We present a model-independent method to study the four-body decay B -> K* (-> K+pi(-) )mu(+)mu(-), based on extracting continuous observables with a moments approach. The method allows the observables to be determined unbinned in both the dilepton and K+pi(-) invariant masses on which the decay dynamics depend. This will allow the method to shed new light on how the observables depend on the P- and S-wave contributions to theK(+)pi(-) system. This approach contrasts with the state-of-the-art analyses, which bin in dilepton and K+pi(-) mass or use a model for the dependence of the underlying decay amplitudes on these masses. The method does not require making a statistical fit and so avoids problems of biases and poor uncertainty estimation when dealing with small samples or a large number of fit parameters. We provide the Standard Model predictions for the unbinned optimized observables, derive new geometrical bounds on their values, and study the robustness of these bounds in the presence of a scalar new physics contribution. We explore the zero-crossing points of P2 and P04;5 observables as a function of a new physics contribution to the dominant vector Wilson coefficient, CNP9 . We also discuss the conditions that can be used to test the theoretical model of the amplitudes needed for an experimental amplitude analysis. Finally, as an illustration, we show how the proposed method might be used to extract the zero-crossing points, make a comparison with the bounds and test a nontrivial relation between the observable values.

We study two-site deconstructions of the SU(2)L gauge group factor of the SM. Models based on this approach can explain the hierarchies of the quark masses and CKM mixing between third and light families if these fields are localised on different sites by the presence of hierarchical new physics scales. The model leads to an accidental global U(2)q × U(3)u × U(3)d flavour symmetry which prevents dangerously large effects in flavour observables, making a TeV extension of the SM possible. Given the structure of the PMNS matrix in the neutrino sector, we explore different possibilities for the arrangement of the leptons on the two sites, and consider different models with U(2)ℓ or U(3)ℓ flavour symmetries. The phenomenology of the models is mostly governed by a massive vector triplet of SU(2)L. We study the interesting interplay between LHC searches and precision observables. In particular, one of the models can give a sizeable lepton flavour universal effect in the Wilson coefficient C9 while naturally suppressing contributions to C10, as suggested by current b → sℓ+ℓ− data, predicting simultaneously a mild positive shift in the W boson mass.

We discuss the impact of the recent LHCb update on the two lepton-flavour universality ratios R_K and R_K^* , and the CMS update of B(B_s →μ ^+μ ^-) regarding the possibility of New Physics in b→ sℓ ^+ℓ ^- decays. We perform global fits of the New Physics Wilson coefficients defined in the model-independent approach of the Weak Effective Theory at the b -quark mass. We discuss three different frameworks for this analysis: (i) an update limited to the experimental data but using the same theoretical framework as in earlier works, (ii) a full update concerning both the experimental inputs and the theoretical framework, (iii) an analysis without the LHCb results on electron modes. The comparison between these various sets of results allows us to identify the differences stemming from the various components of the analysis: new experimental results, new inputs for the hadronic form factors, the role played by LHCb data on electron modes. As expected, the significance of all New Physics hypotheses gets reduced after the LHCb announcements on R_K^(*) while the hypothesis of a lepton-flavour-universal contribution to the Wilson coefficient of the semileptonic O_9ℓ operators (possibly with a very small lepton-flavour-universality violating component) is clearly reinforced. We also discuss the possibility of a long-distance charm-loop contribution through a mode-by-mode analysis and we find that the preferred values for the 𝒞_9μ Wilson coefficient are consistent throughout the different b→ sμ ^+μ ^- modes and that there is no significant evidence of non-constant q^2 dependencies, which would indicate the presence of a long-distance charm-loop contribution beyond those already included.

