We study constraints on new physics from the recent measurement of $\mathrm{B}\mathrm{r}(K^{+}\to {\pi }^{+}\nu \overline{\nu })$ by the E787 and E949 Collaborations. In our analysis, we consider two models of new physics: (a) extra down-type singlet quark model and (b) $R$-parity violating minimal supersymmetric standard model. We find that $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ along with other processes such as $K_L\to {\mu }^{+}{\mu }^{-},{ϵ}^{\prime }/ϵ$ provide useful bounds on the parameter $U_{sd}$, characterizing the off-diagonal $Z-d-\overline{s}$ coupling of model (a). The bounds on $\mathrm{R}\mathrm{e}(U_{sd})$ from $(K_L\to {\mu }^{+}{\mu }^{-}{)}_{\mathrm{S}\mathrm{D}}$ and $\mathrm{I}\mathrm{m}(U_{sd})$ from ${ϵ}^{\prime }/ϵ$ are so tight that the branching ratio of $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ can exceed the standard model value by at most a factor of 2. For model (b), we also obtain stringent bounds on certain combinations of the product of two ${\lambda }_{ijk}^{\prime }$ couplings originating from $L$ number-violating operator $L_i{Q}_j{D}_k^c$ using $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ and $K_L\to {\mu }^{+}{\mu }^{-}$ processes. Even with the stringent constraints on $U_{sd}$ [in model (a)] and on products of two $\mathrm{R̸}$ couplings [model (b)], we find that the branching ratio $\mathcal{B}(K_L\to {\pi }^0\nu \overline{\nu })$ can be substantially different in both of the above models from those predicted in the standard model.

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