Rare and forbidden decays

Abstract

In these lectures I first cover radiative and semileptonic B decays, including the QCD corrections for the quark subprocesses. The exclusive modes and the evaluation of the hadronic matrix elements, i.e. the relevant hadronic form factors, are the second step. Small effects due to the long-distance, spectator contributions, etc. are discussed next. The second section we started with non-leptonic decays, typically $B \to \pi\pi, K\pi, \rho\pi, ...$ We describe in more detail our prediction for decays dominated by the $b\to s \eta_c$ transition. Reports on the most recent experimental results are given at the end of each subsection. In the second part of the lectures I discuss decays forbidden by the Lorentz and gauge invariance, and due to the violation of the angular moment conservation, generally called the Standard Model-forbiden decays. However, the non-commutative QED and/or non-commutative Standard Model (NCSM), developed in a series of works in the last few years allow some of those decay modes. These are, in the gauge sector, $Z\to \gamma\gamma, gg$, and in the hadronic sector, flavour changing decays of the type $K\to \pi \gamma$, $B\to K\gamma$, etc. We shall see, for example, that the flavour changing decay $D^+_s\to \pi^+ \gamma$ dominates over other modes, because the processes occur via charged currents, i.e. on the quark level it arises from the point-like photon $\times$ current $\times$ current interactions. In the last section we present the transition rate of ``transverse plasmon'' decay into a neutrino--antineutrino pair via noncommutative QED, i.e. $\gamma_{;\rm pl};\to \nu\bar\nu$. Such decays gives extra contribution to the mechanism for the energy loss in stars.