We derive the QCD×QED factorization theorem governing the leptonic decay $$ {B}^{-}\to {\mu}^{-}{\overline{\nu}}_{\mu}\left(\gamma \right) $$ at all orders in $\textit{α}$ and $\textit{α}$. Electromagnetic corrections to this decay probe multiple scales, which we disentangle through a sequence of effective field theories (EFTs). The resulting state-of-the-art prediction for the photon-vetoed rate includes the complete structure-dependent component and is accurate at the percent level, establishing the theoretical framework required for future high-precision measurements of this channel, which will allow for a clean determination of |$\textit{V}$ | and powerful tests of new physics. Our work presents the first complete study of QED effects to an exclusive $\textit{B}$-meson decay at next-to-leading power (NLP) in the heavy-quark expansion. Important milestones are (i) the construction of the complete NLP operator basis in soft-collinear effective theory (SCET); (ii) the proposal of a “SCET-friendly” reduction scheme for the Dirac structures of four-fermion operators in dimensional regularization, which avoids power-enhanced evanescent operators; (iii) the consistent refactorization of endpoint-divergent convolution integrals and the first complete resummation of “rapidity logarithms” arising at the boundary between the contributions involving soft and hard-collinear quarks; (iv) the systematic discussion of the EFT below the scale of QCD confinement and the non-perturbative matching of SCET onto this low-energy theory; (v) the decoupling of pseudoscalar mesons in the context of heavy-hadron chiral perturbation theory, so that they can be integrated out for processes in which they do not appear as external particles. We perform a phenomenological analysis of direct and indirect contributions to the decay rate and radiation-energy spectrum, highlighting the importance of the chiral anomaly.

Switzerland

Claudia Cornella

Germany

Max Ferré

Matthias König

United States

Matthias Neubert

The simplest $\textit{B}$ decay, precisely

To date, the appearance and resummation of “super-leading” logarithms in hadron-hadron collisions has been studied only for massless parton states. We extend the formalism to include an arbitrary number of massive final states. We derive the corresponding anomalous dimension and identify an additional Coulomb phase that gives rise to a new source of super-leading logarithms. We then perform a systematic leading-logarithmic resummation of these contributions for 2 → $\textit{M}$ processes. Finally, we analyze the numerical impact in partonic scattering processes for $$ t\overline{t} $$ production, including a treatment of the Sommerfeld enhancement observed near threshold.

Upalaparna Banerjee

Romy Grünhofer

Yibei Li

Josua Scholze

Super-leading logarithms in top-quark pair production at hadron colliders

The consistency of collinear factorization violation with PDF factorization has been an outstanding challenge and subject of considerable debate. In this work we demonstrate their compatibility using a factorization theorem for non-global jet observables. Our analysis relies on consistency relations derived from renormalization conditions in effective field theory. We verify these relations through an explicit computation at three-loop order and show that the double-logarithmic evolution sourcing the super-leading logarithms reduces to single-logarithmic DGLAP running below the lowest perturbative scale. The crucial ingredient reconciling the two evolutions is a perturbative Glauber contribution to the low-energy matrix elements which breaks soft-collinear factorization at the cross section level but restores PDF factorization.

Thomas Becher

Patrick Hager

Sebastian Jaskiewicz

Dominik Schwienbacher

Low-energy theory of jet processes and PDF factorization

Within the Standard Model, the branching fraction of the rare decay $$ {B}_s\to {K}^0{\overline{K}}^0 $$ is related to other decay rates and CP asymmetries through the approximate SU(3) flavor symmetry of the strong interactions and the heavy-quark limit. Three such relations were shown to be violated at a level of about 3$\textit{σ}$ each. By means of a systematic search for new-physics explanations of these puzzles, we find that possible solutions are highly fine-tuned and either excluded by other data or rather implausible. The tight correlation between $$ {B}_s\to K\overline{K} $$ and $\textit{B}$ → $\textit{πK}$ decays, which is maintained even in the presence of flavor-specific new-physics operators, plays a central role in our analysis.

