$$b\rightarrow s\ell ^+\ell ^-$$ b → s ℓ + ℓ - global fits after $$R_{K_S}$$ R K S and $$R_{K^{*+}}$$ R K ∗ +

Eur. Phys. J. C (2022) 82:326 https://doi.org/10.1140/epjc/s10052-022-10231-1 Regular Article - Theoretical Physics b → s+ − global fits after R K S and R K ∗+ Marcel Algueró1,2,a , Bernat Capdevila3 , Sébastien Descotes-Genon4 , Joaquim Matias1,2 , Martín Novoa-Brunet4,5 1 Grup de Física Teòrica (Departament de Física), Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain 2 Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona), Spain 3 Università di Torino and INFN Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy 4 Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France 5 Istituto Nazionale di Fisica Nucleare, Sezione di Bari, Via Orabona 4, 70126 Bari, Italy Received: 17 December 2021 / Accepted: 21 March 2022 © The Author(s) 2022 Abstract We present an up-to-date complete model-independent global fit to b → s observables that confirms patterns of New Physics able to explain the data. We include the recent LHCb measurements of R K , R K S , R K ∗+ , Bs → φμ+ μ− and Bs → 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 C9 μ and C10 μ remains a viable possibility. Second, a lepton flavour universality violating (LFUV) left-handed V = −C V ), often preferred from the lepton coupling (C9μ 10μ model building point of view, accommodates the data better if lepton-flavour universal New Physics is allowed, in particular in C9U . We observe that the LFUV observable Q 5 offers a very interesting possibility to separate both types of scenarios. 1 Introduction The flavour anomalies in b → s processes are currently among the most promising signals of New Physics (NP) [1– 3]. This has been reinforced by the recent LHCb updates of quantities assessing the violation of lepton-flavour universality (LFU). On the one hand, we have the ratio R K [4]: RK = B(B + → K + μ+ μ− ) B(B + → K + e+ e− ) +0.042 +0.013 R [1.1,6] K ,LHCb = 0.846−0.039 −0.012 sured for the experimentally challenging modes [5] B(B 0 → K S μ+ μ− ) B(B 0 → K S e+ e− ) B(B + → K ∗+ μ+ μ− ) R K ∗+ = B(B + → K ∗+ e+ e− ) RK S = (2) with the results +0.20 +0.02 R [1.1,6] K S ,LHCb = 0.66−0.14 −0.04 +0.18 +0.03 R [0.045,6] = 0.70−0.13 −0.04 K ∗+ ,LHCb (3) in agreement each with the SM below the 2σ level but consistent with the downward trend compared to the predictions of the Standard Model (SM). Indeed, in the SM, these ratios are protected from hadronic contributions and are known to be 1 up to (tiny) electromagnetic corrections and (simple) kinematic mass effects. The deviations observed in these modes can be efficiently and consistently analysed in a model-independent effective field theory (EFT) framework (see, for instance, Refs. [6– 16]), where short-distance physics (SM and NP) is encoded in the Wilson coefficients of higher-dimension operators.1 This tool has proven particularly helpful in identifying NP scenarios (or patterns of NP) that could explain the data at the level of the EFT, providing guidelines for the construction of phenomenologically viable NP models. In this context, we present here the latest theoretical and experimental update of our previous works in Refs. [7–9] to (1) with an extended statistics corresponding to 9 fb−1 , reaching the level of statistical evidence (above 3 standard deviations). On the other hand, similar quantities have been recently meaa e-mail: (corresponding author) 0123456789().: V,-vol 1 It is interesting to point out that the results in Ref. [12] are very similar to the ones found in the analysis presented in this article. Although they use a similar set of observables (with the addition of baryon decays), the analyses differ through the treatment of hadronic uncertainties (form factors, charm-loop contributions). This similarity illustrates the robustness of the results with respect to different assumptions on hadronic uncertainties. 123 326 Page 2 of 16 serve as an accurate guideline for model building, as well as an overview of observables relevant for the near future. We follow the same theoretical and statistical approach as in our previous works, updating and adding new experimental inputs and their corresponding SM predictions. It is important at this point to check if the inclusion of this new data alters some of our earlier conclusions, in particular concerning best-fit points and confidence intervals that are required for model building as well as the hierarchy of the various NP scenarios that are favoured by the current global fits. It turns out that our conclusions remain unchanged and are thus very robust. We will therefore discuss the outcome of our updated global fits but we refer the interested reader to Ref. [9] for a more detailed interpretation of our results as well as the differences with respect to other approaches [10–12,14]. The structure of this article is the following. In Sect. 2 we list the additional and updated measurements included. Section 3 is devoted to the methodology of the global fit, with updated results presented in Sect. 4. The link between neutral and charged anomalies using a scenario involving LFUV and LFU NP is discussed in Sect. 5. An overview of the main results and conclusions is given in Sect. 6, together with a proposal to disentangle the main two solutions of the global fit. Finally, the list of experimental inputs and SM predictions for the observables included in our fits is discussed in Appendix A. 2 Observables We consider the same observables and theoretical inputs as in Ref. [9], taking into account the following updated measurements (replacing the previous ones): • The experimental values of R K , R K S and R K ∗+ from the LHCb collaboration already discussed in the introduction [4,5]. We also take into account their update of R K [17] as well as the branching ratios for B 0,+ → K 0,+ μ+ μ− updated by the Belle collaboration [18] (the Belle measurements of R K (∗) correspond to a combination of the charged and neutral channels B 0,+ → K (∗)0,+ + − ). • The experimental value of the branching ratio B(Bs → μ+ μ− ) from the LHCb collaboration [19], which is combined with the results from CMS [20] and ATLAS [21], leading to the average B(Bs → μ+ μ− ) = 2.85+0.34 −0.31 × 10−9 [22]. This is to be compared with the most updated theoretical computation [23]. • The angular distribution of B + → K ∗+ μ+ μ− [24] using the optimised observables Pi [25] measured by LHCb, as well as the longitudinal polarisation and forwardbackward asymmetry measured by the CMS collaboration [26]. Compared to the neutral case, our computation for the charged case takes into account the different spec- 123 Eur. Phys. J. C (2022) 82:326 tator quark not only by modifying the mass and lifetime, but also the annihilation and hard-specta (...truncated)