We present a systematic study of the three-particle di-light-cone distribution amplitudes (DLCDAs) of the B-meson. They are defined through B-meson–to–vacuum matrix elements of trilocal HQET operators, in which the light antiquark and the gluon field-strength tensor are located on two back-to-back light rays. In this sense, the DLCDAs generalise the conventional B-meson light-cone distribution amplitudes to configurations where soft fields couple to collinear degrees of freedom in two distinct directions. As such, they parametrise the non-perturbative dynamics associated with non-factorisable soft-gluon contributions in rare and non-leptonic exclusive B-meson decays. We derive the complete Lorentz decomposition of the matrix elements of generic trilocal operators, identify eight independent DLCDAs, and organise them in a basis of definite twist. Using local operator identities and equations-of-motion constraints, we obtain tree-level relations for their normalisation integrals and first moments in terms of a minimal set of hadronic parameters. These relations allow us to construct simple momentum-space models for all independent DLCDAs. For the leading-twist distribution, we further incorporate the perturbative radiative tail at order α_s and discuss its impact on the resulting parametrisation.

The double-logarithmic series of non-relativistic B_c → η_c form factors at large recoil is governed by a coupled set of integral equations, reflecting an intricate interplay between arbitrarily many soft-quark and soft-gluon exchanges. Whereas we previously derived these integral equations with diagrammatic resummation techniques, we analyze the form factors in the limit m_b ≫ m_c ≫ Λ_ QCD with methods from Soft-Collinear Effective Theory (SCET) in this work. Although the resulting factorization theorem for the so-called soft-overlap contribution is known to be spoilt by endpoint divergences, it can still be used at the level of bare (regularized) quantities at any fixed order in perturbation theory. By calculating the required ingredients, we show that the SCET analysis confirms the predictions of the integral equations up to three-loop order. We also argue that the iterative structure and the intertwined soft-quark and soft-gluon effects can be derived from standard renormalization-group equations of the B_c-meson light-cone distribution amplitudes, provided their inverse moments are regularized with an appropriate cutoff.

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We perform an all-order analysis of double-logarithmic corrections to the so-called soft-overlap contribution to heavy-to-light transition form factors at large hadronic recoil. Specifically, we study Bc → ηc transitions within a perturbative non-relativistic framework, treating both the bottom and charm quarks as heavy with the hierarchy mb ≫ mc ≫ ΛQCD. Our diagrammatic analysis shows that double-logarithmic corrections arise from two distinct sources: exponentiated soft-gluon effects described by standard Sudakov factors, and rapidity-ordered soft-quark configurations, leading to implicit integral equations, which so far have only been studied in the context of energetic muon-electron backward scattering. We find that the all-order structure of the double logarithms is governed by a novel type of coupled integral equations, which encode the non-trivial interplay between these two effects. Whereas a closed-form solution to these equations is currently unknown, we present useful iteration formulas, and derive the asymptotic behaviour of the soft-overlap form factor for infinitely large recoil energies, showing that the Sudakov suppression is somewhat weakened by the intertwined soft-quark and soft-gluon corrections. In a broader context, our findings shed light onto the physical origin and mathematical structure of endpoint divergences arising from soft-collinear factorization and the related Feynman mechanism for power-suppressed hard exclusive processes.

We calculate the so-called radiative tail for the three-particle light-cone distribution amplitudes (LCDAs) of the Λ_b baryon, following from the short-distance expansion of the defining light-ray operators in heavy-quark effective theory (HQET). To illustrate the effect of the radiative tail, we introduce a simple (model-dependent) extrapolation to large distances (respectively small momenta), which preserves the analytic properties of the LCDAs in HQET. We observe a similar qualitative behaviour as has been discussed for the B-meson case.

Using diagrammatic resummation techniques, we investigate the double-logarithmic series of the ``soft-overlap'' contribution to $B_c \to \eta_c$ transition form factors at large hadronic recoil, assuming the scale hierarchy $m_b \gg m_c \gg \Lambda_{\rm QCD}$. In this case, the hadronic bound states can be treated in the non-relativistic approximation and the relevant hadronic matrix elements can be computed perturbatively. This setup defines one of the simplest examples to study the problem of endpoint singularities appearing in the factorization of exclusive $B$-decay amplitudes. We find that the leading double logarithms arise from a peculiar interplay of soft-quark ``endpoint logarithms'' from ladder diagrams with energy-ordered spectator-quark propagators, as well as standard Sudakov-type soft-gluon corrections. We elucidate the all-order systematics, and show that their resummation proceeds via a novel type of integral equations. The current status of the calculation, which includes all double logarithms in the Abelian limit, is reported.

