arXiv subjects

Stefano Frixione

Publications and source records attributed to Stefano Frixione.

At least 19 recordsLinked to original sources

arXiv2026

The electron parton distribution functions at the NNLO in QED

The electron Parton Distribution Functions (PDFs) are essential components in the calculations of cross sections within a collinear-factorisation framework at lepton colliders. We compute them at the next-to-next-to-leading order (NNLO) in QED by working in two different factorisation schemes, namely the standard $\overline{\rm MS}$ one and the so-called $\Delta$ scheme, which was originally defined at the next-to-leading order, and which we generalise in this work by extending its definition to all orders. We present analytical results relevant to the large-$z$ behaviour of the PDFs in both factorisation schemes, and thus show how the soft-logarithm enhancement of the $\overline{\rm MS}$ electron PDF is completely absent in the $\Delta$ scheme. The latter therefore constitutes a natural choice that helps significantly reduce the complexity not only of numerical simulations in phenomenological applications, but also that of analytical computations necessary to achieve the soft resummation of physical observables. We argue that NNLO PDFs are necessary to attain relative-precision targets of $10^{-4}$ or better, for colliders whose centre-of-mass energies are in the hundred-GeV range.

hep-ph↗

arXiv2026

New results on small-x resummation for splitting functions

We revisit the basic steps necessary to obtain next-to-leading-logarithmic accurate small-$x$ results for the DGLAP splitting functions, and their implementations within the HELL framework. We derive new analytical all-order results for the leading-logarithmic $gg$ anomalous dimension, the $qg$ and $gg$ finite Green functions, and most importantly for the $qg$ anomalous dimension, which allows us to arrive for the first time at a properly resummed $qg$ splitting kernel. We use these results as cornerstones of a new implementation of small-$x$ splitting-function resummation which is more solid and numerically better behaved with respect to those available thus far. All of these novelties are included in the upcoming 4.0 version of HELL.

hep-ph↗

arXiv2025

Double neutral-current corrections to NLO electroweak leptonic cross sections

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.

hep-ph↗

arXiv2025

Precision phenomenology at multi-TeV muon colliders

Future lepton colliders, such as those based on linear $e^+e^-$ or circular $\mu^+\mu^-$ 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 $t\bar{t}$ and $W^+W^-$ 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.

hep-ph↗

arXiv2025

Some identities which involve Stirling numbers

During the course of an ongoing work on the small-$x$ behaviour of parton distribution functions, some identities have been found which involve Stirling numbers of the first and the second kind, as well as binomial coefficients. Without any claim of originality I report them in this note.

hep-ph↗

arXiv2024

Correcting for cutoff dependence in backward evolution of QCD parton showers

Monte Carlo event generators for hard hadronic collisions depend on the evolution of parton showers backwards from a high-scale subprocess to the hadronization scale. The evolution is treated as a branching process with a sequence of resolvable parton emissions. The criterion of resolvability involves cutoffs that determine the no-emission probability (NEP) for a given range of the evolution scale. Existing event generators neglect cutoff-dependent terms in the NEP that, although formally power-suppressed, can have significant phenomenological effects. We compute such terms and study their consequences. One important result is that it is not possible for the backward shower to faithfully reproduce the cutoff-independent parton distribution functions (PDFs) used to generate it. We show that the computed NEP corrections mitigate but do not eliminate this problem. An alternative approach is to use cutoff-dependent PDFs that are consistent with the uncorrected NEP. Then one must apply cutoff-dependent corrections to hard subprocess matrix elements. We compute those corrections to the first nontrivial order for the Drell-Yan process and for Higgs production by gluon fusion.

hep-ph↗

arXiv2023

The muon parton distribution functions

We compute the Parton Distribution Functions (PDFs) of the unpolarised muon for the leptons, the photon, the light quarks, and the gluon. We discuss in detail the issues stemming from the necessity of evaluating the strong coupling constant at scales of the order of the typical hadron mass, and compare our novel approach with those currently available in the literature. While we restrict our phenomenological results to be leading-logarithmic accurate, we set up our formalism in a way that renders it straightforward to achieve next-to-leading logarithmic accuracy in the QED, QCD, and mixed QED$\times$QCD contributions.