We review the current status and implications of the anomalies (i.e. deviations from the Standard Model predictions) in semi-leptonic B meson decays, both in the charged and in the neutral current. In b→ sℓ ^+ℓ ^- transitions significant tensions between measurements and the Standard Model predictions exist. They are most pronounced in the branching ratios ℬ_B → Kμ ^+μ ^- and ℬ_B_s→ϕμ ^+μ ^- (albeit quite dependent on the form factors used) as well as in angular observables in B→ K^*μ ^+μ ^- (the P_5^' anomaly). Because the measurements of ℬ_B_s→μ ^+μ ^- and of the ratios R(K) and R(K^*) agree reasonably well with the SM predictions, this points towards (dominantly) lepton flavour universal NP coupling vectorially to leptons, i.e. contributions to C_9^U . In fact, global fits prefer this scenario over the SM hypothesis by 5.8σ . Concerning b→ cτν transitions, R(D) and R(D^*) suggest constructive new physics at the level of 10% (w.r.t. the Standard Model amplitude) with a significance above 3σ . We discuss new physics explanations of both anomalies separately as well as possible combined explanations. In particular, a left-handed vector current solution to R(D^(*)) , either via the U_1 leptoquark or the combination of the scalar leptoquarks S_1 and S_3 , leads to an effect in C_9^U via an off-shell penguin with the right sign and magnitude and a combined significance (including a tree-level effect resulting in C_9^μ =-C_10^μ and R(D^(*)) ) of 6.3σ . Such a scenario can be tested with b → s τ ^+τ ^- decays. Finally, we point out an interesting possible correlation of R(D^(*)) with non-leptonic B anomalies.

The exploration of rare neutral current $b\to s\ell^+\ell^-$ transitions is pivotal in testing the Standard Model (SM) and probing the presence of New Physics (NP) phenomena. This proceedings article offers an overview of recent developments in the examination of anomalies, deviations from SM predictions, in semi-leptonic $B$ meson decays. It encompasses both experimental and theoretical aspects within the domain of global analyses of $b\to s\ell^+\ell^-$ observables. We start by reviewing the current status of the experimental measurements for the key observables that define the decay modes included in global analyses. Subsequently, we delve into the determination of non-perturbative contributions, crucial for the computation of the amplitudes of the various $b\to s\ell^+\ell^-$ modes. Our focus extends to recent advancements in local and non-local form factor calculations and their implications for SM predictions. This sets the stage for a detailed exploration of the outcomes from recent global analyses in the context of one-dimensional (1D) and two-dimensional (2D) fits. We underscore the importance of lepton flavour universality (LFU) throughout this discussion. Furthermore, we explore the interconnections between the tensions in $b\to s\ell^+\ell^-$ data and the anomalies in charged current $b\to c\ell\nu$ transitions, most notably in the $R(D)$ and $R(D^*)$ ratios. Lastly, we comment on the enhancement of $b\to s\tau^+\tau^-$ processes that follows from general NP explanations of the $R(D)$ and $R(D^*)$ anomalies within the Standard Model Effective Theory (SMEFT), under current constraints.

We present an up-to-date complete model-independent global fit to b→ sℓℓ 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^*+ , B_s →ϕμ ^+μ ^- and 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 𝒞_9'μ and 𝒞_10'μ remains a viable possibility. Second, a lepton flavour universality violating (LFUV) left-handed lepton coupling ( 𝒞_9μ^V=-𝒞_10μ^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 𝒞_9^U . We observe that the LFUV observable Q_5 offers a very interesting possibility to separate both types of scenarios.

