arXiv subjects

Charalampos Anastasiou

Publications and source records attributed to Charalampos Anastasiou.

At least 19 recordsLinked to original sources

arXiv2026

Ward identity preserving local ultraviolet counterterms for photoproduction at two loops in QCD

We review the construction of locally finite two-loop amplitude integrands for photoproduction via quark annihilation, presented in arXiv:2509.07805. Building on established techniques for off-shell colorless production, we extend this local subtraction framework to handle transient singularities arising from real outgoing photons. These singularities manifest only at the integrand level, yielding finite contributions upon integration. In these proceedings, we provide the explicit construction of ultraviolet counterterms that satisfy necessary Ward identity cancellations, ensuring that the integrand is rendered integrable. This work provides a locally finite amplitude integrand that is ready for numerical integration in momentum space. Furthermore, it establishes the foundation for extending local subtraction frameworks to processes involving final-state jets.

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arXiv2026

Efficient evaluation of the dark-matter two-loop power spectrum in the EFT of LSS

Rapid progress in cosmological Large Scale Structure (LSS) surveys motivates precise theoretical predictions. The Effective Field Theory of Large-Scale Structure (EFTofLSS) is routinely applied to data, and requires fast computation of its predictions when sampling the large space of cosmological parameters. Going beyond existing one-loop techniques, we present a method to rapidly evaluate the two-loop power spectrum. Our method decomposes the typically small difference between a given linear power spectrum and a reference power spectrum into a cosmology-independent basis of functions resembling massive scalar propagators in Quantum Field Theory. By taking the leading terms in such a small difference, we numerically evaluate the cosmology-independent loop integrals where in the integrand only the relevant combinations of basis functions appear. We achieve an efficient numerical evaluation via physically motivated local ultraviolet subtractions and by arranging the cancellation of infrared singularities locally in the integrands. Final predictions are obtained by contracting these precomputed integrals with the cosmology-dependent coordinates of the expansion in the fixed basis. We present and publicly release the precomputed integrals for the renormalized two-loop dark-matter power spectrum in the EFTofLSS. These require eight EFT counterterms, which include the effect of generated vorticity, and are sufficient to analyze the lensing galaxy signal in LSS surveys at this order.

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arXiv2026

Local finiteness for real-virtual corrections to electroweak production in partonic collisions

We present a local subtraction scheme that enables the combined integration of loop momenta and the final-state parton phase space in real-virtual NNLO QCD corrections to cross sections for hadroproduction of electroweak and other colorless states. All initial- and final-state infrared singularities are subtracted at the integrand level in momentum space, yielding a locally finite integral ready for numerical integration in four dimensions. The subtraction terms are all based on the well-understood process of single-Higgs production. The core of our subtraction scheme relies on achieving local factorization in all infrared limits of real and virtual momenta. This necessitates systematic modifications of the original Feynman integrand for loop amplitudes, enabling gauge symmetry cancellations before performing integrations. Our approach provides an essential step toward NNLO cross-section calculations for hadron collider processes, where both loop and phase-space integrations are carried out numerically.

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arXiv2025

General finite two-loop amplitude integrand for photoproduction in quark annihilation

The construction of integrands free of infrared and ultraviolet singularities may enable the application of numerical methods to evaluate loop amplitudes that are inaccessible with analytic techniques. At two loops, finite amplitude integrands have been constructed for the production of off-shell or massive colorless particles via quark annihilation. In this article, we extend this class of processes to include real photons in the final state. To achieve this, we introduce appropriate momentum flows and counterterms to eliminate singularities that occur because the photons are massless. These singularities arise only locally at the integrand level and do not lead to divergences upon integration. Our treatment also eliminates all power singularities arising from self-energy corrections in the integrand. We extend the analysis to gluon emission from virtual quarks. We believe these new insights will be useful for future extensions of infrared subtraction methods to processes with final-state jets.

