Kaon physics without new physics in varepsilon _K

Abstract

Despite the observation of significant suppressions of brightarrow smu ^+mu ^- branching ratios no clear sign of New Physics (NP) has been identified in Delta F=2 observables Delta M_{d,s}, varepsilon _K and the mixing induced CP asymmetries S_{psi K_S} and S_{psi phi }. Assuming negligible NP contributions to these observables allows to determine CKM parameters without being involved in the tensions between inclusive and exclusive determinations of |V_{cb}| and |V_{ub}|. Furthermore this method avoids the impact of NP on the determination of these parameters present likely in global fits. Simultaneously it provides SM predictions for numerous rare K and B branching ratios that are most accurate to date. Analyzing this scenario within Z^prime models we point out, following the 2009 observations of Monika Blanke and ours of 2020, that despite the absence of NP contributions to varepsilon _K, significant NP contributions to K^+rightarrow pi ^+nu {bar{nu }}, K_{L}rightarrow pi ^0nu {bar{nu }}, K_Srightarrow mu ^+mu ^-, K_Lrightarrow pi ^0ell ^+ell ^-, varepsilon '/varepsilon and Delta M_K can be present. In the simplest scenario, this is guaranteed, as far as flavour changes are concerned, by a single non-vanishing imaginary left-handed Z^prime coupling g^L_{sd}. This scenario implies very stringent correlations between the Kaon observables considered by us. In particular, the identification of NP in any of these observables implies automatically NP contributions to the remaining ones under the assumption of non-vanishing flavour conserving Z^prime couplings to q{bar{q}}, nu {bar{nu }}, and mu ^+mu ^-. A characteristic feature of this scenario is a strict correlation between K^+rightarrow pi ^+nu {bar{nu }} and K_{L}rightarrow pi ^0nu {bar{nu }} branching ratios on a branch parallel to the Grossman-Nir bound. Moreover, Delta M_K is automatically suppressed as seems to be required by the results of the RBC-UKQCD lattice QCD collaboration. Furthermore, there is no NP contribution to K_Lrightarrow mu ^+mu ^- which otherwise would bound NP effects in K^+rightarrow pi ^+nu {bar{nu }}. Of particular interest are the correlations of K^+rightarrow pi ^+nu {bar{nu }} and K_{L}rightarrow pi ^0nu {bar{nu }} branching ratios and of Delta M_K with the ratio varepsilon '/varepsilon . We investigate the impact of renormalization group effects in the context of the SMEFT on this simple scenario.