hep-ph↗

arXiv2023

Matrix element corrections in the Pythia8 parton shower in the context of matched simulations at next-to-leading order

We discuss the role of matrix element corrections (MEC) to parton showers in the context of MC@NLO-type matchings for processes that feature unstable resonances, where MEC are liable to result in double-counting issues, and are thus generally not employed. By working with Pythia8, we show that disabling all MEC is actually unnecessary in computations based on the narrow-width approximation, and we propose alternative MEC settings which, while still avoiding double counting, allow one to include hard-recoil effects in the simulations of resonance decays. We illustrate our findings by considering top-antitop production at the LHC, and by comparing MadGraph_aMC@NLO predictions with those of POWHEG-BOX and standalone Pythia8.

hep-ph↗

arXiv2021

On factorisation schemes for the electron parton distribution functions in QED

The electron, positron, and photon Parton Distribution Functions (PDFs) of the unpolarised electron have recently been computed at the next-to-leading logarithmic accuracy in QED, by adopting the $\overline{\rm MS}$ factorisation scheme. We present here analogous results, obtained by working in a different framework that is inspired by the so-called DIS scheme. We derive analytical solutions relevant to the large-$z$ region, where we show that the behaviour of the PDFs depends in a dramatic way on whether running-$α$ effects are included to all orders, as opposed to being truncated to some fixed order. By means of suitable initial and evolution conditions, next-to-leading logarithmic accurate PDFs are obtained whose large-$z$ functional forms are identical to those of their leading logarithmic counterparts.

hep-ph↗

arXiv2021

The role of colour flows in matrix element computations and Monte Carlo simulations

We discuss how colour flows can be used to simplify the computation of matrix elements, and in the context of parton shower Monte Carlos with accuracy beyond leading-colour. We show that, by systematically employing them, the results for tree-level matrix elements and their soft limits can be given in a closed form that does not require any colour algebra. The colour flows that we define are a natural generalization of those exploited by existing Monte Carlos; we construct their representations in terms of different but conceptually equivalent quantities, namely colour loops and dipole graphs, and examine how these objects may help to extend the accuracy of Monte Carlos through the inclusion of subleading-colour effects. We show how the results that we obtain can be used, with trivial modifications, in the context of QCD+QED simulations, since we are able to put the gluon and photon soft-radiation patterns on the same footing. We also comment on some peculiar properties of gluon-only colour flows, and their relationships with established results in the mathematics of permutations.

hep-ph↗

arXiv2021

HL-LHC Computing Review Stage-2, Common Software Projects: Event Generators

This paper has been prepared by the HEP Software Foundation (HSF) Physics Event Generator Working Group (WG), as an input to the second phase of the LHCC review of High-Luminosity LHC (HL-LHC) computing, which is due to take place in November 2021. It complements previous documents prepared by the WG in the context of the first phase of the LHCC review in 2020, including in particular the WG paper on the specific challenges in Monte Carlo event generator software for HL-LHC, which has since been updated and published, and which we are also submitting to the November 2021 review as an integral part of our contribution.

hep-ph↗

arXiv2021

Lepton collisions in MadGraph5_aMC@NLO

MadGraph5_aMC@NLO is a software package that allows one to simulate processes of arbitrary complexity, at both the leading and the next-to-leading order perturbative accuracy, with or without matching and multi-jet merging to parton showers. It has been designed for, and so far primarily employed in the context of, hadronic collisions. In this note, we document the implementation of a few technical features that are necessary to extend its scope to realistic ee collider environments. We limit ourselves to discussing the unpolarized beam case, but we point out that the treatment of polarized beams is conceptually identical, and that the structure we set up can easily be extended to carry out simulations at muon colliders.

