We present a method for improving next-to-leading order electroweak (EW) predictions for lepton-scattering processes by consistently including double neutral-current corrections arising from vector-boson-fusion topologies, which are formally of higher order. By combining, in a process-independent manner, exact fixed-order results, collinear resummation of QED radiation, and a subtraction procedure, we obtain results which are gauge invariant and valid in the entire phase space, retain any dependence on the masses of electroweak bosons, and can be systematically improved, while avoiding the need for complete next-to-next-to-leading order calculations. This paper is devoted to the development and validation of the formalism; phenomenological applications are presented in a companion study, where we also discuss and motivate why our approach is superior to the one based on EW parton distribution functions for targeting percent-level precision at multi-TeV lepton colliders.

Italy

Stefano Frixione

Belgium

Fabio Maltoni

Davide Pagani

Marco Zaro

Double neutral-current corrections to NLO electroweak leptonic cross sections

Future lepton colliders, such as those based on linear $\textit{e}$ $\textit{e}$ or circular $\textit{μ}$ $\textit{μ}$ accelerators, are expected to attain centre-of-mass energies in the multi-TeV range. In this regime the impact of QED and of weak radiation, in both the initial and the final state, can become a leading effect. By employing a general framework presented in a companion paper — suitable for any flavour of colliding leptons — we improve next-to-leading order electroweak predictions by including higher-order contributions, which encompass, but are not limited to, vector-boson-fusion processes. We apply this approach to the study of $$ t\overline{t} $$ and $\textit{W}$ $\textit{W}$ production at a muon collider operating at centre-of-mass energies up to 10 TeV. We show that such an approach, where both QED and weak contributions are included at fixed order, in addition to the all-order resummation of initial-state QED effects, can provide predictions for arbitrary observables in all of the phase space which are precise at the percent level.

Precision phenomenology at multi-TeV muon colliders

In the Standard Model (SM), electroweak (EW) corrections become significant at high energies, particularly at the tera-electronvolt scale and beyond, due to the presence of Sudakov logarithms. At these energy scales, the Standard Model Effective Field Theory (SMEFT) framework provides an enhanced sensitivity to potential new physics effects. This motivates the inclusion of EW corrections not only for SM predictions but also for analyses within SMEFT. In this work, we compute EW corrections in the high-energy limit for a selected set of dimension-six operators, specifically the class of four-fermion contact interactions, in key hard-scattering processes relevant to both current and future colliders: top-quark pair production at the Large Hadron Collider (LHC) and in a muon collider scenario, as well as the Drell-Yan process at the LHC. We first discuss the technical details and challenges associated with evaluating EW Sudakov logarithms in SMEFT, contrasting them with the SM case. We then present phenomenological results for the aforementioned processes, highlighting the non-trivial effects introduced by EW corrections arising from the insertion of dimension-six, four-fermion operators. Importantly, the resulting $\textit{K}$-factors exhibit significant deviations from their SM counterparts, with dependencies not only on the process but also on the specific operators considered. Finally, we explore the potential to lift flat directions in the SMEFT parameter space by incorporating higher-order corrections, using Fisher information techniques.

United Kingdom

Hesham El Faham

Ken Mimasu

Claudio Severi

Eleni Vryonidou

Electroweak corrections in the SMEFT: four-fermion operators at high energies

In this work we investigate several phenomenological and technical aspects related to electroweak (EW) corrections at a high-energy muon collider, focusing on direct production processes (no vector-boson-fusion configurations). We study in detail the accuracy of the Sudakov approximation, in particular the Denner-Pozzorini algorithm, comparing it with exact calculations at next-to-leading-order EW accuracy. We also assess the relevance of resumming EW Sudakov logarithms at 3 and 10 TeV collisions. Furthermore, we scrutinize the impact of additional heavy boson radiation, namely the weak emission of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>W</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>Z</mi></mrow></math>, and Higgs bosons in inclusive and semi-inclusive configurations. All results are obtained via the fully automated and publicly available code madgraph5_amc@nlo.

