Structure Effects in Weak Interactions

Abstract

The standard way to formulate the theory (or model?) of weak, interactions is to write down the “effective Lagrangian”

$${{\rm{L}}_{\rm{w}}}\,{\rm{ = }}\,{{\rm{G}} \over {\sqrt {\rm{2}} }}\,{\rm{J}}_{\rm{\lambda }}^{\rm{\dag }}{\rm{(x)}}\,{{\rm{J}}^{\rm{\lambda }}}{\rm{(x)}}$$

(1)

with

$${{\rm{J}}_{\rm{\lambda }}}{\rm{(x)}}\,{\rm{ = }}\,{\ell _{\rm{\lambda }}}{\rm{(x)}}\,{\rm{ + }}\,{\rm{cos\theta }}\,\,{\rm{j}}_{\rm{\lambda }}^{{\rm{(\pi )}}}\,{\rm{(x)}}\,{\rm{ + }}\,{\rm{sin\theta }}\,{\rm{j}}_{\rm{\lambda }}^{\left( {\rm{K}} \right)}\,{\rm{(x)}}$$

(2)

Here, θ is the Cabibbo angle and j ⁽ⁱ⁾_λ (x) are the hyper charge conserving and hypercharge changing hadron currents. The lepton current ℓ_λ(x) is given by [1]

$${\ell _{\rm{\lambda }}}{\rm{(x)}}\,{\rm{ = }}\,\sum\limits_\ell {\,\mathop {{\psi _\ell }}\limits^ - {\rm{(x)}}} \,\,{{\rm{\gamma }}_{\rm{\lambda }}}\,{\rm{(1 + }}{{\rm{\gamma }}_{\rm{5}}}{\rm{)}}\,\,{{\rm{\psi }}_{{{\rm{\nu }}_\ell }}}\,{\rm{(x)}}\,\,\,\,\,\,\ell {\rm{ = e,\mu }}$$

(3)

Seminar given at IX. Internationale Universitätswochen für Kernphysik, Schladming,February 23 — March 7,1970.

Supported by “Fonds zur Förderung der wiss. Forschung”