QED corrections and new physics effects in the determination of V_cb and V_ub for Belle II and LHCb
Final Report Abstract
3 Summary The work on the QED corrections in exclusive decays focused on the simplest leptonic decays Bq → µ+ µ− and Bu → µ¯µ . The specific kinematic situation of a heavy initial hadronic state that releases all ν its mass into the light energetic two-body final state enables for the first time a complete factorization of the leading QED effects for an exclusive B-meson decay. The factorization is technically achieved via a stack of effective theories (EFT) for the intermediate energy regions that arise due to the external kinematic situation, providing a systematic treatement of these effects. In particular the process-specific structure-dependent corrections were factorized at the level of the amplitude in Soft-Collinear Effective Theory (SCET). A rearrangement of infrared divergences between the involved collinear and soft sectors allows the definition of generalized hadronic matrix elements, namely the B-meson decay constant and the light-cone distribution amplitude. In the absence of QED corrections, both are quantities that appear universally in many B-meson processes, however in the presence of QED corrections they become process-specific. The QED corrections analyzed in this work are actually an example of subleading-power resummation in SCET, a field that only recently gained more attention. The effect of ultra-soft QED corrections was factorized at the level of the amplitude-squared using a heavy-lepton EFT. The exponentiation of these QED corrections known from the soft-photon approximation (SPA) is recovered. However, our EFT framework provides properly a cutoff of virtual ultrasoft contributions, usually assumed in SPA, and connects them correctly with the structuredependent corrections, avoiding any double counting. Our predictions of the non-radiative and radiative branching fractions include the largest QED corrections and strengthen further the theoretical predictions of leptonic B-decays as the most precise branching fraction of an exclusive B-decay. Within the range of validity of our calculation it can be used to gain control over simulation tools like PHOTOS usually employed to perform the SPA in experimental analyses. Our analysis has revealed that QED corrections lead to hadronic matrix elements, which are non-local time-ordered products. This has to be considered when these quantities are evaluated with nonperturbative methods, such as lattice gauge theory. The situation becomes even more complicated for exclusive semileptonic decays, where different process-dependent nonperturbative objects have to be defined for different phase-space regions. The number of nonperturbative objects will proliferate, as in this case it will also be necessary to include QED effects for the final-state hadrons. The analysis of effects beyond the Standard Model (SM) using the model-independent parameterization of the framework of SMEFT has for the first time revealed the full spectrum of potential ij ¯ correlations of neutral meson mixing, described by the ∆F = 2 quantity M12 for the systems K 0 − K 0 ¯ ¯ (ij = ds), D0 − D0 (ij = cu) and Bs,d − Bs,d (ij = bd and ij = bs), to other processes. Contrary to the strong correlations in the SM based solely on the common dependence on quark-mixing elements of the unitary CKM matrix, the presence of additional flavour-violating higher-dimensional operators in SMEFT can lift SM correlations and induce novel ones to nonleptonic ∆F = 1 processes, modified Z- and W -boson couplings and semileptonic processes. These correlations are fully quantified in our “SMEFT Atlas of ∆F = 2 transtions” in the most general way directly applicable to specific UV completions at some new physics scale µNP , including complete next-to-leading order (NLO) QCD resummation below the electroweak scale µEW , NLO threshold corrections at µEW and LO resummation above µEW for the full SM gauge and Higgs sector. Ongoing work in progress will supplement the corresponding NLO QCD corrections for the ∆F = 1 sector, putting the accuracy for new physics contributions on the same level as the SM ones in order to establish a combined SMEFT analysis of ∆F = 2 and nonleptonic ∆F = 1 processes. ¯ The ongoing work of analysis of effects beyond the SM in b → c ν for = e, µ, τ in the modelindependent framework of the weak EFT (WEFT) has revealed the need for better communication of experimental results, specifically the angular distribution of B → D∗+ (→ D0 π + ) ν . Eventually 0 ¯ the results of this work will provide constraints on parameter spaces of specific UV completions or model-independently on SMEFT Wilson coefficients at the electroweak scale µEW .
Publications
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“Power-enhanced leading-logarithmic QED corrections to Bq → µ+ µ−”, JHEP 10 (2019) 232
M. Beneke, C. Bobeth and R. Szafron