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arXiv2024

Locally finite two-loop amplitudes for electroweak production through gluon fusion

The computation of two-loop amplitudes for the production of multiple Higgs and electroweak gauge bosons via gluon fusion with exact dependence on quark masses relies primarily on numerical methods. We propose a framework that enables their numerical evaluation in momentum space. The method is inspired by the factorization of infrared divergences in QCD scattering amplitudes. It extends techniques introduced for electroweak gauge boson production from quark-antiquark annihilation to processes with external gluons. By combining diagrammatic integrands, we make use of local cancellations between diagrams that automatically eliminate most non-factoring infrared singularities. With a limited number of counterterms, we then derive two-loop integrands for which all soft and collinear singularities factorize locally. We hope that the local subtraction techniques presented in this article will play a useful role in extending the local factorization formalism to two-loop amplitudes for arbitrary processes.

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arXiv2023

Tensor reduction of loop integrals

The computational cost associated with reducing tensor integrals to scalar integrals using the Passarino-Veltman method is dominated by the diagonalisation of large systems of equations. These systems of equations are sized according to the number of independent tensor elements that can be constructed using the metric and external momenta. In this article, we present a closed-form solution of this diagonalisation problem in arbitrary tensor integrals. We employ a basis of tensors whose building blocks are the external momentum vectors and a metric tensor transverse to the space of external momenta. The scalar integral coefficients of the basis tensors are obtained by mapping the basis elements to the elements of an orthogonaldual basis. This mapping is succinctly expressed through a formula that resembles the ordering of operators in Wick's theorem. Finally, we provide examples demonstrating the application of our tensor reduction formula to Feynman diagrams in QCD $2 \to 2$ scattering processes, specifically up to three loops.

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arXiv2023

Efficiently evaluating loop integrals in the EFTofLSS using QFT integrals with massive propagators

We develop a new way to analytically calculate loop integrals in the Effective Field Theory of Large Scale-Structure. Previous available methods show severe limitations beyond the one-loop power spectrum due to analytical challenges and computational and memory costs. Our new method is based on fitting the linear power spectrum with cosmology-independent functions that resemble integer powers of quantum field theory massive propagators with complex masses. A remarkable small number of them is sufficient to reach enough accuracy. Similarly to former approaches, the cosmology dependence is encoded in the coordinate vector of the expansion of the linear power spectrum in our basis. We first produce cosmology-independent tensors where each entry is the loop integral evaluated on a given combination of basis vectors. For each cosmology, the evaluation of a loop integral amounts to contracting this tensor with the coordinate vector of the linear power spectrum. The 3-dimensional loop integrals for our basis functions can be evaluated using techniques familiar to particle physics, such as recursion relations and Feynman parametrization. We apply our formalism to evaluate the one-loop bispectrum of galaxies in redshift space. The final analytical expressions are quite simple and can be evaluated with little computational and memory cost. We show that the same expressions resolve the integration of all one-loop $N$-point function in the EFTofLSS. This method, which is originally presented here, has already been applied in the first one-loop bispectrum analysis of the BOSS data to constraint $Λ$CDM parameters and primordial non-Gaussianities, see arXiv:2206.08327 and arXiv:2201.11518.

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arXiv2022

Locally finite two-loop QCD amplitudes from IR universality for electroweak production

We describe the implementation of infrared subtractions for two-loop QCD corrections to quark-antiquark annihilation to electroweak final states. The subtractions are given as form-factor integrands whose integrals are known. The resulting subtracted amplitudes are amenable to efficient numerical integration. Our procedure is based on the universality of infrared singularities and requires a relatively limited set of subtractions, whose number grows as the number of two-loop diagrams, rather than with the number of singular regions of integration.

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arXiv2020

Light Quark Mediated Higgs Boson Threshold Production in the Next-to-Leading Logarithmic Approximation

We study the amplitude of the Higgs boson production in gluon fusion mediated by a light quark loop and evaluate the logarithmically enhanced radiative corrections to the next-to-leading logarithmic approximation which sums up the terms of the form $α_s^n\ln^{2n-1}(m_H/m_q)$ to all orders in the strong coupling constant. This result is used for the calculation of the process cross section near the production threshold and gives a quantitative estimate of the three and four-loop bottom quark contribution to the Higgs boson production at the Large Hadron Collider.

