibilities.
(b) Explain why muon neutrinos can interact with electrons only via neutral
currents and not charged currents.
11.44. Electron neutrinos produced in beta decays are actually a mixture of two mass
eigenstates, ν1 and ν2, | νe〉 = cosθ | ν1〉 + sinθ | ν2〉 .
(a) Deduce the equation that gives the probability of observing the neutrino
as a muon neutrino for vacuum oscillations.
(b) Consider electron neutrinos from the decays of 8 B in the sun. Assume
θ =45degandm 2 2 − m2 1 =5× 10−5 eV 2 . Plot the electron neutrino
energy spectrum on earth assuming vacuum oscillations.
11.45. (a) Explain why the total cross section for high energy muon neutrinos to
scatter off hadronic targets is three times larger than for antineutrinos.
(b) Would you expect electron neutrinos to have approximately the same,
larger, or smaller cross sections than those for muon neutrinos?
(c) Repeat for electron antineutrinos.
11.46. Assume that the Sun obtains its energy from the transformation of 4 protons
into a doubly ionized He atom, liberating ≈ 26 MeV: 4p → 4 He ++ +2e + +2νe
and use the solar luminosity on Earth, 1.4 kWatt/m 2 , to derive the expected
intensity of neutrinos (number per unit time and area) on Earth.
11.47. Estimate Vud using the ft values for the decays Λ0 → pe − νe and n → pe − νe
from Tables 11.2 and 11.3.