Role of hadronic dynamics in proton decay

Abstract

Aspects of hadronic dynamics which play a crucial role in proton decay (exclusive and inclusive) are examined in the context of a comprehensive Bethe-Salpeter (BS) formalism forq\(\bar q\) andqqq systems, under harmonic confinement. The BS model which is characterized by two basic parameters—the universal spring constant\(\tilde \omega \) GeV and the quark massm q =0.28 GeV, has already provided an impressive set of agreements in respect of a large number and variety of hadronic observables (mass spectra, and an extensive list of e.m. and pionic couplings of both mesons and baryons). TheSU(5) GUT parameters, on the other hand, are kept fixed at the ‘standard’ values, (see e.g. Langacker's review). The absolute normalization of the baryon, which is rather crucial in this case, is fixed with reference to the (topologically equivalent) process of its ‘dissociation’ into three quarks by a hard photon, which makes use of the structure function sum rule\(\int\limits_0^1 {dxF_2^p (x)/x = \sum {Q_i^2 } } \), instead of the usual BS normalization (which amounts to the conservation of charge). Thee+ inclusive rate, which is about three times that of thee+π0 mode, works out at0.54×10 −33 yr −1 which is smaller than most contemporary calculations by two orders of magnitude. Other exclusive modes are also consistent with the above estimate. The theoretical implications of these results vis a vis contemporary calculations as well as current experimental searches are discussed.