arXiv subjects

Giuseppe De Laurentis

Publications and source records attributed to Giuseppe De Laurentis.

At least 19 recordsLinked to original sources

arXiv2026

Primary Decompositions in Lorentz-Covariant Rings

An effective strategy for constructing compact representations of integral coefficients in scattering amplitudes is to make their singularity structure manifest. This is naturally achieved by treating them as elements of fraction fields of polynomial quotient rings, where poles correspond to algebraic vanishing loci. Simplification via partial fraction decomposition relies on exploiting the structure of the numerators and is governed, at least in a first approximation, by their behaviour on irreducible codimension-two varieties. These are identifiable through primary decompositions of the associated ideals. Despite the availability of general algorithms, primary decompositions remain computationally challenging and often require tailored strategies. In this work, we extend an approach based on ideal saturation, identify an issue related to the breaking of Lorentz covariance in the choice of ideal generators, and present a solution based on fitting ansätze in special kinematic limits. We also provide substantial improvements to an algorithm for the generation of numerical points in proximity of given varieties and to one for testing primality of unmixed ideals, both of which rely on a semi-numerical procedure for computing independent sets and variety dimensions. Finally, we present new codimension-two primary decompositions for five-point massless amplitudes at higher powers in the dimensional regulator, and for finite remainders with five-point one-mass kinematics, where a new spurious singular locus appears.

hep-th↗

arXiv2026

Two-loop leading-color QCD corrections for Higgs plus two-jet production in the heavy-top limit

We present the leading-color two-loop QCD corrections for Higgs-boson production in association with two jets through gluon fusion in the heavy-top effective theory. We provide analytic expressions for the finite remainders of the helicity amplitudes, written in terms of one-mass pentagon functions with spinor-helicity coefficients. These expressions are obtained by reconstructing the amplitudes from numerical finite-field samples computed within the numerical unitarity framework. The reconstruction is made possible by several advances in exploiting the analytic structure of the amplitudes, which both reduce the number of required samples and lead to compact representations. In particular, we introduce a new algorithm for multivariate partial fraction decomposition, based on a generic bivariate slice and a simplified treatment of ideal intersections. Using the resulting analytic expressions, we provide an efficient and stable implementation of their numerical evaluation, ready for phenomenological applications. Finally, we study the singularity structure of the remainders and confirm the existence of a threshold at non-degenerate physical momentum configurations, usually associated with massive virtual particle exchanges.

hep-ph↗

arXiv2026

Linac: linear algebra with CUDA over finite fields

Solving linear systems of polynomial equations is a ubiquitous problem in both mathematics and physics. The standard approach, Gaussian elimination, scales cubically with system size and often constitutes a computational bottleneck. The algorithm's inherent parallelism makes it well-suited for modern computing architectures, namely graphics processing units (GPUs), which offer significantly higher throughput than CPUs. Additionally, the use of finite fields -- integers modulo a prime -- in place of floating-point arithmetic offers a scalable solution to the issue of numerical precision loss, which becomes increasingly problematic at large system sizes. With Linac, we present a high-performance, open-source, parallel implementation of Gaussian elimination over finite fields and floating-point arithmetic. This tool has been developed for applications to analytic reconstruction of scattering amplitudes in quantum field theory.

physics.comp-ph↗

arXiv2026

Polarization structure and spin covariance of massive vector-boson amplitudes in QCD

Nearly thirty years ago, Bern, Dixon and Kosower computed all helicity amplitudes for the annihilation of an electron-positron pair into four QCD partons through an electroweak vector boson. More recently, the leading-color two-loop amplitudes for the same process were obtained. When such amplitudes are expressed in the massless spinor-helicity formalism, they effectively correspond to the decay of a transversely polarized vector boson. However, for several reasons, it is highly desirable to extend these calculations to the case where the polarization of the vector boson is longitudinal. Due to the complexity of such computations, repeating them to obtain the result for the ''missing'' polarization of the electroweak boson is a significant undertaking even at one loop. Besides, when attempting new higher-loop computations, it is beneficial to identify the minimal set of quantities (e.g. form factors) that must be determined to obtain the full amount of physically-relevant information. In this paper, we show that amplitudes involving vector-boson decays to massless leptons-although they appear to project onto the transverse polarization-still encode the full information about all polarization states of the vector boson, including the longitudinal one. This follows from the little-group (spin) covariance of the amplitude, which allows us-largely through simple replacement rules-to rewrite the helicity amplitudes as a matrix with open SU(2) spin indices in the massive spinor-helicity (or spin-spinor) formalism. Therefore, knowledge of an amplitude for any polarization component suffices to reconstruct the full covariant matrix.

