Impacts on searching for signatures of new physics from $K^+\to \pi^+ \nu \overline \nu$ decay

Abstract

We study impacts on new physics search from the rare decay \(K^+\to \pi^+ \nu \overline \nu\). In a certain class of new physics models, the extra contributions to FCNC processes can be parametrized by its ratio to the standard model (SM) contribution with the common CKM factors. The ratio \(R_1\) has been used in the analysis of \(x_d\) and \(\epsilon_K\) parameters. In the above class of models, the \(K^+\to \pi^+ \nu \overline \nu\) decay amplitude can be parametrized by the ratio \(R_2\). Then the experimentally allowed region for new physics contributions can be given in terms of \(R_1,R_2\) and the CP violating phase \(\delta\) of the CKM matrix. Constraints on \(R_1\) and \(\cos\delta\) are obtained by taking account of current experimental data and theoretical uncertainties on \(B^0\)-\(\overline{B^0}\) and \(K^0\)-\(\overline{K^0}\) mixings. We study impacts of future improved measurements by using \((R_1, R_2, \cos\delta)\) basis. We discuss contributions in the minimal supersymmetric SM and the two Higgs doublet model as examples.