Yang Ma

EW corrections and heavy boson radiation at a high-energy muon collider

In this work we present a new method for the combination of electroweak (EW) corrections at high energies, the so-called EW Sudakov logarithms (EWSL), and next-to-leading-order QCD predictions matched to parton-shower simulations (NLO+PS). Our approach is based on a reweighting procedure of NLO+PS events. In particular, both events with and without an extra hard emission from matrix elements are consistently reweighted via the inclusion of the corresponding EWSL contribution. We describe the technical details and the implementation in the MadGraph5_aMC@NLO framework. Via a completely automated procedure, events at this level of accuracy can be obtained for a vast class of hadroproduction processes. As a byproduct we provide results for phenomenologically relevant physical distributions from top-quark pair and Higgs boson associated production ( $$t {\bar{t}} H$$ <math> <mrow> <mi>t</mi> <mover> <mrow> <mi>t</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mi>H</mi> </mrow> </math> ) and from the associated production of three Z gauge bosons (ZZZ).

Sweden

Timea Vitos

Improving NLO QCD event generators with high-energy EW corrections

We present a new simulation for Higgs boson production in association with bottom quarks ( <math> <mi>b</mi> <mover> <mi>b</mi> <mo>¯</mo> </mover> <mi>H</mi> </math> $$ b\overline{b}H $$ ) at next-to-leading order (NLO) accuracy matched to parton showers in hadronic collisions. Both contributions, the standard one proportional to the bottom-quark Yukawa coupling and the loop-induced one proportional to the top-quark Yukawa coupling from the gluon-fusion process, are taken into account in a scheme with massive bottom quarks. Therefore, we provide the full simulation of the <math> <mi>b</mi> <mover> <mi>b</mi> <mo>¯</mo> </mover> <mi>H</mi> </math> $$ b\overline{b}H $$ final state in the Standard Model, which constitutes also a crucial background to measurements for Higgs-boson pair (HH) production at the Large Hadron Collider when at least one of the Higgs bosons decays to bottom quarks. So far, the modeling of the <math> <mi>b</mi> <mover> <mi>b</mi> <mo>¯</mo> </mover> <mi>H</mi> </math> $$ b\overline{b}H $$ final state induced one of the dominant theoretical uncertainties to HH measurements, as the gluon-fusion component was described only at the leading order (LO) with uncertainties of <math> <mi>O</mi> </math> $$ \mathcal{O} $$ (100%). Including NLO corrections in its simulation allows us to reduce the scale dependence to <math> <mi>O</mi> </math> $$ \mathcal{O} $$ (50%) so that it becomes subdominant with respect to other systematic uncertainties. As a case study, we provide an in-depth analysis of the <math> <mi>b</mi> <mover> <mi>b</mi> <mo>¯</mo> </mover> <mi>H</mi> </math> $$ b\overline{b}H $$ background to HH measurements with realistic selection cuts in the 2b2γ channel. We also compare our novel simulation with the currently-employed ones, discussing possible issues and shortcomings of a scheme with massless bottom quarks. Finally, we propagate the effect of the new <math> <mi>b</mi> <mover> <mi>b</mi> <mo>¯</mo> </mover> <mi>H</mi> </math> $$ b\overline{b}H $$ simulation to HH searches in the 2b2γ and 2b2τ final states, and we find an improvement of up to 10% (20%) on the current (HL-LHC) limits on <math> <msubsup> <mi>σ</mi> <mi>SM</mi> <mi>HH</mi> </msubsup> </math> $$ {\sigma}_{\textrm{SM}}^{HH} $$ .