hep-ph↗

arXiv2025

Accelerating Berends-Giele recursion for gluons in arbitrary dimensions over finite fields

This work provides a proof of concept for the computation of pure gluonic amplitudes in quantum chromodynamics (QCD) on graphics processing units (GPUs). The implementation relies on the Berends-Giele recursion algorithm and, for the first time on a GPU, enables the numerical computation of amplitudes in an arbitrary number of space-time dimensions and over finite fields. This demonstrates the advantages of hardware acceleration, not only for the computation of tree-level amplitudes for real-radiation processes in four dimensions over complex numbers but also for generating loop integrands for virtual corrections in $d$ dimensions over finite fields. The associated computer program is publicly available.

hep-ph↗

arXiv2025

Analytic reconstruction with massive particles: one-loop amplitudes for $0 \to \bar{q}qt\bar{t}H$

We present an analytic reconstruction of one-loop amplitudes for the process $0 \to \bar{q}qt\bar{t}H$. Our calculation is a novel use of analytic reconstruction, retaining explicit covariance in the massive spin states through the massive spinor-helicity formalism. The analytic reconstruction relies on embedding the massive five-point kinematics in a fully massless eight-point phase space while still building a minimal ansatz directly in the five-point phase space. In order to obtain compact analytic expressions it is necessary to identify suitable partial fraction decompositions and extract common numerator factors, which we achieve through careful inspection of limits in which pairs of denominators vanish. We find that the resulting amplitudes are more numerically efficient than ones computed using automatic methods but that the gains are not as significant as in the massless case, at least at present. The method opens the door to applications at two-loop order, where numerical efficiency and improvements in the reconstruction methodology are more crucial, especially with regards to the number of free parameters in the ansatz.

hep-ph↗

arXiv2025

An analytic result for the $0 \to ggHHH$ amplitude

We present a fully analytic calculation of the leading-order one-loop amplitude for triple Higgs production via gluon fusion, $gg \to HHH$, retaining full dependence on the mass of the heavy quark circulating in the loop. This amplitude provides a direct probe of the triple and quartic Higgs self-couplings, the measurement of which is a central goal of current and future colliders. The amplitude can be presented in compact form thanks to the use of analytic reconstruction techniques, based on finite-field and $p$-adic evaluations, partial fraction decompositions, and primary decompositions to identify common numerator factors. Our results provide a compact and efficient representation of the matrix element for this process, enabling evaluations that are more than an order of magnitude faster than existing numerical alternatives.

hep-ph↗

arXiv2025

Compact Two-Loop QCD Corrections for $Vjj$ Production in Proton Collisions

We present compact two-loop QCD corrections in the leading-color approximation for the production of an electroweak vector boson, $V = \{W^{\pm}, Z,γ^\star\}$, in association with two light jets ($Vjj$) at hadron colliders. Leptonic decays of the electroweak boson are included at the amplitude level. Working in the analytic-reconstruction approach, we develop two techniques to build compact partial-fraction forms for individual rational functions. One approach exploits their analytic structure. In the other, we iteratively construct subtraction terms that match the rational functions in singular limits. Moreover, we show how the singular behavior of the rational functions can be systematically used to find a more compact basis of the space that they span. We apply our techniques to the $Vjj$ amplitudes, yielding a representation that is three orders of magnitude smaller than previous results. We then use these compact expressions to provide an efficient and stable C++ numerical implementation suitable for phenomenological applications.

