Testing the $ΔS=ΔQ$ Rule with Exclusive Semi-Leptonic Kaon Decays

Abstract

We consider the possibility of violations of the selection rule $ΔS=ΔQ$ at an appreciable level in {\it exclusive} semi-leptonic decays of Kaons. At $Φ$-Factories, intense Kaon beams will be available and will probe among others, the semi-leptonic decays $K_{l4}$ and $K_{l3γ}$ in addition to $K_{l3}$ and could provide novel testing grounds for the $ΔS=ΔQ$ rule. In particular, the branching ratio of $K_{l3γ}$ is non-negligible and could be used to probe new phenomena associated with the violation of this selection rule. Furthermore, we modify certain di-lepton event rate ratios and asymmetries and time asymmetries that have been constructed by Dass and Sarma for di-lepton events from Beon decays to test the $ΔB=ΔQ$ at the $Υ(4S)$, to the Kaon system at the $ϕ(1020)$. We find that the large width of the $K_S$ relative to that of $K_L$ plays an important role in enhancing some of the time asymmetries.