We review recent progress in the computation of structure-dependent QED corrections to exclusive B decays in the factorization approach.

We investigate for the first time a certain class of non-factorisable contributions of the four-quark operators 𝒪 3−6 in the weak effective Hamiltonian to the Λb → Λℓ+ℓ− decay amplitude. We focus on the case where a virtual photon is radiated from one of the light constituents of the Λb baryon, in the kinematic situation of large hadronic recoil with an energetic Λ baryon in the final state. The effect on the suitably defined “non-local form factors” is calculated using the light-cone sum rule approach for a correlator with an interpolating current for the light Λ baryon. We find that this approach requires the introduction of new soft functions that generalise the standard light-cone distribution amplitudes (LCDAs) for the heavy Λb baryon. We give a heuristic discussion of their properties and a model that relates them to the standard LCDAs. Within this framework, we provide numerical results for the size of the non-local form factors considered.

We construct a factorization theorem that allows one to systematically include QCD corrections to the contribution of the electromagnetic dipole operator in the effective weak Hamiltonian to the decay amplitude. We first rederive the known result for the leading-order QED box diagram, which features a double-logarithmic enhancement associated with the different rapidities of the light quark in the B over bar s meson and the energetic muons in the final state. We provide a detailed analysis of the cancellation of the related endpoint divergences appearing in individual momentum regions, and show how the rapidity logarithms can be isolated by suitable subtractions applied to the corresponding bare factorization theorem. This allows us to include in a straightforward manner the QCD corrections arising from the renormalization-group running of the hard matching coefficient of the electromagnetic dipole operator in soft-collinear effective theory, the hard-collinear scattering kernel, and the Bs-meson distribution amplitude. Focusing on the contribution from the double endpoint logarithms, we derive a compact formula that resums the leading-logarithmic QCD corrections. B over bar s -> mu+mu-

Abstract We investigate the differences between the light-cone distribution amplitudes (LCDAs) of B s mesons and B q mesons (with q = u, d) induced by a non-vanishing strange-quark mass m s ≠ 0 (compared to m q ≃ 0). To this end, we consider the so-called “radiative tail” which is related to the short-distance expansion of the relevant light-ray operators in heavy-quark effective theory. We extend the calculation of the according matching coefficients, including operators linear in m s for both the leading and sub-leading 2-particle LCDAs. Based on a generic parameterization for the leading LCDA, we discuss the effect on its shape on a quantitative level, and compare our findings with recent results on the inverse moments of the B q and B s LCDAs from QCD sum rules.

We investigate for the first time a certain class of non-factorisable contributions of the four-quark operators ${\cal O}_{3-6}$ in the weak effective Hamiltonian to the $\Lambda_b \to \Lambda \ell^+\ell^-$ decay amplitude. We focus on the case where a virtual photon is radiated from one of the light constituents of the $\Lambda_b$ baryon, in the kinematic situation of large hadronic recoil with an energetic $\Lambda$ baryon in the final state. The effect on the suitably defined ``non-local form factors'' is calculated using the light-cone sum rule approach for a correlator with an interpolating current for the light $\Lambda$ baryon. We find that this approach requires the introduction of new soft functions that generalise the standard light-cone distribution amplitudes (LCDAs) for the heavy $\Lambda_b$ baryon. We give a heuristic discussion of their properties and a model that relates them to the standard LCDAs. Within this framework, we provide numerical results for the size of the non-local form factors considered.

We construct a factorization theorem that allows one to systematically include QCD corrections to the contribution of the electromagnetic dipole operator in the effective weak Hamiltonian to the ${\overline{B}}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ decay amplitude. We first rederive the known result for the leading-order QED box diagram, which features a double-logarithmic enhancement associated with the different rapidities of the light quark in the ${\overline{B}}_{s}$ meson and the energetic muons in the final state. We provide a detailed analysis of the cancellation of the related endpoint divergences appearing in individual momentum regions, and show how the rapidity logarithms can be isolated by suitable subtractions applied to the corresponding bare factorization theorem. This allows us to include in a straightforward manner the QCD corrections arising from the renormalization-group running of the hard matching coefficient of the electromagnetic dipole operator in soft-collinear effective theory, the hard-collinear scattering kernel, and the ${B}_{s}$-meson distribution amplitude. Focusing on the contribution from the double endpoint logarithms, we derive a compact formula that resums the leading-logarithmic QCD corrections.

