Correlating $\epsilon^\prime/\epsilon$ to hadronic $B$ decays via $U(2)^3$ flavour symmetry

TL;DR

This paper explores how a $U(2)^3$ flavor symmetry can simultaneously explain deviations in CP violation observables in B and Kaon decays, using an effective field theory approach and fitting to experimental data.

Contribution

It identifies specific operators within a $U(2)^3$ flavor symmetry framework that can account for anomalies in CP violation measurements and performs a global fit to validate this model.

Findings

A consistent new physics pattern explains $ ext{Re}(rac{ ext{CP violation}}{ ext{Standard Model}})$ deviations.

The $U(2)^3$ symmetry predicts specific effects in $b o d$ transitions.

The model fits well with recent measurements of CP asymmetries in B decays.

Abstract

There are strong similarities between charge-parity (CP) violating observables in hadronic $B$ decays (in particular $\Delta A^-_{\rm CP}$ in $B\to K\pi$) and direct CP violation in Kaon decays ($\epsilon^\prime$): All these observables are very sensitive to new physics (NP) which is at the same time CP and isospin violating (i.e. NP with complex couplings which are different for up quarks and down quarks). Intriguingly, both the measurements of $\epsilon^\prime$ and $\Delta A^-_{\rm CP}$ show deviations from their Standard Model predictions, calling for a common explanation (the latter is known as the $B\to K\pi$ puzzle). For addressing this point, we parametrize NP using a gauge invariant effective field theory approach combined with a global $U(2)^3$ flavor symmetry in the quark sector (also known as less-minimal flavour violation). We first determine the operators which can provide a common explanation of $\epsilon^\prime$ and $\Delta A^-_{\rm CP}$ and then perform a global fit of their Wilson coefficients to the data from hadronic $B$ decays. Here we also include e.g. the recently measured CP asymmetry in $B_s\to KK$ as well as the purely isospin violating decay $B_s\to\phi\rho^0$, finding a consistent NP pattern providing a very good fit to data. Furthermore, we can at the same time explain $\epsilon^\prime/\epsilon$ for natural values of the free parameters within our $U(2)^3$ flavour approach, and this symmetry gives interesting predictions for hadronic decays involving $b\to d$ transitions.