hep-ph↗

arXiv2021

Colourful FKS subtraction

I formulate in a colour-friendly way the FKS method for the computation of QCD cross sections at the next-to-leading order accuracy. This is achieved through the definition of subtraction terms for squared matrix elements, constructed with single colour-dressed or pairs of colour-ordered amplitudes. The latter approach relies on the use of colour flows, is exact to all orders in $N$, and is thus particularly suited to being organized as a systematic expansion in 1/N.

hep-ph↗

arXiv2021

Challenges in Monte Carlo event generator software for High-Luminosity LHC

We review the main software and computing challenges for the Monte Carlo physics event generators used by the LHC experiments, in view of the High-Luminosity LHC (HL-LHC) physics programme. This paper has been prepared by the HEP Software Foundation (HSF) Physics Event Generator Working Group as an input to the LHCC review of HL-LHC computing, which has started in May 2020.

hep-ph↗

arXiv2020

HL-LHC Computing Review: Common Tools and Community Software

Common and community software packages, such as ROOT, Geant4 and event generators have been a key part of the LHC's success so far and continued development and optimisation will be critical in the future. The challenges are driven by an ambitious physics programme, notably the LHC accelerator upgrade to high-luminosity, HL-LHC, and the corresponding detector upgrades of ATLAS and CMS. In this document we address the issues for software that is used in multiple experiments (usually even more widely than ATLAS and CMS) and maintained by teams of developers who are either not linked to a particular experiment or who contribute to common software within the context of their experiment activity. We also give space to general considerations for future software and projects that tackle upcoming challenges, no matter who writes it, which is an area where community convergence on best practice is extremely useful.

physics.comp-ph↗

arXiv2020

Model-independent approach for incorporating interference effects in collider searches for new resonances

The presence of large-mass resonances in the data collected at the Large Hadron Collider would provide direct evidence of physics beyond the Standard Model. A key challenge in current resonance searches at the LHC is the modelling of signal--background interference effects, which can severely distort the shape of the reconstructed invariant mass distribution relative to the case where there is no interference. Such effects are strongly dependent on the beyond the Standard Model theory that must be considered as unknown if one aims to minimise any theoretical bias on the search results. In this paper, we describe a procedure which employs a physically-motivated, model-independent template functional form that can be used to model interference effects, both for the characterisation of positive discoveries, and in the presentation of null results. We illustrate the approach with the example of a scalar resonance decaying into a pair of photons.

hep-ph↗

arXiv2019

Initial conditions for electron and photon structure and fragmentation functions

In the computation of short-distance cross sections initiated by electrons and photons one can adopt the so-called structure-function approach, in which these particles play formally the same roles as hadrons do in QCD factorisation theorems, and must thus be associated with PDFs (equivalently known as structure functions in this context). At variance with their QCD counterparts, such PDFs are entirely calculable in QED. In this paper we present the results, at the next-to-leading order in the QED coupling constant $α$, for the initial conditions of the unpolarised electron and photon PDFs, which are a necessary ingredient for their eventual collinear evolution at the next-to-leading logarithmic accuracy. We also compute the analogous final-state quantities, namely the initial conditions for fragmentation functions into electrons and photons.

hep-ph↗

arXiv2019

Automated simulations beyond the Standard Model: supersymmetry

The MadGraph5 aMC@NLO framework aims to automate all types of leading- and next-to-leading-order-accurate simulations for any user-defined model that stems from a renormalisable Lagrangian. In this paper, we present all of the key ingredients of such models in the context of supersymmetric theories. In order to do so, we extend the FeynRules package by giving it the possibility of dealing with different renormalisation options that are relevant to supersymmetric models. We also show how to deal with the problem posed by the presence of narrow resonances, thus generalising the so-called on-shell subtraction approaches. We extensively compare our total rate results with those of both Prospino2 and Resummino, and present illustrative applications relevant to the 13 TeV LHC, both at the total-rate and differential levels. The computer programs that we have used to obtain the predictions presented here are all publicly available.

hep-ph↗