Muon-neutrino electron scattering in the theory of pure leptonic weak interaction with induced shadow states

Abstract

With in the framework of the theory of shadow states (x), a finite theory for pure leptonic weak interact ion (2) was proposed before by WANG and by one of the present authors (CHIA~G). However, the theory is not sat isfactory mainly for two reasons: 1) neutral currents are not included, 2) since the shadow masses are free parameters in the theory, i t is aesthetical ly not appealing. Recently (s) i t has been observed tha t for the 4-fermion self-interaction, the current with point spl i t t ing would induce indefinite-metric states which are effectively equivalent to the shadow states in the finite quantum electrodyuamics proposed by AReas, HAN and SUD~SHAN (4), and by CHIA.~G and GL~.SO.~ (5) and also to the shadow states in the finite theory for the pure leptonic weak interact ion above-mentioned. The shadow masses are uniquely re la ted to the current-current coupling constant . By making use of the point-spl i t t ing mechanism, we have proposed (s) a finite theory for pure leptonic weak interact ion including neutral currents. In this approach the neutral currents play a crucial role in connection with the finiteness of the theory. The shadow states are induced by the neutral current self-interaction, and the theory involves only two parameters , the charged current coupling constant and the neutralcurrent coupling constant. In this note we present our computa t ion for the elast ic-scattering processes e -~a(~a) -~e-+-~(+~) . The result of our computat ion shows tha t our theory is compatible with the exper imenta l da ta available at present. To s tar t with, let us recall the in teract ion Lagrangian in ref. (6).