Yuval Grossman

Israel

Yosef Nir

Yogev Shpilman

Yehonatan Viernik

$$ {B}_s\to {K}^0{\overline{K}}^0 $$ beyond the Standard Model

<p>We analyze the low-energy dynamics of gap-between-jets cross sections at hadron colliders, for which phase factors in the hard amplitudes spoil collinear cancellations and lead to double (“super-leading”) logarithmic behavior. Based on a method-of-regions analysis, we identify three-loop contributions from perturbative active-active Glauber-gluon exchanges with the right structure to render the cross section consistent with PDF factorization below the gap veto scale. The Glauber contributions we identify are unambiguously defined without regulators beyond dimensional regularization.</p>

Factorization Restoration through Glauber Gluons

Jet observables at hadron colliders feature “super-leading” logarithms, double-logarithmic corrections resulting from a breakdown of color coherence due to complex phases in hard-scattering amplitudes. While these effects only arise in high orders of perturbation theory and are suppressed in the large-$\textit{N}$ limit, they formally constitute leading logarithmic corrections to the cross sections. We present the first analysis of the corresponding contributions to a hadronic cross section, including all partonic channels and interference effects. Interestingly, some interference terms in partonic $$ q\overline{q} $$ → $$ q\overline{q} $$ scattering are only linearly suppressed in 1$\textit{/N}$ . Our results for the $\textit{pp}$ → 2 jets gap-between-jets cross section demonstrate the numerical importance of super-leading logarithms for small values of the veto scale $\textit{Q}$ , showing that these contributions should be accounted for in precision studies of such observables.

Giuliano Martinelli

Michel Stillger

Super-leading logarithms in $\textit{pp →}$ 2 jets

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 $\textit{N}$ can be resummed in closed form in renormalization-group improved perturbation theory. This remarkable observation suggests that large-$\textit{N}$ 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.

Philipp Böer

Xiaofeng Xu

Resummation of Glauber phases in non-global LHC observables for large $\textit{N}$ $\textit{c}$

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 → $\textit{M}$ scattering processes. Moreover, the asymptotic scaling of subleading logarithmic corrections from higher-order Glauber exchanges is determined, demonstrating their parametric suppression.

Renormalization-group improved resummation of super-leading logarithms

The weak decays K  ±  → π  ±  a offer a powerful probe of axion-like particles (ALPs). In this work, we provide a comprehensive analysis of these processes within chiral perturbation theory, extending existing calculations by including complete next-to-leading order (NLO) contributions and isospin-breaking corrections at first order in (m  d  – m  u ). We show that the consistent incorporation of ALPs in the QCD and weak chiral Lagrangians requires a non-trivial extension of the corresponding operator bases, which we describe in detail. Furthermore, we show that in the presence of an ALP the so-called “weak mass term”, which is unobservable in the Standard Model, is non-redundant already at leading order. We find that NLO corrections associated with flavor-violating ALP couplings modify the leading-order result by a few percent, with negligible uncertainties. NLO corrections proportional to flavor-conserving ALP couplings lead to potentially larger corrections, which, however, are accompanied by sizable uncertainties mainly due to the currently limited knowledge of various low-energy constants. We study how these corrections impact bounds on the ALP couplings, first model independently, and then specializing to the case of an ALP with flavor-universal couplings in the UV. Our findings confirm that the decays K  ±  → π  ±  a provide the strongest particle-physics constraints for m  a  ≲ 300 MeV. In addition, we point out that these bounds have interesting implications for the ALP couplings to nucleons, which were so far only constrained by astrophysical measurements and non-accelerator experiments.

Anne Galda

Daniel Wyler

K ± → π ±a at next-to-leading order in chiral perturbation theory and updated bounds on ALP couplings

Axions and axion-like particles emerge in many models for physics beyond the Standard Model. Thus, they have gained increasing research interest in both experimental and theoretical physics apart from their original proposition as a solution to the strong CP-problem. Among other aspects it has recently been shown that ALPs can potentially provide a solution to the long-lasting discrepancy between theory and experiment of the anomalous magnetic moment of the muon. Provided that the ALP has flavor-violating couplings to leptons, they can also mediate flavor-violating decays like  $$\mu \rightarrow e\gamma $$  <math> <mrow> <mi>μ</mi> <mo>→</mo> <mi>e</mi> <mi>γ</mi> </mrow> </math>  . Both processes are mediated through related form factors that we compute to two-loop order. We further show numerical implications of our calculations and how they might affect constraints on ALP couplings derived from experiments.