Note on the Beta Interaction

Abstract

It is shown that the most general Lorentz invariant interaction between four mutually anticommuting fields leads to matrix elements of the form $\mathrm{}(S-T+P)\mathrm{}{f}_1(n, m)+(V-A)\mathrm{}{f}_2(n, m)+(S-A-P)\mathrm{}{f}_3(n, m).\mathrm{}$ In the charge-exchange order, neutron and muon decay are compatible with $f_2=f_3=0\mathrm{}$; charged pion decay appears to correspond to $f_1=f_3=0\mathrm{}$. It is noted that the hypothesis of the same interaction between all fermions does not imply that $f_1$, $f_2$, and $f_3$ are numerical constants; it is possible that they are functions of new variables ($n, m$) needed to characterize the associated Feynman diagrams: $n$ indicates the number of particles produced in the reaction and $m$ the number of particles minus antiparticles. One can make a simple choice of the $f_i$ in such a way that the interaction is sometimes $S-T+P$, sometimes $V-A$, and never $S-A-P$.