hep-ph↗

arXiv2024

The Two-Loop Lipatov Vertex in QCD

High-energy factorization of 2 -> 2 amplitudes in QCD has been recently pushed to the next-to-next-to-leading logarithmic order by determining the three-loop gluon Regge trajectory. This was based on computing multi-Reggeon exchanges using rapidity evolution in the shock-wave formalism, and disentangling between the Regge pole and Regge cut contributions. In the present paper we extend the relevant theoretical framework to 2 -> 3 processes, and compute all multi-Reggeon exchanges necessary for extracting the two-loop Reggeon-gluon-Reggeon Lipatov vertex from 2 -> 3 amplitudes. Then, specializing general amplitude methods to multi-Regge kinematics, we derive analytic expressions for non-planar two-loop gg -> ggg, gq -> ggq and qq -> qgq QCD amplitudes in that limit. Matching these to the multi-Reggeon computation, we determine the QCD Lipatov vertex in dimensional regularization at two loops through finite terms. We also determine the one-loop vertex through O(epsilon^4). All results are expressed in a compact form in terms of a basis of single-valued generalised polylogarithms, manifesting target-projectile symmetry and reality properties. Furthermore, our basis of functions is explicitly finite in the soft limit, featuring delicate cancellation of spurious rational poles by transcendental functions. Agreement between all three partonic channels, as well agreement of the maximal weight contributions with the super Yang-Mills Lipatov vertex provide robust checks of the result.

hep-ph↗

arXiv2024

Analytic amplitudes for a pair of Higgs bosons in association with three partons

The pair production of Higgs bosons at the LHC can give information about the triple Higgs boson coupling. We perform an analytic one-loop calculation of the amplitudes for a pair of Higgs bosons in association with three partons, retaining the exact dependence on the quark mass circulating in the loop. These amplitudes constitute the real radiation corrections in the calculation of Higgs boson pair production at next-to-leading order in the strong coupling. The results of an analytic generalised-unitarity computation are simplified via analytic reconstruction in spinor variables. Compact ansätze for kinematic pole residues are iteratively fitted via $p$-adic evaluations near said poles and subtracted until no pole remains. A new ansatz construction is introduced to minimally parametrise coefficients of amplitudes with multiple massive external legs. The simplified expressions are faster to evaluate than automatic codes and can lead to more stable results near singular regions.

hep-ph↗

arXiv2024

Two-Loop Five-Point One-Mass Amplitudes in the Spinor-Helicity Formalism

Processes involving electroweak vector bosons in association with jets are crucial for precision studies of the Standard Model at the Large Hadron Collider. Accurate predictions for the process $pp\rightarrow V(\rightarrow\bar\ell\ell)jj$ at next-to-next-to-leading order (NNLO), as well as N$^3$LO ones for the process with one fewer jet, require two-loop five-point one-mass amplitudes. These exhibit a significant increase in complexity compared to their massless counterparts. We present results for the partonic processes $\bar qQ\bar Qq\bar\ell\ell$ and $\bar qggq\bar\ell\ell$, with a forthcoming package for phenomenology. The present recalculation is based on the previous analytic results from ref. [1]. For the first time, we express two-loop five-point one-mass amplitudes in the spinor-helicity formalism. We achieve three orders of magnitude smaller expressions compared to previous results. This will facilitate phenomenological studies and help clarify mathematical properties of the amplitude.

hep-ph↗

arXiv2024

Non-Planar Two-Loop Amplitudes for Five-Parton Scattering

We review the current status of high-multiplicity double-virtual QCD corrections to processes relevant for LHC phenomenology. In particular, we discuss the recent full-color calculation of the five-parton process, whose two-loop amplitudes are required to obtain next-to-next-to-leading order predictions for three-jet production at the LHC. We address various aspects of the computation, including color decomposition, renormalization, partial amplitudes, color identities and the construction of the finite remainder. We review the method of numerical unitarity, which is used to generate finite-field samples of the amplitude. We then focus on the analytic reconstruction of the coefficient functions from these numerical samples via Ansatz techniques. A novel algorithm, based on the correlation of codimension-one residues, helps manage the complexity of the calculation. Little-group rescalings of the gluon amplitude, inspired by supersymmetry Ward identities, facilitate the computation of the quark amplitudes. We conclude with an outlook towards upcoming computations with an increased number of scales, leading to larger Ansätze and more complicated alphabets.

hep-ph↗

arXiv2024

Double-Virtual NNLO QCD Corrections for Five-Parton Scattering: The Gluon Channel

