Physics of Neutrinos pp 59-142 | Cite as

# Applications of the Electroweak Theory

Chapter

## Abstract

The weak decay processes known from early times are all described by charged-current interactions. As given in (2.6), the charged current is the sum of leptonic and hadronic currents: , where and .

$${J_\mu } = J_{_\mu }^{(l)} + J_{_\mu }^{(h)} $$

(3.1)

$$J_{_\mu }^{(l)} = \overline {{v_e}} {\gamma _\mu }(1 - {\gamma _5}){e^ - } + \overline {{v_\mu }} {\gamma _\mu }(1 - {\gamma _5}){\mu ^ - } + \overline {{v_\tau }} {\gamma _\mu }(1 - {\gamma _5}){\tau ^ - }$$

(3.2)

$$J_{_\mu }^{(h)} = (\overline u ,\overline c ,\overline t ){U_q}{\gamma _\mu }(1 - {\gamma _5})(\begin{array}{*{20}{c}} d \\ s \\ b \\ \end{array} ) $$

(3.3)

## Keywords

Matrix Element Shell Model Radiative Correction Beta Decay Solar Neutrino
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## References

- 1.This treatment is invalid for relativistic wave functions, which are singular at the origin. More appropriately, the Fermi function is given by the wave functions at the nuclear radius rather than at the origin.Google Scholar
- 2.For more accurate correction factors using a numerical solution of the Dirac equation for finite nuclei, see [345].Google Scholar
- 3.The authors thank T. Kubota for discussion.Google Scholar
- 9.The corrections are identical with those for μ decay, and hence the effects are absorbed into G
_{F}. See [403].Google Scholar - 10.For antineutrinos, the background can be efficiently reduced by a coincidence technique using produced neutrons, and hence other methods can be successfully used.Google Scholar
- 11.
^{18}O is an exceptional case; the neutrino cross section of^{18}O is close to 2 × δ (*νn**)*Google Scholar - 12.This is due to a somewhat tricky, but lucky situation. The cross section for the neutrino flux other than B neutrinos is solely determined by the GT(gs), which is well determined. For the B neutrino capture cross section a large change from García et al.’s
*B(GT)*to Trinder et al.’s*B(GT)*is mostly a redistribution of the GT strengths at low-lying levels. It is fortunate that the first excited level of A is located above the maximum energies of all solar neutrino fluxes other than B neutrinos and that the GT strength to the first excited state is estimated by subtraction from the total decay rate, which is well constrained. The calculation of Kuramoto et al. takes into account the large GT strengths for*E >*5 MeV levels, as expected from the*(pn)*experiment.Google Scholar - 16.See also Butler and Chen [484], who used nucleon-nucleon effective field theory to calculate
*νd*cross sections. In their calculation, however, there is one free parameter (an isovector axial two-body matrix element), and the results agree with those of either Kubodera et al. or Haxton et al. depending on the choice of this parameter. The calculation is limited to a low-energy region > 20 MeV. This contrasts with the earlier conclusion of Ying et al. [482], which is ascribed to an error in their computer code [473,483].Google Scholar

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© Springer-Verlag Berlin Heidelberg 2003