We construct a factorization theorem that allows to systematically include QCD corrections to the contribution of the electromagnetic dipole operator in the effective weak Hamiltonian to the B̅_s →μ^+μ^- decay amplitude. We first rederive the known result for the leading-order QED box diagram, which features a double-logarithmic enhancement associated to the different rapidities of the light quark in the B̅_s meson and the energetic muons in the final state. We provide a detailed analysis of the cancellation of the related endpoint divergences appearing in individual momentum regions, and show how the rapidity logarithms can be isolated by suitable subtractions applied to the corresponding bare factorization theorem. This allows us to include in a straightforward manner the QCD corrections arising from the renormalization-group running of the hard matching coefficient of the electromagnetic dipole operator in soft-collinear effective theory, the hard-collinear scattering kernel, and the B_s-meson distribution amplitude. Focusing on the contribution from the double endpoint logarithms, we derive a compact formula that resums the leading-logarithmic QCD corrections.

A bstract We argue that energetic muon-electron scattering in the backward direction can be viewed as a template case to study the resummation of large logarithms related to endpoint divergences appearing in the effective-theory formulation of hard-exclusive processes. While it is known since the mid sixties that the leading double logarithms from QED corrections resum to a modified Bessel function on the amplitude level, the modern formulation in Soft-Collinear Effective Theory (SCET) shows a surprisingly complicated and iterative pattern of endpoint-divergent convolution integrals. In contrast to the bottom-quark induced h → γγ decay, for which a renormalized factorization theorem has been proposed recently, we find that rapidity logarithms generate an infinite tower of collinear-anomaly exponents. This can be understood as a generic consequence of the underlying 2 → 2 kinematics. Using endpoint refactorization conditions for the collinear matrix elements, we show how the Bessel function is reproduced in the effective theory from consistency relations between quantities in a “bare” factorization theorem.

A bstract We propose a parametrization of the leading B -meson light-cone distribution amplitude (LCDA) in heavy-quark effective theory (HQET). In position space, it uses a conformal transformation that yields a systematic Taylor expansion and an integral bound, which enables control of the truncation error. Our parametrization further produces compact analytical expressions for a variety of derived quantities. At a given reference scale, our momentum-space parametrization corresponds to an expansion in associated Laguerre polynomials, which turn into confluent hypergeometric functions 1 F 1 under renormalization-group evolution at one-loop accuracy. Our approach thus allows a straightforward and transparent implementation of a variety of phenomenological constraints, regardless of their origin. Moreover, we can include theoretical information on the Taylor coefficients by using the local operator product expansion. We showcase the versatility of the parametrization in a series of phenomenological pseudo-fits.

We give a brief overview of phenomenological developments in the analysis of angular observables for exclusive decay modes of $B$ mesons and $\Lambda_b$ baryons, with focus on recent results and some important aspects related to the theoretical background (which mostly concern the treatment of hadronic uncertainties).

A bstract We investigate the viability of extending the Standard Model with S 1 and S 3 scalar leptoquarks when the flavour structure is parametrized in terms of Froggatt-Nielsen charges. In contrast to a similar analysis with a vector leptoquark, we find essentially two solutions for the charges that fit the experimental constraints, which are dominated by the current tensions in B decays. These two scenarios differ in their estimate of the anomalous magnetic moment of the muon, ( g − 2), but they both predict sizeable contributions to τ → μγ , $$ {\overline{B}}_s $$ B ¯ s → τ ± μ ∓ and B + → K + τ + μ − decays, whose branching ratios are close to the current experimental limits.

We give a brief overview of phenomenological developments in the analysis of angular observables for exclusive decay modes of $B$ mesons and $Λ_b$ baryons, with focus on recent results and some important aspects related to the theoretical background (which mostly concern the treatment of hadronic uncertainties).

Extending the Standard Model with higher-dimensional operators in an effective field theory (EFT) approach provides a systematic framework to study new physics (NP) effects from a bottom-up perspective, as long as the NP scale is sufficiently large compared to the energies probed in the experimental observables. However, when taking into account the different quark and lepton flavours, the number of free parameters in- creases dramatically, which makes generic studies of the NP flavour structure infeasible. In this paper, we address this issue in view of the recently observed "flavour anomalies" in B-meson decays, which we take as a motivation to develop a general framework that allows us to systematically reduce the number of flavour parameters in the EFT. This framework can be easily used in global fits to flavour observables at Belle II and LHCb as well as in analyses of flavour-dependent collider signatures at the LHC. Our formalism represents an extension of the well-known minimal-flavour-violation approach, and uses Froggatt-Nielsen charges to define the flavour power-counting. As a relevant illustration of the formalism, we apply it to the flavour structures which could be induced by a U-1 vector leptoquark, which represents one of the possible explanations for the recent hints of flavour non-universality in semileptonic B-decays. We study the phenomenological viability of this specific framework performing a fit to low-energy flavour observables.