Possible inconsistencies in calculations of semi-leptonic processes involving charged Higgs-Kibble scalars

Abstract

Recently calculations have been made on various models of unified theories of weak and electromagnetic interactions. The Salam-Weinberg (1) model is essentially in difficulty owing to the existence of neutral currents, while the Georgi-Glashow (2) fivequark model gives an unacceptably large value for KL--> ~ . Models incorporating the cancellation mechanism of Glashow-Maiani-Iliopoulos (GMI)(8) give a zero value for KL-+ ~ t when there is an S U 4 invarianee among the quarks. The Lee-Prentki-Zumino model (LPZ)(4) is one such model. Some authors assume that the charmed and corresponding uneharmed quarks have a nonzero mass difference. Given this assumption, the data for K L ~ t and K1-K 2 mass difference give incompatible bounds on the quark mass differences (5). However since strong-interaction effects are appreciable in the K1-K 2 mass difference such considerations do not rule out the model completely. In this note we discuss how plausible any quanti tat ive calculations are for models such as LPZ for semi-leptonic processes. I t seems to us that present calculations should be regarded with some scemptieism. We find that we are unable to calculate ]~ and ]z mutually consistently. Unfortunately purely leptonic processes yield rather trivial constraints on the model. An analysis of ~.-e scattering data gives a lower bound on the mass of the charged Higgs-Kibble (6) scalar of 3 MeV! We consider K h and Kt~ decays since the data are reasonably good. In addition to vector-boson exchanges, Higgs-Kibble particles can be exchanged (eft Fig. 1, 2 and 3)