Constraints on New Physics from $K\to \pi \nu \bar{\nu }$

Abstract

We study constraints on new physics from the recent measurement of Br ($K^{+}\to {\pi }^{+}\nu \bar{\nu })$ by the E787 and E949 Collaborations. In our analysis we consider two models of new physics: $(a)$ extra down type singlet quark model (EDSQ) and $(b)$ R-parity violating Minimal Supersymmetric Standard Model(MSSM). We find that $K^{+}\to {\pi }^{+}\nu \bar{\nu }$ along with other processes like $K_L\to {\mu }^{+}{\mu }^{-},{ϵ}^{\prime }/ϵ$ provide useful bounds on the parameter $U_{sd}$, characterizing the off-diagonal $Z-d-\bar{s}$ coupling of model $(a)$. The bounds on the $\mathrm{Re}(U_{sd})$ from $(K_L\to {\mu }^{+}{\mu }^{-}{)}_{\mathrm{SD}}$ and $\mathrm{Im}(U_{sd})$ from ${ϵ}^{\prime }/ϵ$ are so tight that the branching ratio of $K^{+}\to {\pi }^{+}\nu \bar{\nu }$ can exceed the standard model value by at most a factor of two For model b), we also obtain stringent bounds on certain combinations of product of two ${\text{lp}}_{ijk}$ couplings originating from $L$ number violating operator $L_i{Q}_j{D}_k^c$ using $K^{+}\to {\pi }^{+}\nu \bar{\nu }$ and $K_L\to {\mu }^{+}{\mu }^{-}$ processes. Even with the stringent constraints on $U_{sd}$ (in model $(a)$) and on products of two $\text{rp}$couplings (model $(b)$), we find that the branching ratios for $K_L\to {\pi }^0\nu \bar{\nu }$ and $K_L\to {\pi }^0{e}^{+}{e}^{-}$ can be substantially different in both the above models from those predicted in the standard model.

Comments: K_L --> pi^0 e+ e- section has been altered, new references to this process are cited. One Figure has been removed and other Figure modified