Hadronic and New Physics Contributions to $b \to s$ Transitions

Assuming the source of the anomalies observed recently in $b \to s$ data to be new physics, there is a priori no reason to believe that - in the effective field theory language - only one type of operator is responsible for the tensions. We thus perform for the first time a global fit where all the Wilson coefficients which can effectively receive new physics contributions are considered, allowing for lepton flavour universality breaking effects as well as contributions from chirality flipped and scalar and pseudoscalar operators, and find the SM pull taking into account all effective parameters. As a result of the full fit to all available $b \to s$ data including all relevant Wilson coefficients, we obtain a total pull of 4.1$\sigma$ with the SM hypothesis assuming 10% error for the power corrections. Moreover, we make a statistical comparison to find whether the most favoured explanation of the anomalies is new physics or underestimated hadronic effects using the most general parameterisation which is fully consistent with the analyticity structure of the amplitudes. This Wilks' test will be a very useful tool to analyse the forthcoming $B\to K^* \mu^+ \mu^-$ data. Because the significance of the observed tensions in the angular observables in $B \to K^* \mu^+\mu^-$ is presently dependent on the theory estimation of the hadronic contributions to these decays, we briefly discuss the various available approaches for taking into account the long-distance hadronic effects and examine how the different estimations of these contributions result in distinct significance of the new physics interpretation of the observed anomalies.