Natural Suppression of FCNCs at the One-Loop Level in $Z^\prime$ Models with Implications for K, D and B Decays

TL;DR

This paper demonstrates that in $Z^\prime$ models, one-loop FCNC processes are naturally suppressed due to hermitian flavor matrices, with negligible contributions to K, D, and B decays, and introduces a new parametrization of flavor interactions.

Contribution

It introduces a hermitian, unitary matrix framework for $Z^\prime$ flavor interactions, ensuring suppression of FCNCs at one-loop and providing a novel parametrization distinct from the CKM matrix.

Findings

One-loop $Z^\prime$ contributions to FCNCs are suppressed by quark mass ratios.

The framework distinguishes flavor interactions from CKM, highlighting new CP-violating phases.

Suppression is especially significant for $K$, $D$, and $B$ meson systems.

Abstract

We analyse $Z^\prime$ contributions to FCNC processes at the one-loop level. In analogy to the CKM matrix we introduce two $3\times3$ unitary matrices $\hat\Delta_d(Z^\prime)$ and $\hat\Delta_u(Z^\prime)$ which are also hermitian. They govern the flavour interactions mediated by $Z^\prime$ between down-quarks and up-quarks, respectively, with $\hat\Delta_d(Z^\prime)=\hat\Delta_u(Z^\prime)\equiv \hat\Delta_L(Z^\prime)$ for left-handed currents due to the unbroken $\text{SU(2)}_L$ gauge symmetry. This assures the suppression of these contributions to all $Z^\prime$ mediated FCNC processes at the one-loop level. As, in contrast to the GIM mechanism, one-loop $Z^\prime$ contributions to flavour observables in $K$ and $B_{s,d}$ systems are governed by down-quark masses, they are ${\cal O}(m^2_b/M^2_{Z^\prime})$ and negligible. With the ${\cal O}(m^2_t/M^2_{Z^\prime})$ suppression they are likely negligible also in the $D$ system. We present an explicit parametrization of $\hat\Delta_L(Z^\prime)$ in terms of two mixing angles and two complex phases that distinguishes it profoundly from the CKM matrix. This framework can be generalized to purely leptonic decays with matrices analogous to the PMNS matrix but profoundly different from it. Interestingly, the breakdown of flavour universality between the first two generations and the third one, both for quark and lepton couplings to $Z^\prime$, is identified as a consequence of $\hat\Delta_L(Z^\prime)$ being hermitian. The importance of the unitarity for both $\hat\Delta_L(Z^\prime)$ and the CKM matrix in the light of the Cabibbo anomaly is emphasized.