New Physics in \({\varvec{b \rightarrow s \ell ^+ \ell ^-}}\) confronts new data on lepton universality

Eur. Phys. J. C (2019) 79:719 https://doi.org/10.1140/epjc/s10052-019-7210-9 Regular Article - Theoretical Physics New Physics in b → s+ − confronts new data on lepton universality Marco Ciuchini1,a , António M. Coutinho2,b , Marco Fedele3,c , Enrico Franco4,d , Ayan Paul5,6,e , Luca Silvestrini4,6,7,f , Mauro Valli8,g 1 INFN, Sezione di Roma Tre, Via della Vasca Navale 84, 00146 Rome, Italy 2 CFTP, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais 1, 1049-001 Lisbon, Portugal 3 Dept. de Física Quàntica i Astrofísica, Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, Martí Franquès 1, 08028 Barcelona, Spain 4 INFN, Sezione di Roma, P.le A. Moro 2, 00185 Rome, Italy 5 DESY, Notkestraße 85, 22607 Hamburg, Germany 6 Institut für Physik, Humboldt-Universität zu Berlin, 12489 Berlin, Germany 7 Theoretical Physics Department, CERN, Geneva, Switzerland 8 Department of Physics and Astronomy, University of California, Irvine, CA 92697-4575, USA Received: 12 April 2019 / Accepted: 8 August 2019 / Published online: 27 August 2019 © The Author(s) 2019 Abstract In light of the very recent updates on the R K and R K ∗ measurements from the LHCb and Belle collaborations, we systematically explore here imprints of New Physics in b → s+ − transitions using the language of effective field theories. We focus on effects that violate Lepton Flavour Universality both in the Weak Effective Theory and in the Standard Model Effective Field Theory. In the Weak Effective Theory we find a preference for scenarios with the simultaneous presence of two operators, a left-handed quark current with vector muon coupling and a right-handed quark current with axial muon coupling, irrespective of the treatment of hadronic uncertainties. In the Standard Model Effective Field Theory we select different scenarios according to the treatment of hadronic effects: while an aggressive estimate of hadronic uncertainties points to the simultaneous presence of two operators, one with left-handed quark and muon couplings and one with left-handed quark and right-handed muon couplings, a more conservative treatment of hadronic matrix elements leaves room for a broader set of scenarios, including the one involving only the purely left-handed operator with muon coupling. a e-mail: b e-mail: c e-mail: d e-mail: e e-mail: f e-mail: g e-mail: 1 Introduction The past few years have brought us a thriving debate on the possible hints of New Physics (NP) from measurements of semileptonic B decays. In particular, Flavour Changing Neutral Current (FCNC) decay modes into multi-body final states, e.g. B → K (∗) + − and Bs → φ + − , bring forth a large number of experimental handles, see e.g. [1], that are extremely useful for NP investigations while also allowing to probe the Standard Model (SM) itself in detail [2–6]. The inference of what pattern is being revealed by the experimental observations is the crux of the debate. Two distinct classes of observables characterize these semileptonic decays. The first is the class of angular observables arising from the kinematic distribution of the differential decay widths that have been measured at LHCb [7– 13], Belle [14], ATLAS [15] and CMS [16–18]. These observables, mostly related to the muonic decay channel, while being sensitive to NP [6,19–22] are besieged by hadronic uncertainties [23–28]. The latter, associated with QCD long-distance effects – hard to estimate from first principles [29,30] – can saturate the measurements so as to be interpreted as possibly arising from the SM or can obfuscate the gleaning of NP from SM contributions [31–33]. Therefore, in the absence of a complete and reliable calculation of the hadronic long-distance contributions, a clear resolution of this debate based solely on the present set of angular measurements is hard to achieve. Improved experimental information in the near future [34] concerning, in particular, the electron modes is a subject of current cross-talk between the 123 719 Page 2 of 27 Eur. Phys. J. C (2019) 79:719 theoretical and experimental communities [35,36], and may shed new light on this matter [37–39]. The second class of observables then becomes crucial to this debate. These are the Lepton Flavour Universality Violating (LFUV) ratios that hold the potential to conclusively disentangle NP contributions from SM hadronic effects. The latter are indeed lepton flavour universal [2,40]. Several hints in favour of LFUV have surfaced in the past few years in experimental searches at LHCb [41,42] and Belle [14]. These have led to a plethora of theoretical investigations [43–161], all oriented towards physics Beyond the Standard Model (BSM) able to accommodate such LFUV signals, mainly involving Z  or leptoquark mediators at scales typically larger than a few TeV and with some peculiar flavour structure needed to avoid clashing with the stringent bounds from meson–antimeson mixing and from other observables. Despite possible model-building challenges, the primary message here is clear: a statistically significant measurement of LFUV effects in FCNCs such as b → s+ − decays would herald the discovery of NP unambiguously [162–167]. In this work we focus on the progress of this debate with the new measurements of R K and R K ∗ recently presented by the LHCb [168] and Belle collaborations [169]:   Br B + → K + μ+ μ−   R K [1.1, 6] ≡ Br B + → K + e+ e− +0.016 = 0.846+0.060 −0.054 −0.014 (LHCb),   Br B → K ∗ μ+ μ− R K ∗ [0.045, 1.1] ≡ R K ∗ [1.1, 6] = 0.96+0.45 −0.29 ± 0.11 (Belle). We review our theoretical framework in Sect. 2, where we also present a fresh look at the anatomy of R K in light of the new LHCb measurement. We then provide a thorough description of our analysis procedure in Sect. 3. Finally, we collect and discuss all our main results in Sect. 4, supported also by Appendix A and Appendix B. We present our conclusions in Sect. 5. 2 Theoretical framework (1)   Br B → K ∗ e+ e− +0.36 = 0.52−0.26 ± 0.05 (Belle), – We revisit our approach to QCD power corrections streamlined for efficiently capturing long-distance effects, which are of utmost relevance in the interpretation of the current experimental information on the B → K ∗ μ+ μ− channel. We discuss several novelties about our new parameterization of hadronic contributions, recently introduced in [39]; – We make use of two distinct Effective Field Theory (EFT) frameworks, namely the ΔB = 1 Weak Effective Hamiltonian and the Standard Model Effective Field Theory (SMEFT). The former EFT allows us to obtain a better insight on the dynamics at the decay scale, while the latter can offer a deeper link with BSM interpretations. (2) (3) As an introduction to the basic ingredients of our analysis we start by reviewing the standard EFT for ΔB = 1 transitions, highlighting the distinction between short-distance and hadronic contributions. We then move on to LFUV effects in terms of SM gauge-invariant di (...truncated)