Exhaustive Model Selection in $b \to s \ell \ell$ Decays: Pitting Cross-Validation against AIC$_c$

Abstract

In the light of recent data, we study the new physics effects in the exclusive $b \to s \ell^+\ell^-$ decays from a model independent perspective. Different combinations of the dimension six effective operators along with their respective Wilson coefficients are chosen for the analysis. To find out the operator or sets of operators that can best explain the available data in this channel, we simultaneously apply popular model selection tools like cross-validation and the information theoretic approach like Akaike Information Criterion (AIC). There are one, two, and three-operator scenarios which survive the test and a left-handed quark current with vector muon coupling is common among them. This is also the only surviving one-operator scenario. Best-fit values and correlations of the new Wilson coefficients are supplied for all the selected scenarios. We find that the angular observables play the dominant role in the model selection procedure. We also note that while a left-handed quark current with axial-vector muon coupling is the only one-operator scenario able to explain the ratios $R_{K^{(*)}}$ ($R_{K^*}$ for $q^2\in [ 0.045, 1.1] {\rm GeV}^2$ in particular), there are also a couple of two operator scenarios that can simultaneously explain the measured $R_{K^{(*)}}$.