We present an up-to-date complete model-independent global fit to $$b\rightarrow s\ell \ell $$ b → s ℓ ℓ observables that confirms patterns of New Physics able to explain the data. We include the recent LHCb measurements of $$R_K$$ R K , $$R_{K_S}$$ R K S , $$R_{K^{*+}}$$ R K ∗ + , $$B_s \rightarrow \phi \mu ^+\mu ^-$$ B s → ϕ μ + μ - and $$B_s\rightarrow \mu ^+\mu ^-$$ B s → μ + μ - in our analysis, which now includes 254 observables. This updates our previous analyses and strengthens their two main outcomes. First, the presence of right-handed couplings encoded in the Wilson coefficients $${{\mathcal {C}}}_{9'\mu }$$ C 9 ′ μ and $${{\mathcal {C}}}_{10'\mu }$$ C 10 ′ μ remains a viable possibility. Second, a lepton flavour universality violating (LFUV) left-handed lepton coupling ($${{\mathcal {C}}}_{9\mu }^{\mathrm{V}}=-{{\mathcal {C}}}_{10\mu }^{\mathrm{V}}$$ C 9 μ V = - C 10 μ V ), often preferred from the model building point of view, accommodates the data better if lepton-flavour universal New Physics is allowed, in particular in $${{\mathcal {C}}}_{9}^{\mathrm{U}}$$ C 9 U . We observe that the LFUV observable $$Q_5$$ Q 5 offers a very interesting possibility to separate both types of scenarios.

This paper is an addendum to Ref. Eur. Phys. J. C79 (2019) no. 8, 714 that supersedes all results (Tables and Figures) in that paper after including the new data on the $$B\rightarrow K^*\mu \mu $$B→K∗μμ angular distribution released in 2020 by the LHCb collaboration. The new results confirm all the conclusions in Eur. Phys. J. C79 (2019) no. 8, 714, exhibiting an increase in the coherence and significance of the hypotheses and confirming the existence of a puzzle.

We apply the formalism of amplitude symmetries to the angular distribution of the decays B → D * ν for = e, µ, τ . We show that the angular observables used to describe the distribution of this class of decays are not independent in absence of New Physics contributing to tensor operators. We derive sets of relations among the angular coefficients of the decay distribution for the massless and massive lepton cases which can be used to probe in a very general way the consistency among the angular observables and the underlying New Physics at work. We use these relations to access the longitudinal polarisation fraction of the D * using different angular coefficients from the ones used by Belle experiment. This in the near future can provide an alternative strategy to measure F D * L in B → D * τ ν and to understand the relatively high value measured by the Belle experiment. Using the same symmetries, we identify three observables which may exhibit a tension if the experimental value of F D * L remains high. We discuss how these relations can be exploited for binned measurements. We also propose a new observable that could test for specific scenarios of New Physics generated by light right-handed neutrinos. Finally we study the prospects of testing these relations based on the projected experimental sensitivity of new experiments.