In this letter we propose a strategy for discerning if new physics in the Wilson coefficient C 9 µ is dominantly lepton flavour universality violating or if it contains a sizable lepton flavour universal component ( C U9 ). Distinguishing among these two cases, for which the model independent fit of the related scenarios exhibits similar pulls with respect to the Standard Model, is crucial to advance our understanding of the B anomalies. We first identify the origin of the degeneracy of these two cases and point out the key observables that can break it. In particular, while the observables measured so far that test lepton flavour universality exhibit similar dependencies to all the relevant Wilson coefficients, the forthcoming measurement of Q 5 = P (cid:48) µ 5 − P (cid:48) e 5 is particularly sensitive to C 9 µ − C 9 e . In fact, if Q 5 were found to be small (i.e. close to its Standard Model value), this would imply a small C 9 µ − C 9 e but a sizable C U9 , given the preference of global fits for a large negative new physics contribution in C 9 µ . We discuss the possible origins of C U9 , in particular how it could originate from new physics. Here, a promising scenario, that could even link b → s(cid:96) + (cid:96) − to R D ( ∗ ) , is the one in which C U9 is generated from a tau loop via an off-shell photon penguin diagram. This setup predicts the branching ratios of B s → τ + τ − and B → K ( ∗ ) τ + τ − to lie within the reach of LHCb, CMS and Belle II. Alternatively, in case of a non-observation of these tauonic processes, we show that the most natural possibility to generate C U9 is a Z (cid:48) with partially lepton flavour universal couplings.

The field of particle physics is at the crossroads. The discovery of a Higgs-like boson completed the Standard Model (SM), but the lacking observation of convincing resonances Beyond the SM (BSM) offers no guidance for the future of particle physics. On the other hand, the motivation for New Physics has not diminished and is, in fact, reinforced by several striking anomalous results in many experiments. Here we summarise the status of the most significant anomalies, including the most recent results for the flavour anomalies, the multi-lepton anomalies at the LHC, the Higgs-like excess at around 96 GeV, and anomalies in neutrino physics, astrophysics, cosmology, and cosmic rays. While the LHC promises up to 4/ab of integrated luminosity and far-reaching physics programmes to unveil BSM physics, we consider the possibility that the latter could be tested with present data, but that systemic shortcomings of the experiments and their search strategies may preclude their discovery for several reasons, including: final states consisting in soft particles only, associated production processes, QCD-like final states, close-by SM resonances, and SUSY scenarios where no missing energy is produced. New search strategies could help to unveil the hidden BSM signatures, devised by making use of the CERN open data as a new testing ground. We discuss the CERN open data with its policies, challenges, and potential usefulness for the community. We showcase the example of the CMS collaboration, which is the only collaboration regularly releasing some of its data. We find it important to stress that individuals using public data for their own research does not imply competition with experimental efforts, but rather provides unique opportunities to give guidance for further BSM searches by the collaborations. Wide access to open data is paramount to fully exploit the LHCs potential.

The most statistically significant hints for new physics in the flavor sector are discrepancies between theory and experiment in $B$ decays to lepton pairs ($b\ensuremath{\rightarrow}s{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$) and a deficit in the unitarity constraints to the 1st row of the Cabibbo-Kobayashi-Maskawa matrix (the Cabibbo angle anomaly). We propose that these anomalies can be reconciled by a simplified model with massive gauge bosons transforming in the adjoint representation of $SU(2{)}_{L}$. After calculating the impact of this model on $B$ decays, observables testing charged current lepton flavor universality (LFU), electro-weak precision observables and LHC searches we perform a global fit to all available data. We find that our model can provide a consistent common explanation of both anomalies and that the fit to the data is more than $7\ensuremath{\sigma}$ better than the fit of the Standard Model. The model also predicts interesting correlations between LFU violation in the charged current and $b\ensuremath{\rightarrow}s{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ data which can be tested experimentally in the near future.

Marcel Algueró, Bernat Capdevila, Sébastien Descotes-Genon, Joaquim Matias and Mart́ın Novoa-Brunet a Grup de F́ısica Teòrica (Departament de F́ısica), Universitat Autònoma de Barcelona, E-08193 Bellaterra (Barcelona), Catalunya. b Institut de F́ısica d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, E-08193 Bellaterra (Barcelona), Catalunya. c Università di Torino and INFN Sezione di Torino, Via P. Giuria 1, Torino I-10125, Italy. d Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France.

