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Piotr Bargiela

Publications and source records attributed to Piotr Bargiela.

15 recordsLinked to original sources
arXiv2026

The spectrum of Feynman-integral geometries at two loops

We provide a complete classification of the Feynman-integral geometries at two-loop order in four-dimensional Quantum Field Theory with standard quadratic propagators. Concretely, we consider a finite basis of integrals in the 't Hooft--Veltman scheme, i.e. with $D$-dimensional loop momenta and four-dimensional external momenta, which belong to 79 independent topologies, or sectors. Then, we analyze the leading singularities of the integrals in those sectors for generic values of the masses and momenta, using the loop-by-loop Baikov representation. Aside from the Riemann sphere, we find that elliptic curves, hyperelliptic curves of genus 2 and 3 as well as K3 surfaces occur. Moreover, we find a smooth and non-degenerate Del Pezzo surface of degree 2, a particular Fano variety known to be rationalizable, resulting in a curve of geometric genus 3. These geometries determine the space of functions relevant for Quantum Field Theories at two-loop order, including in the Standard Model.

hep-th↗
arXiv2026

All-loop four-quark Bethe-Salpeter kernel

We analytically calculate the all-loop bare perturbative part of the four-quark Bethe-Salpeter kernel using modern scattering amplitude methods. We work to subleading order in the large number of quark flavors approximation of massless Quantum Chromodynamics, which simultaneously makes an all-loop calculation feasible, is systematically improvable, and preserves asymptotic freedom. It also allows for avoiding the ambiguity of choosing a truncation scheme in Dyson-Schwinger equations. We exploit state-of-the-art methods in Integration-By-Parts reduction of Lorentz scalar Feynman integrals into a minimal Master Integral basis, and direct integration into Generalized Polylogarithms. As a byproduct of our calculation, we also provide the result for the gluon and quark propagators. We discuss a path towards nonperturbative formulation and potential future phenomenological applications.

hep-ph↗
arXiv2026

Light-by-light scattering at three loops in massless QCD and QED: amplitudes and cross sections

We present the calculation of three-loop massless QCD and QED helicity amplitudes for light-by-light scattering. We make use of Lorentz tensor decomposition in the 't Hooft-Veltman dimensional regularisation scheme to reduce the complexity of the computation. Our analytic amplitude results are remarkably compact and can be efficiently evaluated numerically. We employ them to compute the corresponding NNLO differential cross-section predictions in the invariant mass and rapidity distributions of the di-photon system, for which we find agreement with the experimental ATLAS data from ultra-peripheral heavy-ion collisions.

hep-ph↗
arXiv2025

The integrand form of infrared singularities of two-loop QCD scattering amplitudes

In this work, we express the singular part of a scattering amplitude in terms of Feynman integrals compatible with topologies appearing in the bare amplitude, and we choose a basis of locally finite Master Integrals. In two-loop massless QCD, we find such a representation of the amplitude singularities using a systematic ansatz reconstruction of the integrand from a predicted integrated form. As an example application, we write the finite part of an amplitude for the digluon production in quark annihilation for some helicity configurations as manifestly locally finite.

hep-ph↗
arXiv2025

On the finite basis of two-loop `t Hooft-Veltman Feynman integrals

In this work, we investigate the finite basis topologies of two-loop dimensionally regularized Feynman integrals in the `t Hooft-Veltman scheme in the Standard Model. We present a functionally distinct finite basis of Master Integrals which spans the whole transcendental space of all two-loop Feynman integrals with external momenta in four dimensions. We also indicate that all the two-loop Master Integrals, in an appropriate basis, with more than 8 denominators do not contribute to the finite part of any two-loop scattering amplitude. In addition, we elaborate on the application of the `t Hooft-Veltman decomposition to improve the performance of numerical evaluation of Feynman integrals using AMFlow and DCT packages. Moreover, we analyze the spectrum of special functions and the corresponding geometries appearing in any two-loop scattering amplitude. Our work will allow for a reduction in the computational complexity required for providing high-precision predictions for future high-multiplicity collider observables, both analytically and numerically.

