Philipp Böer

A bstract: 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 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.

A bstract: 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.

We report on progress towards including next-to-leading order (NLO) radiative corrections to the subleading-power factorization formula for the 𝑄 𝑞 1-𝑄 7𝛾 interference contribution in B → 𝑋 𝑠 𝛾 at large photon energies, 𝑚 𝑏-2𝐸 𝛾 = O (Λ QCD). The novel ingredients for a NLO analysis are the one-loop anomalous dimension of the subleading shape function 𝑔 17 (𝜔, 𝜔 1 ; 𝜇), which was recently computed by us, and the two-loop corrections to the jet function with an internal charm loop. Here we summarize the renormalization of 𝑔 17 (𝜔, 𝜔 1 ; 𝜇), and further discuss that our insights allow for a simplified renormalization of a specific generalization of a three-particle 𝐵meson light-cone distribution amplitude, but with non-aligned light-like separations of the fields.

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 B _c → η _c transitions within a perturbative non-relativistic framework, treating both the bottom and charm quarks as heavy with the hierarchy m _b ≫ m _c ≫ Λ_QCD. 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.

A bstract: A new strategy is presented for systematically treating super-leading logarithmic contributions including higher-order Glauber exchanges for non-global LHC observables in renormalization-group (RG) improved perturbation theory. This represents an important improvement over previous approaches, as it allows for the consistent inclusion of the scale dependence of the strong coupling, thereby providing more reliable estimates of the scale uncertainties in theoretical predictions. The key idea is to rearrange the relevant RG evolution operator in such a way that all double-logarithmic corrections are exponentiated from the outset. This forms the starting point for the first resummation of super-leading logarithms at leading order in RG-improved perturbation theory for arbitrary 2 → M scattering processes. Moreover, the asymptotic scaling of subleading logarithmic corrections from higher-order Glauber exchanges is determined, demonstrating their parametric suppression.

A bstract: The Glauber series for non-global jet observables at hadron colliders simultaneously includes the super-leading logarithms alongside an arbitrary number of Glauber phases. Building on the formalism of [1], it is shown that the leading terms in this series for large N _c can be resummed in closed form in renormalization-group improved perturbation theory. This remarkable observation suggests that large- N _c methods might also be helpful to study other aspects of non-global logarithms at hadron colliders, and to combine our analytic results with amplitude-level parton showers.

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

The resummation of the “Glauber series” in non-global LHC observables is extended to processes with gluons in the initial state. This series simultaneously incorporates large double-logarithmic corrections, the so-called “super-leading logarithms”, together with higher-order exchanges of pairs of Glauber gluons associated with the large numerical factor (iπ)². On a technical level, the main part of this work is devoted to the systematic reduction of the appearing color traces and construction of basis structures, which consist of thirteen elements for gg and eleven elements for qg scattering. Numerical estimates for wide-angle gap-between-jet cross sections at the parton level show that, in particular for gg scattering at relatively small vetoes Q ₀, the contribution involving four Glauber exchanges gives a sizeable correction and should not be neglected.