We discuss the impact of the recent O(αs3) calculations of the semileptonic width of the b quark and of the relation between pole and kinetic heavy quark masses by Fael et al. on the inclusive determination of |Vcb|. The most notable effect is a reduction of the uncertainty. Our final result is |Vcb|=42.16(51)10−3.

We compute the O(α_s) corrections to the Wilson coefficients of the dimension five operators in inclusive semileptonic B decays in the limit of a massless final quark. Our calculation agrees with reparameterization invariance and with previous results for the total width and places constraints on the shape functions that enter those decays.

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 RK , RKS , RK∗+ , Bs → φμ+μ− and Bs → μμ 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 lepton coupling (CV 9μ = −CV 10μ), often preferred from the model building point of view, accommodates the data better if lepton-flavour universal New Physics is allowed, in particular in CU 9 . We observe that the LFUV observable Q5 offers a very interesting possibility to separate both types of scenarios.

We perform a model-independent global fit to $$b\rightarrow s\ell ^+\ell ^-$$ observables to confirm existing New Physics (NP) patterns (or scenarios) and to identify new ones emerging from the inclusion of the updated LHCb and Belle measurements of $$R_K$$ and $$R_{K^*}$$, respectively. Our analysis, updating Refs. Capdevila et al. (J Virto JHEP 1801:093, 2018) and Algueró et al. (J Matias Phys Rev D 99(7):075017, 2019) and including these new data, suggests the presence of right-handed couplings encoded in the Wilson coefficients $${{{\mathcal {C}}}}_{9'\mu }$$ and $${{{\mathcal {C}}}}_{10'\mu }$$. It also strengthens our earlier observation that a lepton flavour universality violating (LFUV) left-handed lepton coupling ($${{{\mathcal {C}}}}_{9\mu }^{\mathrm{V}}=-\,{{{\mathcal {C}}}}_{10\mu }^{\mathrm{V}}$$), often preferred from the model building point of view, accommodates the data better if lepton-flavour universal (LFU) NP is allowed, in particular in $${{{\mathcal {C}}}}_{9}^{\mathrm{U}}$$. Furthermore, this scenario with LFU NP provides a simple and model-independent connection to the $$b\rightarrow c\tau \nu $$ anomalies, showing a preference of $$\approx 7\,\sigma $$ with respect to the SM. It may also explain why fits to the whole set of $$b\rightarrow s\ell ^+\ell ^-$$ data or to the subset of LFUV data exhibit stronger preferences for different NP scenarios. Finally, motivated by $$Z^\prime $$ models with vector-like quarks, we propose four new scenarios with LFU and LFUV NP contributions that give a very good fit to data.

Discrepancies between measurements of decay modes with an underlying quark level transition $$b\rightarrow s \ell ^+\ell ^-$$ and standard model (SM) predictions have persisted for several years, particularly for the muon channels. The inadequacy of the SM becomes more compelling in a global fit. For example, Capdevila et al. (JHEP 01, 093. arXiv:1704.05340 , 2018) described 175 observables by six parameters encoding new physics and quantified the disagreement with the SM at about the $$5\sigma $$ level. While certain one and two parameter fits have previously been considered in detail, we establish a framework for the detailed discussion of the full 6d fit. We visualize and quantify the 6d $$1\sigma $$ region around the best fit point and define fit uncertainties for both current and future observables. We then define metrics quantifying the deviations between measurements and both SM and best fit predictions. These metrics relate observables to directions in parameter space, revealing their precise role in the fit, thus providing guidance for future theoretical and experimental work. Some metrics further quantify the role of correlated uncertainties, which turns out to be significant. For example the relevance of angular observables such as $$P_5^\prime $$ is reduced in this context. Finally, studying the space of observables allows us to discuss the internal tensions in the fit.