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arXiv2020

Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation

We study the singularity structure of two-loop QED amplitudes for the production of multiple off-shell photons in massless electron-positron annihilation and develop counterterms that remove their infrared and ultraviolet divergences point by point in the loop integrand. The remainders of the subtraction are integrable in four dimensions and can be computed in the future with numerical integration. The counterterms capture the divergences of the amplitudes and factorize in terms of the Born amplitude and the finite remainder of the one-loop amplitude. They consist of simple one- and two-loop integrals with at most three external momenta and can be integrated analytically in a simple manner with established methods. We uncover novel aspects of fully local IR factorization, where vertex and self-energy subdiagrams must be modified by new symmetrizations over loop momenta, in order to expose their tree-like tensor structures and hence factorization of IR singularities prior to loop integration. This work is a first step towards isolating locally the hard contributions of generic gauge theory amplitudes and rendering them integrable in exactly four dimensions with numerical methods.

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arXiv2020

Quark mass effects in two-loop Higgs amplitudes

We provide two two-loop amplitudes relevant for precision Higgs physics. The first is the two-loop amplitude for Higgs boson production through gluon fusion with exact dependence on the top quark mass up to squared order in the dimensional regulator $ε$. The second result we provide is the two-loop amplitude for the decay of a Higgs boson into a pair of massive bottom quarks through the Higgs-to-gluon coupling in the infinite top mass limit. Both amplitudes are computed by finding canonical bases of master integrals, which we evaluate explicitly in terms of harmonic polylogarithms. We obtain the bare, renormalized and IR-subtracted amplitude and provide the results in terms of building blocks suitable to changing renormalization schemes.

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arXiv2018

One-loop QCD contributions to differential cross-sections for Higgs production at N$^3$LO

We present one-loop contributions to the fully differential Higgs boson gluon-fusion cross-section for Higgs production via gluon fusion. Our results constitute a necessary ingredient of a complete N$^3$LO determination of the cross-section. We perform our computation using a subtraction method for the treatment of soft and collinear singularities. We identify the infrared divergent parts in terms of universal splitting and eikonal functions, and demonstrate how phase-space integrations yield poles (up to $1/ε^6$ ) in the dimensional regulator $ε=(4-d)/2$. We compute the coefficients of the $ε$ expansion, including the finite part numerically. As a demonstration of our numerical implementation, we present the corrections at N$^3$LO due to one-loop amplitudes in the rapidity and transverse momentum of the Higgs boson.

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arXiv2018

Removing infrared divergences from two-loop integrals

Feynman amplitudes at higher orders in perturbation theory generically have complex singular structures. Notwithstanding the emergence of many powerful new methods, the presence of infrared divergences poses significant challenges for their evaluation. In this article, we develop a systematic method for the removal of the infrared singularities, by adding appropriate counterterms that approximate and cancel divergent limits point-by-point at the level of the integrand. We provide a proof of concept for our method by applying it to master-integrals that are found in scattering amplitudes for representative two-to-two scattering processes of massless particles. We demonstrate that, after the introduction of counterterms, the remainder is finite in four dimensions. In addition, we find in these cases that the complete singular dependence of the integrals can be obtained simply by analytically integrating the counterterms. Finally, we observe that our subtraction method can be also useful in order to extract in a simple way the asymptotic behavior of Feynman amplitudes in the limit of small mass parameters.

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arXiv2018

Mixed QCD-electroweak corrections to Higgs production via gluon fusion in the small mass approximation

We compute the mixed QCD-electroweak corrections to the cross section for the production of a Higgs boson via gluon fusion, in the limit of a small mass of the electroweak gauge bosons. This limit is regular and we calculate it by setting the W, Z masses to zero in the Feynman rules for their propagators. Our analytic results provide an independent check, in a non-trivial limit, of a recent exact computation for the three-loop mixed QCD and electroweak virtual corrections and the corresponding contribution to the cross section in the soft-virtual approximation. From our calculation in the small mass approximation, we can infer the second term in the expansion of the cross section around the threshold limit with its exact dependence on the masses of the W, Z bosons. Furthermore we find that in the small mass approximation the non-factorizable contributions from the real radiation, so far unknown for full gauge boson mass dependence, are modest in comparison to the known factorizable and virtual contributions to the full ${\cal O}(α_s^3 α^2)$ mixed QCD and electroweak cross-section. This furnishes a new phenomenological test of estimates for the mixed QCD and electroweak corrections, which were based on the hypothesis of factorization of QCD and electroweak corrections.

