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Assuming the source of the anomalies observed recently in $b \to s$ data tobe new physics, there is a priori no reason to believe that - in the effectivefield theory language - only one type of operator is responsible for thetensions. We thus perform for the first time a global fit where all the Wilsoncoefficients which can effectively receive new physics contributions areconsidered, allowing for lepton flavour universality breaking effects as wellas contributions from chirality flipped and scalar and pseudoscalar operators,and find the SM pull taking into account all effective parameters. As a resultof the full fit to all available $b \to s$ data including all relevant Wilsoncoefficients, we obtain a total pull of 4.1$\sigma$ with the SM hypothesisassuming 10% error for the power corrections. Moreover, we make a statisticalcomparison to find whether the most favoured explanation of the anomalies isnew physics or underestimated hadronic effects using the most generalparameterisation which is fully consistent with the analyticity structure ofthe amplitudes. This Wilks' test will be a very useful tool to analyse theforthcoming $B\to K^* \mu^+ \mu^-$ data. Because the significance of theobserved tensions in the angular observables in $B \to K^* \mu^+\mu^-$ ispresently dependent on the theory estimation of the hadronic contributions tothese decays, we briefly discuss the various available approaches for takinginto account the long-distance hadronic effects and examine how the differentestimations of these contributions result in distinct significance of the newphysics interpretation of the observed anomalies.

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