Discrepancies between measurements of decay modes with an underlying quark level transition b→ s ℓ ^+ℓ ^- and standard model (SM) predictions have persisted for several years, particularly for the muon channels. The inadequacy of the SM becomes more compelling in a global fit. For example, Capdevila et al. (JHEP 01 , 093. arXiv:1704.05340 , 2018 ) described 175 observables by six parameters encoding new physics and quantified the disagreement with the SM at about the 5σ level. While certain one and two parameter fits have previously been considered in detail, we establish a framework for the detailed discussion of the full 6d fit. We visualize and quantify the 6d 1σ region around the best fit point and define fit uncertainties for both current and future observables. We then define metrics quantifying the deviations between measurements and both SM and best fit predictions. These metrics relate observables to directions in parameter space, revealing their precise role in the fit, thus providing guidance for future theoretical and experimental work. Some metrics further quantify the role of correlated uncertainties, which turns out to be significant. For example the relevance of angular observables such as P_5^' is reduced in this context. Finally, studying the space of observables allows us to discuss the internal tensions in the fit.

Abstract Discrepancies between measurements of decay modes with an underlying quark level transition $$b\rightarrow s \ell ^+\ell ^-$$ b→sℓ+ℓ- and standard model (SM) predictions have persisted for several years, particularly for the muon channels. The inadequacy of the SM becomes more compelling in a global fit. For example, Capdevila et al. (JHEP 01, 093. arXiv:1704.05340, 2018) described 175 observables by six parameters encoding new physics and quantified the disagreement with the SM at about the $$5\sigma $$ 5σ level. While certain one and two parameter fits have previously been considered in detail, we establish a framework for the detailed discussion of the full 6d fit. We visualize and quantify the 6d $$1\sigma $$ 1σ region around the best fit point and define fit uncertainties for both current and future observables. We then define metrics quantifying the deviations between measurements and both SM and best fit predictions. These metrics relate observables to directions in parameter space, revealing their precise role in the fit, thus providing guidance for future theoretical and experimental work. Some metrics further quantify the role of correlated uncertainties, which turns out to be significant. For example the relevance of angular observables such as $$P_5^\prime $$ P5′ is reduced in this context. Finally, studying the space of observables allows us to discuss the internal tensions in the fit.

We perform a model-independent global fit to $b\to s\ell^+\ell^-$ observables to confirm existing New Physics (NP) patterns (or scenarios) and to identify new ones emerging from the inclusion of the updated LHCb and Belle measurements of $R_K$ and $R_{K^*}$, respectively. Our analysis, updating Refs. [1,2] and including these new data, suggests the presence of right-handed couplings encoded in the Wilson coefficients ${\cal C}_{9'\mu}$ and ${\cal C}_{10'\mu}$. It also strengthens our earlier observation that a lepton flavour universality violating (LFUV) left-handed lepton coupling (${\cal C}_{9\mu}^{\rm V}=-{\cal C}_{10\mu}^{\rm V}$), often preferred from the model building point of view, accommodates the data better if lepton-flavour universal (LFU) NP is allowed, in particular in ${\cal C}_{9}^{\rm U}$. Furthermore, this scenario with LFU NP provides a simple and model-independent connection to the $b\to c\tau \nu$ anomalies, showing a preference of $\approx 7\,\sigma$ with respect to the SM. It may also explain why fits to the whole set of $b\to s\ell^+\ell^-$ data or to the subset of LFUV data exhibit stronger preferences for different NP scenarios. Finally, motivated by $Z^\prime$ models with vector-like quarks, we propose four new scenarios with LFU and LFUV NP contributions that give a very good fit to data. We provide also an addendum collecting our updated results after including the data for the $B\to K^*\mu\mu$ angular distribution released in 2020 by the LHCb collaboration.

This is an Addendum to the articles JHEP 1801 (2018) 093 and arXiv:1809.08447 [hep-ph]. We update here the main results of the global fits of both papers to take into account the recent updates of $R_K$ from the LHCb collaboration and $R_{K^*}$, $R_{D^{(*)}}$ from Belle.