Low-energy effective field theories for lepton universality violation in B decays

In the last few years the experimental collaborations of LHCb, Belle and Babar reported indications of lepton flavor universality violation in the processes B → K* l l and B → D* l ν. Since the universality of weak interactions is one of the key predictions of the Standard Model (SM), these results have triggered a large interest about possible New Physics (NP) interpretations. In the present work we analyse the lepton flavor universality ratios RK μ/e and RD τ/l in a model-independent way, assuming that NP originates at a scale Λ ≈ 1TeV. We start by building the NP Lagrangian at the scale Λ in terms of five six-dimensional semi-leptonic operators. Then we derive the low-energy effective Lagrangian extensively: we address running effects from Λ to the electroweak scale by employing one-loop renormalization group equations (RGE) in the limit of exact electroweak symmetry, and, after integrating out heavy degrees of freedom, we describe the evolution down to 1 GeV using RGE dominated by the electromagnetic interaction. In the last part of our work, we study the most relevant phenomenological consequences of the derived Lagrangian. After considering B anomalies and other B decays receiving NP contribution at tree level, we investigate the phenomenology arising at one loop. Since the most important effects of the running are the modification of the Z and W couplings and the generation of a purely leptonic effective lagragian, we focuse on lepton flavor universality and lepton flavor violation in Z-pole observables and in τ decays. Motivated by the global fits regarding NP in b → s μ μ transitions, we finally consider the scenario where only the Wilson coefficient C9 receives NP contributions, with the aim of quantifying the impact of one-loop-induced constraints on RK μ/e and RD τ/l .