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arXiv2016

CP-even scalar boson production via gluon fusion at the LHC

In view of the searches at the LHC for scalar particle resonances in addition to the 125 GeV Higgs boson, we present the cross section for a CP-even scalar produced via gluon fusion at N3LO in perturbative QCD assuming that it couples directly to gluons in an effective theory approach. We refine our prediction by taking into account the possibility that the scalar couples to the top-quark and computing the corresponding contributions through NLO in perturbative QCD. We assess the theoretical uncertainties of the cross section due to missing higher-order QCD effects and we provide the necessary information for obtaining the cross section value and uncertainty from our results in specific scenarios beyond the Standard Model. We also give detailed results for the case of a 750 GeV scalar, which will be the subject of intense experimental studies.

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arXiv2016

High precision determination of the gluon fusion Higgs boson cross-section at the LHC

We present the most precise value for the Higgs boson cross-section in the gluon-fusion production mode at the LHC. Our result is based on a perturbative expansion through N$^3$LO in QCD, in an effective theory where the top-quark is assumed to be infinitely heavy, while all other Standard Model quarks are massless. We combine this result with QCD corrections to the cross-section where all finite quark-mass effects are included exactly through NLO. In addition, electroweak corrections and the first corrections in the inverse mass of the top-quark are incorporated at three loops. We also investigate the effects of threshold resummation, both in the traditional QCD framework and following a SCET approach, which resums a class of $π^2$ contributions to all orders. We assess the uncertainty of the cross-section from missing higher-order corrections due to both perturbative QCD effects beyond N$^3$LO and unknown mixed QCD-electroweak effects. In addition, we determine the sensitivity of the cross-section to the choice of parton distribution function (PDF) sets and to the parametric uncertainty in the strong coupling constant and quark masses. For a Higgs mass of $m_H = 125~{\rm GeV}$ and an LHC center-of-mass energy of $13~{\rm TeV}$, our best prediction for the gluon fusion cross-section is \[ σ= 48.58\,{\rm pb} {}^{+2.22\, {\rm pb}\, (+4.56\%)}_{-3.27\, {\rm pb}\, (-6.72\%)} \mbox{ (theory)} \pm 1.56 \,{\rm pb}\, (3.20\%) \mbox{ (PDF+$α_s$)} \]

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arXiv2015

Soft Expansion of Double-Real-Virtual Corrections to Higgs Production at N$^3$LO

We present methods to compute higher orders in the threshold expansion for the one-loop production of a Higgs boson in association with two partons at hadron colliders. This process contributes to the N$^3$LO Higgs production cross section beyond the soft-virtual approximation. We use reverse unitarity to expand the phase-space integrals in the small kinematic parameters and to reduce the coefficients of the expansion to a small set of master integrals. We describe two methods for the calculation of the master integrals. The first was introduced for the calculation of the soft triple-real radiation relevant to N$^3$LO Higgs production. The second uses a particular factorization of the three body phase-space measure and the knowledge of the scaling properties of the integral itself. Our result is presented as a Laurent expansion in the dimensional regulator, although some of the master integrals are computed to all orders in this parameter.

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arXiv2015

Higgs boson gluon-fusion production in N3LO QCD

We present the cross-section for the production of a Higgs boson at hadron-colliders at next-to- next-to-next-to-leading order (N3LO) in perturbative QCD. The calculation is based on a method to perform a series expansion of the partonic cross-section around the threshold limit to an arbitrary order. We perform this expansion to sufficiently high order to obtain the value of the hadronic cross at N3LO in the large top-mass limit. For renormalisation and factorisation scales equal to half the Higgs mass, the N3LO corrections are of the order of +2.2%. The total scale variation at N3LO is 3%, reducing the uncertainty due to missing higher order QCD corrections by a factor of three.

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