hep-th↗
arXiv2024

On the finite basis topologies for multi-loop high-multiplicity Feynman integrals

In this work, we systematically analyse Feynman integrals in the `t Hooft-Veltman scheme. We write an explicit reduction resulting from partial fractioning the high-multiplicity integrands to a finite basis of topologies at any given loop order. We find all of these finite basis topologies at two loops in four external dimensions. Their maximal cut and the leading singularity are expressed in terms of the Gram determinant and Baikov polynomial. By performing an Integration-By-Parts reduction without any cut constraint on a numerical probe for one of these topologies, we show that the computational complexity drops significantly compared to the Conventional Dimensional Regularization scheme. Formally, our work implies an upper bound on the rigidity of special functions appearing in the iterated integral solutions at each loop order in perturbative Quantum Field Theory. Phenomenologically, the integrand-level reduction we present will substantially simplify the task of providing high-precision predictions for future high-multiplicity collider observables.

hep-ph↗
arXiv2024

Integrated Unitarity for Scattering Amplitudes

We present a new method for computing multi-loop scattering amplitudes in Quantum Field Theory. It extends the Generalized Unitarity method by constraining not only the integrand of the amplitude but also its full integrated form. Our approach exploits the relation between cuts and discontinuities of the amplitude. Explicitly, by the virtue of analyticity and unitarity of the S-matrix, the amplitude can be expressed in terms of lower-loop on-shell amplitudes dispersively integrated along cuts. As both cuts and discontinuities can be computed systematically in dimensional regularization, we validated our method by reproducing the four-gluon amplitude in two-loop massless Quantum Chromodynamics. Moreover, since our approach improves the performance of the calculation, we provide a new result for the four-loop four-point massless planar ladder Feynman integral. It is expressed in terms of Harmonic Polylogarithms with letters 0 and 1.

hep-th↗
arXiv2023

Two-loop mixed QCD-electroweak amplitudes for $Z+$jet production at the LHC: bosonic corrections

We present a calculation of the bosonic contribution to the two-loop mixed QCD-electroweak scattering amplitudes for $Z$-boson production in association with one hard jet at hadron colliders. We employ a method to calculate amplitudes in the 't Hooft-Veltman scheme that reduces the amount of spurious non-physical information needed at intermediate stages of the computation, to keep the complexity of the calculation under control. We compute all the relevant Feynman integrals numerically using the Auxiliary Mass Flow method. We evaluate the two-loop scattering amplitudes on a two-dimensional grid in the rapidity and transverse momentum of the $Z$ boson, which has been designed to yield a reliable numerical sampling of the boosted-$Z$ region. This result provides an important building block for improving the theoretical modelling of a key background for monojet searches at the LHC.

hep-ph↗
arXiv2023

High-precision scattering amplitudes for LHC phenomenology

In this work, we consider scattering amplitudes relevant for high-precision Large Hadron Collider (LHC) phenomenology. We analyse the general structure of amplitudes, and we review state-of-the-art methods for computing them. We discuss advantages and shortcomings of these methods, and we point out the bottlenecks in modern amplitude computations. As a practical illustration, we present frontier applications relevant for multi-loop multi-scale processes. We compute the helicity amplitudes for diphoton production in gluon fusion and photon+jet production in proton scattering in three-loop massless Quantum Chromodynamics (QCD). We have adopted a new projector-based prescription to compute helicity amplitudes in the 't Hooft-Veltman scheme. We also rederived the minimal set of independent Feynman integrals for this problem using the differential equations method, and we confirmed their intricate analytic properties. By employing modern methods for integral reduction, we provide the final results in a compact form, which is appropriate for efficient numerical evaluation. Beyond QCD, we have computed the two-loop mixed QCD-electroweak amplitudes for Z+jet production in proton scattering in light-quark-initiated channels, without closed fermion loops. This process provides important insight into the high-precision studies of the Standard Model, as well as into Dark Matter searches at the LHC. We have employed a numerical approach based on high-precision evaluation of Feynman integrals with the modern Auxiliary Mass Flow method. The obtained numerical results in all relevant partonic channels are evaluated on a two-dimensional grid appropriate for further phenomenological applications.

