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

In recent years, theoretical and phenomenological studies with effective field theories have become a trending and prolific line of research in the field of high-energy physics. In order to discuss present and future prospects concerning automated tools in this field, the SMEFT-Tools 2022 workshop was held at the University of Zurich from 14th–16th September 2022. The current document collects and summarizes the content of this workshop.

Jason Aebischer

CERN

Matteo Fael

Spain

Javier Fuentes-Martìn

Anders Thomsen

Javier Virto

Lukas Allwicher

Supratim Bakshi

Croatia

Hermès Bélusca-Maïto

Jorge Blas

Mikael Chala

Juan Criado

Greece

Athanasios Dedes

Renato Fonseca

Angelica Goncalves

Amon Ilakovac

India

Sunando Patra

Paul Kühler

Marija Mador-Božinović

Poland

Mikołaj Misiak

Italy

Víctor Miralles

Ignacy Nałȩcz

United Kingdom

Méril Reboud

Laura Reina

Janusz Rosiek

Michal Ryczkowski

José Santiago

Luca Silvestrini

Peter Stangl

Dominik Stöckinger

Peter Stoffer

Avelino Vicente

Matthias Weißwange

Computing tools for effective field theories

We derive a factorization theorem for the structure-dependent QED effects in the weak exclusive process <math><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>μ</mi></mrow></msub></mrow></math>, i.e., effects probing the internal structure of the <math><mi>B</mi></math> meson. The derivation requires a careful treatment of end-point-divergent convolutions common to subleading-power factorization formulas. We find that the decay amplitude is sensitive to two- and three-particle light-cone distribution amplitudes of the <math><mi>B</mi></math> meson as well as to a new hadronic quantity <math><mrow><mi>F</mi><mo>(</mo><mi>μ</mi><mo>,</mo><mi>Λ</mi><mo>)</mo></mrow></math>, which generalizes the notion of the <math><mi>B</mi></math>-meson decay constant in the presence of QED effects. This is one of the first derivations of a subleading-power factorization theorem in which the soft functions are nonperturbative hadronic matrix elements.

Structure-dependent QED effects in exclusive <math><mi>B</mi></math> decays at subleading power

Studying the impact of new-physics models on low-energy observables necessitates matching to effective field theories at the relevant mass thresholds. We introduce the first public version of Matchete, a computer tool for matching weakly-coupled models at one-loop order. It uses functional methods to directly compute all matching contributions in a manifestly gauge-covariant manner, while simplification methods eliminate redundant operators from the output. We sketch the workings of the program and provide examples of how to match simple Standard Model extensions. The package, documentation, and example notebooks are publicly available at  https://gitlab.com/matchete/matchete  .

Javier Fuentes-Martín

Julie Pagès

Felix Wilsch

A proof of concept for matchete: an automated tool for matching effective theories

Effective Field Theory calculations used in countless phenomenological analyses employ dimensional regularization, and at intermediate stages of computations, the operator bases extend beyond the four-dimensional ones. The extra pieces — the evanescent operators — can ultimately be removed with a suitable renormalization scheme, resulting in a finite shift of the physical operators. Modern Effective Field Theory matching techniques relying on the method of expansion by regions have to be extended to account for this. After illustrating the importance of these shifts in two specific examples, we compute the finite shifts required to remove all evanescent operators appearing in the one-loop matching of generic ultraviolet theories to the Standard Model Effective Field Theory and elucidate the formalism for generic Effective Field Theory calculations.

Evanescent operators in one-loop matching computations

We discuss the possibility of performing precise tests of  $$\mu /e$$  <math> <mrow> <mi>μ</mi> <mo>/</mo> <mi>e</mi> </mrow> </math>   universality in  $$B \rightarrow \pi \ell ^+\ell ^-$$  <math> <mrow> <mi>B</mi> <mo>→</mo> <mi>π</mi> <msup> <mi>ℓ</mi> <mo>+</mo> </msup> <msup> <mi>ℓ</mi> <mo>-</mo> </msup> </mrow> </math>   decays. We show that in wide regions of the dilepton invariant mass spectrum the ratio between muonic and electronic decay widths can be predicted with high accuracy, both within and beyond the Standard Model. We present numerical expressions which can be used to extract precise information on short-distance dynamics if a deviation from universality is observed in the data.

Marzia Bordone

Gino Isidori

The LFU ratio  $$R_\pi $$  <math> <msub> <mi>R</mi> <mi>π</mi> </msub> </math>   in the Standard Model and beyond

We present SuperTracer, a Mathematica package aimed at facilitating the functional matching procedure for generic UV models. This package automates the most tedious parts of one-loop functional matching computations. Namely, the determination and evaluation of all relevant supertraces, including loop integration and Dirac algebra manipulations. The current version of SuperTracer also contains a limited set of output simplifications. However, a further reduction of the output to a minimal basis using Fierz identities, integration by parts, simplification of Dirac structures, and/or light field redefinitions might still be necessary. The code and example notebooks are publicly available at   .1

SuperTracer: a calculator of functional supertraces for one-loop EFT matching

The two linear relations between operators shown in eq. (3.29) were missing an integral over the momentum fraction u on the right-hand side. In the one-particle anomalous dimensions in eq. (5.7) two fractions were mistyped.

Stefan Alte

Erratum to: Effective field theory after a new-physics discovery

We construct an effective field theory describing the decays of a heavy vector resonance V into Standard Model particles. The effective theory is built using an extension of Soft-Collinear Effective Theory called SCETBSM, which provides a rigorous framework for parameterizing decay matrix elements with manifest power counting in the ratio of the electroweak scale and the mass of the resonance, λ ∼ v/m  V . Using the renormalization-group evolution of the couplings in the effective Lagrangian, large logarithms associated with this scale ratio can be resummed to all orders. We consider in detail the two-body decays of a heavy Z′ boson and of a Kaluza-Klein gluon at leading and subleading order in λ. We illustrate the matching onto SCETBSM with a concrete example of a UV-complete new-physics model.

Mathias Heiles

Effective field theory for heavy vector resonances coupled to the Standard Model