CERN

Stefano Manzoni

Elena Mazzeo

Switzerland

Javier Mazzitelli

Germany

Marius Wiesemann

Taming a leading theoretical uncertainty in HH measurements via accurate simulations for <math> <mi>b</mi> <mover> <mi>b</mi> <mo>¯</mo> </mover> <mi>H</mi> </math> $$ \textrm{b}\overline{\textrm{b}}\textrm{H} $$ production

We present an update of the Universal FeynRules Output model format, commonly known as the UFO format, that is used by several automated matrix-element generators and high-energy physics software. We detail different features that have been proposed as extensions of the initial format during the last ten years, and collect them in the current second version of the model format that we coin the Universal Feynman Output format. Following the initial philosophy of the UFO, they consist of flexible and modular additions to address particle decays, custom propagators, form factors, the renormalisation group running of parameters and masses, and higher-order quantum corrections.

France

Luc Darmé

Céline Degrande

Claude Duhr

Benjamin Fuks

Mark Goodsell

Gudrun Heinrich

Valentin Hirschi

United States

Stefan Höche

Marius Höfer

Joshua Isaacson

Olivier Mattelaer

Thorsten Ohl

Jürgen Reuter

Peter Richardson

Steffen Schumann

Hua-Sheng Shao

Frank Siegert

UFO 2.0: the ‘Universal Feynman Output’ format

Within the framework of local analytic sector subtraction, we present the subtraction of next-to-leading-order QCD singularities for processes featuring massless coloured particles in the initial as well as in the final state. The features of the method are explained in detail, including the introduction of an optimisation procedure aiming at improving numerical stability at the cost of no extra analytic complexity. A numerical validation is provided for a variety of processes relevant to lepton as well as hadron colliders. This work constitutes a relevant step in view of the application of our subtraction method to processes involving initial-state radiation at next-to-next-to-leading order in QCD.

Gloria Bertolotti

Paolo Torrielli

Sandro Uccirati

Local analytic sector subtraction for initial- and final-state radiation at NLO in massless QCD

We compute the perturbative component of the fragmentation function of the b quark to the best of the present theoretical knowledge. The fixed-order calculation to order <math> <msubsup> <mi>α</mi> <mi>s</mi> <mn>2</mn> </msubsup> </math> $$ {\alpha}_s^2 $$ of the fragmentation function at the initial scale is matched with soft-emission logarithm resummation to next-to-next-to-leading logarithmic accuracy, so that order- <math> <msubsup> <mi>α</mi> <mi>s</mi> <mn>2</mn> </msubsup> </math> $$ {\alpha}_s^2 $$ corrections are accounted for exactly, and logarithmically enhanced contributions from loops of b quarks are included. This requires the calculation of the Mellin transform of the order- <math> <msubsup> <mi>α</mi> <mi>s</mi> <mn>2</mn> </msubsup> </math> $$ {\alpha}_s^2 $$ result in the whole complex plane for the Mellin variable, which we provide for the first time for all the fragmenting partons. Evolution is performed to next-to-next-to-leading log accuracy, and mixing with the gluon fragmentation function is taken into account. The perturbative fragmentation functions are made available via LHAPDF grids.

Giovanni Ridolfi

Maria Ubiali

Resummation effects in the bottom-quark fragmentation function

In this work we revisit the algorithm of Denner and Pozzorini for the calculation of one-loop electroweak Sudakov logarithms and we automate it in the MadGraph5_aMC-@NLO framework. We adapt the formulas for modern calculations, keeping light-quarks and photons strictly massless and dealing with infrared divergences via dimensional regularisation. We improve the approximation by taking into account additional logarithms that are angular dependent. We prove that an imaginary term has been previously omitted and we show that it cannot be in general neglected for 2 → n processes with n &gt; 2. We extend the algorithm to NLO EW corrections to squared matrix-elements that involve also QCD corrections on top of subleading LO terms. Furthermore, we discuss the usage of this algorithm for approximating physical observables and cross sections. We propose a new approach in which the QED component is consistently removed and we show how it can be superior to the commonly used approaches. The relevance of all the novelties introduced in this work is corroborated by numerical results obtained for several processes in a completely automated way. We thoroughly compare exact NLO EW corrections and their Sudakov approximations both at the amplitude level and for physical observables in high-energy hadronic collisions.

One-loop electroweak Sudakov logarithms: a revisitation and automation