We present a detailed discussion of the current theoretical and experimental situation of the anomaly in the angular distribution of B → K * (→ Kπ)µ + µ − , observed at LHCb in the 1 fb −1 dataset and recently confirmed by the 3 fb −1 dataset. The impact of this data and other recent measurements on b → s + − transitions ( = e, µ) is considered. We review the observables of interest, focusing on their theoretical uncertainties and their sensitivity to New Physics, based on an analysis employing the QCD factorisation approach including several sources of hadronic uncertainties (form factors, power corrections, charmloop effects). We perform fits to New Physics contributions including experimental and theoretical correlations. The solution that we proposed in 2013 to solve the B → K * µ + µ − anomaly, with a contribution C NP 9 −1, is confirmed and reinforced. A wider range of New-Physics scenarios with high significances (between 4 and 5 σ) emerges from the fit, some of them being particularly relevant for model building. More data is needed to discriminate among them conclusively. The inclusion of b → se + e − observables increases the significance of the favoured scenarios under the hypothesis of New Physics breaking lepton flavour universality. Several tests illustrate the robustness of our conclusions.

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We present the library Collier for the numerical evaluation of one-loop scalar and tensor integrals in perturbative relativistic quantum field theories. The code provides numerical results for arbitrary tensor and scalar integrals for scattering processes in general quantum field theories. For tensor integrals either the coefficients in a covariant decomposition or the tensor components themselves are provided. Collier supports complex masses, which are needed in calculations involving unstable particles. Ultraviolet and infrared singularities are treated in dimensional regularization. For soft and collinear singularities mass regularization is available as an alternative.Keywords: NLO computations; radiative corrections; one-loop integrals; higher orders; tensor reduction; scalar integrals PROGRAM SUMMARY

Abstract:The recent LHCb angular analysis of the exclusive decay B → K * µ + µ − has indicated significant deviations from the Standard Model expectations. Accurate predictions can be achieved at large K * -meson recoil for an optimised set of observables designed to have no sensitivity to hadronic input in the heavy-quark limit at leading order in α s . However, hadronic uncertainties reappear through non-perturbative Λ QCD /m b power corrections, which must be assessed precisely. In the framework of QCD factorisation we present a systematic method to include factorisable power corrections and point out that their impact on angular observables depends on the scheme chosen to define the soft form factors. Associated uncertainties are found to be under control, contrary to earlier claims in the literature. We also discuss the impact of possible non-factorisable power corrections, including an estimate of charm-loop effects. We provide results for angular observables at large recoil for two different sets of inputs for the form factors, spelling out the different sources of theoretical uncertainties. Finally, we comment on a recent proposal to explain the anomaly in B → K * µ + µ − observables through charm-resonance effects, and we propose strategies to test this proposal identifying observables and kinematic regions where either the charm-loop model can be disentangled from New Physics effects or the two options leave different imprints.

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Abstract:We introduce the computer code Recola for the recursive generation of tree-level and oneloop amplitudes in the Standard Model. Tree-level amplitudes are constructed using off-shell currents instead of Feynman diagrams as basic building blocks. One-loop amplitudes are represented as linear combinations of tensor integrals whose coefficients are calculated similarly to the tree-level amplitudes by recursive construction of loop off-shell currents. We introduce a novel algorithm for the treatment of colour, assigning a colour structure to each off-shell current which enables us to recursively construct the colour structure of the amplitude efficiently. Recola is interfaced with a tensor-integral library and provides complete one-loop Standard Model amplitudes including rational terms and counterterms. As a first application we consider Z + 2 jets production at the LHC and calculate with Recola the next-to-leading-order electroweak corrections to the dominant partonic channels.

Recent measurements of b → sµ + µ − processes at LHCb and BELLE have revealed tensions at the 2 − 3 σ level between the Standard Model (SM) prediction and the experimental results in the channels B → K * µ + µ − and B s → φµ + µ − , as well as in the lepton-flavor universality violating observable R K = Br(B → Kµ + µ − )/Br(B → Ke + e − ). Combined global fits to the available b → sµ + µ − data suggest that these tensions might have their common origin in New Physics (NP) beyond the SM because some NP scenarios turn out to be preferred over the SM by 4 − 5 σ. The fact that all these anomalies are related to muons further suggests a connection (and a common NP explanation) with the long-standing anomaly in the anomalous magnetic moment of the muon, a µ . In this article, we study the impact of a generic class of NP models featuring new heavy scalars and fermions that couple to the SM fermions via Yukawa-like interactions. We consider two different scenarios, introducing either one additional fermion and two scalars or two additional fermions and one scalar, and examine all possible representations of the new particles under the SM gauge group with dimension up to the adjoint one. The models induce one-loop contributions to b → sµ + µ − and a µ which are capable of solving the respective anomalies at the 2σ level, albeit a relatively large coupling of the new particles to muons is required. In the case of b → sµ + µ − , stringent constraints from B s − B s mixing arise which can be relaxed if the new fermion is a Majorana particle.

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