We compute the two-loop helicity amplitudes for the scattering of five gluons, including all contributions beyond the leading-color approximation. The analytic expressions are represented as linear combinations of transcendental functions with rational coefficients, which we reconstruct from finite-field samples obtained with the numerical unitarity method. Guided by the requirement of removing unphysical singularities, we find a remarkably compact generating set of rational coefficients, which we are able to display entirely in the manuscript. We implement our results in a public code, which provides efficient and reliable numerical evaluations for phenomenological applications.

hep-ph↗

arXiv2024

Double-Virtual NNLO QCD Corrections for Five-Parton Scattering: The Quark Channels

We complete the computation of two-loop helicity amplitudes required to obtain next-to-next-to-leading order QCD corrections for three-jet production at hadron colliders, including all contributions beyond the leading-color approximation. The analytic expressions are reconstructed from finite-field samples obtained with the numerical unitarity method. We find that the reconstruction is significantly facilitated by exploiting the overlaps between rational coefficient functions of quark and gluon processes, and we display their compact generating sets in the appendix of the paper. We implement our results in a public code, and demonstrate its suitability for phenomenological applications.

hep-ph↗

arXiv2023

Two-Loop Five-Parton Leading-Colour Finite Remainders in the Spinor-Helicity Formalism

We present all two-loop five-parton leading-colour finite remainders in the spinor-helicity formalism by analysing numerical evaluations of their known expressions in terms of Mandelstam invariants. Recasting them in terms of spinor-helicity variables allows us to obtain expressions which are more compact, faster to evaluate, numerically more stable and manifestly free from poles of higher order than necessary. At the same time, due to the better scaling of our reconstruction strategy with the complexity of the input, we required one order of magnitude fewer numerical samples to complete the analytical reconstruction than were needed by the authors of Ref. \cite{Abreu:2019odu}, albeit using higher numerical working precision. This places our reconstruction technique as an alternative to the finite-field single-numerator reconstruction for future applications.

hep-ph↗

arXiv2023

Two-Loop QCD Corrections for Three-Photon Production at Hadron Colliders

We complete the computation of the two-loop helicity amplitudes for the production of three photons at hadron colliders, including all contributions beyond the leading-color approximation. We reconstruct the analytic form of the amplitudes from numerical finite-field samples obtained with the numerical unitarity method. This method requires as input surface terms for all relevant five-point non-planar integral topologies, which we obtain by solving the associated syzygy problem in embedding space. The numerical samples are used to constrain compact spinor-helicity ansätze, which are optimized by taking advantage of the known one-loop analytic structure. We make our analytic results available in a public C++ library, which is suitable for immediate phenomenological applications. We estimate that the inclusion of the subleading-color contributions will decrease the size of the two-loop corrections by about 30% to 50%, and the NNLO cross sections by a few percent, compared to the results in the leading-color approximation.

hep-ph↗

arXiv2023

Extracting analytical one-loop amplitudes from numerical evaluations

In this article we present a method to generate analytic expressions for the integral coefficients of loop amplitudes using numerical evaluations only. We use high-precision arithmetic to explore the singularity structure of the coefficients and decompose them into parts of manageable complexity. To illustrate the usability of our method we provide analytical expressions for all helicity configurations of the colour-ordered six-point gluon amplitudes at one loop with a gluon in the loop.

hep-ph↗

arXiv2023

Lips: p-adic and singular phase space

I present new features of the open-source Python package lips, which leverages the newly developed pyadic and syngular libraries. These developments enable the generation and manipulation of massless phase-space configurations beyond real kinematics, defined in terms of four-momenta or Weyl spinors, not only over complex numbers ($\mathbb{C}$), but now also over finite fields ($\mathbb{F}_p$) and p-adic numbers ($\mathbb{Q}_p$). The package also offers tools to evaluate arbitrary spinor-helicity expressions in any of these fields. Furthermore, using the algebraic-geometry submodule, which utilizes Singular [1] through the Python interface syngular, one can define and manipulate ideals in spinor variables, enabling the identification of irreducible surfaces where scattering amplitudes have well-defined zeros and poles. As an example application, I demonstrate how to infer valid partial-fraction decompositions from numerical evaluations.

hep-th↗