hep-ph↗
arXiv2022

Three-loop helicity amplitudes for photon+jet production

We present three-loop helicity amplitudes for the production of a single photon in association with one jet in Quantum Chromodynamics, a final state which provides a standard candle of the Standard Model at the Large Hadron Collider. We employ a recently-proposed variation of the so-called tensor projection method in the 't Hooft-Veltman scheme (tHV) which avoids the computation of contributions due to unphysical (-2$ε$)-dimensional polarisations of the external states. We obtain compact analytic results expressed in terms of harmonic polylogarithms.

hep-ph↗
arXiv2022

Signal-background interference effects in Higgs-mediated diphoton production beyond NLO

In this paper we consider signal-background interference effects in Higgs-mediated diphoton production at the LHC. After reviewing earlier works that show how to use these effects to constrain the Higgs boson total decay width, we provide predictions beyond NLO accuracy for the interference and related observables, and study the impact of QCD radiative corrections on the Higgs width determination. In particular, we use the so-called soft-virtual approximation to estimate interference effects at NNLO in QCD. The inclusion of these effects reduce the NNLO prediction for the total Higgs cross-section in the diphoton channel by about 1.7%. We study in detail the impact of QCD corrections on the Higgs-boson line-shape and its implications for the Higgs width extraction. Assuming an experimental resolution of about 150~MeV on interference-induced modifications of the Higgs-boson line-shape, our NNLO analysis shows that one could constrain the Higgs-boson total width to about 10-20 times its Standard Model value.

hep-ph↗
arXiv2022

Three-loop four-particle QCD amplitudes

We present recent advancements in the computation of three-loop four-particle helicity amplitudes in full-color massless QCD. In this contribution, we focus on the $gg \to γγ$ process. We show how to obtain compact analytic formulae for the three-loop scattering amplitude. Our results can be expressed in terms of harmonic polylogarithms, which allows for an efficient numerical evaluation. The results presented here can be used for improving theoretical predictions relevant for Higgs physics at hadron colliders.

hep-ph↗
arXiv2022

Three-loop helicity amplitudes for diphoton production in gluon fusion

We present a calculation of the helicity amplitudes for the process $gg\toγγ$ in three-loop massless QCD. We employ a recently proposed method to calculate scattering amplitudes in the 't Hooft-Veltman scheme that reduces the amount of spurious non-physical information needed at intermediate stages of the computation. Our analytic results for the three-loop helicity amplitudes are remarkably compact, and can be efficiently evaluated numerically. This calculation provides the last missing building block for the computation of NNLO QCD corrections to diphoton production in gluon fusion.

hep-ph↗
arXiv2017

Limitations in the $2D$ description of the electromagnetic waves propagation in thin dielectric and magnetic layers

The propagation of electromagnetic waves trapped within dielectric and magnetic layers is considered. The description within the three-dimensional theory is compared with the simplified analysis in two dimensions. Two distinct media configurations with different topology are dealt with: a plane slab and a hollow cylinder. Choosing the appropriate values for the geometrical parameters (layer thickness, radius of the cylinder) and for the electromagnetic properties of the media one can trap exactly one mode corresponding to that obtained within the two-dimensional electromagnetism. However, the symmetry between electric and magnetic fields suggests, that the two versions of the simplified electromagnetism ought to be taken into account. Its usual form is incomplete to describe all modes. It is also found that there is a domain of optimal values of parameters for which the $2D$ model works relatively correctly. In the case of a cylindrical surface we observe, however, several differences which are attributed to the curvature of the layer, and which exclude the propagation of evanescent modes. The two-dimensional electrodynamics, whichever form used, turns out still too poor to describe the so called `hybrid modes' excited in a real layer. The obtained results can be important for proper description of the propagating waves within thin layers for which $3D$ approach is not available due to mathematical complexity, and reducing the layer to a lower-dimensional structure seems the only possible option.

physics.class-ph↗