arXiv subjects

Syed Mehedi Hasan

Publications and source records attributed to Syed Mehedi Hasan.

9 recordsLinked to original sources

arXiv2026

Radiative Corrections to Elastic Lepton-Proton Scattering with Focus on Two-Photon-Exchange Diagrams

Lepton (electron and muon) scattering experiments are excellent tools to gain insight into the nucleon structure. Elastic electron-proton scattering probes the spatial distribution of charge and magnetization inside the proton, and comparing electron-proton and muon-proton scattering data tests lepton universality. The availability of a plethora of scattering data with increased precision and observed discrepancies such as the proton form factor puzzle and the proton radius puzzle motivated a renewed effort to improve the theoretical framework. Realizing that the one-photon-exchange approximation (OPE), i.e. the Born approximation, is not sufficient, radiative corrections in QED, especially the two-photon-exchange (TPE) diagrams, are under investigation. The TPE diagrams are of special interest among the radiative corrections, since they depend on the proton structure. In this work, we present a complete calculation of QED radiative corrections to elastic electron-proton and muon-proton scattering at next-to-leading order, taking into account loop-momentum-dependent form factors. In the discussion of their numerical impact on lepton-proton scattering cross sections, we pay special attention to the TPE diagrams and compare them with existing theoretical predictions and lepton-proton scattering data.

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arXiv2026

Phase-space integrals through Mellin-Barnes representation

We compute angular phase-space integrals with three and four denominators analytically, working within dimensional regularisation via the Mellin-Barnes (MB) representation. The approach converts multifold MB integrals into real parametric integrals and expresses all results in terms of Goncharov polylogarithms (GPLs). For three denominators, all-massless results are obtained to $\mathcal{O}(ε^2)$ and the single-massive case to $\mathcal{O}(ε)$; for four denominators, both the massless and single-massive cases are solved to $\mathcal{O}(ε^0)$. Integrals with multiple massive momenta follow from a partial fraction decomposition reducing them to the single-massive case. Recursion relations relating integrals with higher denominator powers to master integrals are derived. These are essential ingredients to solving full phase-space integrals.

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arXiv2025

Angular phase-space integrals with four denominators through Mellin--Barnes

We compute four-denominator angular phase-space integrals using the Mellin--Barnes (MB) technique in dimensional regularisation. Independent of the scattering process, an angular integral can be categorised based on the nature of the momenta appearing in the denominators. We address all scenarios involving fully massless and massive momenta. We present a partial fraction decomposition that relates angular integrals with multiple massive momenta to those with a single massive momentum. By solving six- and seven-fold MB integrals, we express the final results up to the finite order in the dimensional regulator in terms of Goncharov polylogarithms.

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arXiv2025

NNLO phase-space integrals for semi-inclusive deep-inelastic scattering

We evaluate the phase-space integrals that arise in double real emission diagrams for semi-inclusive deep-inelastic scattering at next-to-next-to-leading order (NNLO) in QCD. Utilizing the reverse unitarity technique, we convert these integrals into loop integrals, allowing us to employ integration-by-parts identities and reduce them to a set of master integrals. The master integrals are then solved using the method of differential equations and expressed in terms of Goncharov polylogarithms. By examining the series expansion in the dimensional regulator, we discover additional relations among some of the master integrals. As an alternative approach, we solve the master integrals by decomposing them into angular and radial components. The angular parts are evaluated using Mellin-Barnes representation, while special attention is given to the singular structures of the radial integrals to handle them accurately. Here the results are provided in terms of one-fold integrals over classical polylogarithms. This approach provides a clearer understanding of the origin of soft and collinear singularities.

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arXiv2024

Phase-space integrals through Mellin-Barnes representation

This letter introduces a novel analytical approach to calculating phase-space integrals, crucial for precision in particle physics. We develop a method to compute angular components using multifold Mellin-Barnes integrals, yielding results in terms of Goncharov polylogarithms for integrals involving three denominators. Our results include expressions for massless momenta up to $\cal{O}(ε^2)$ and for one massive momentum up to $\cal{O}(ε)$. Additionally, we derive recursion relations that reduce integrals with higher powers of denominators to simpler ones. We detail how to combine the angular part with the radial one which requires a careful handling of singularities.

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arXiv2024

Two-loop Vertices with Vacuum Polarization Insertion

We present the analytic evaluation of the second-order corrections to the massive form factors, due to two-loop vertex diagrams with a vacuum polarization insertion, with exact dependence on the external and internal fermion masses, and on the squared momentum transfer. We consider vector, axial-vector, scalar and pseudoscalar interactions between the external fermion and the external field. After renormalization, the finite expressions of the form factors are expressed in terms of polylogarithms up to weight three.

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arXiv2021

Towards NNLO corrections to muon-electron scattering

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arXiv2020

Master Integrals for the mixed QCD-QED corrections to the Drell-Yan production of a massive lepton pair

We showcase the calculation of the master integrals needed for the two loop mixed QCD-QED virtual corrections to the neutral current Drell-Yan process $(q\bar{q}\rightarrow l^+ l^-)$. After establishing a basis of 51 master integrals, we cast the latter into canonical form by using the Magnus algorithm. The dependence on the lepton mass is then expanded such that potentially large logarithmic contributions are kept. After determining all boundary constants, we give the coefficients of the Taylor series around four space-time dimensions in terms of generalized polylogarithms up to weight four.

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arXiv2020

Towards muon-electron scattering at NNLO

The recently proposed MUonE experiment at CERN aims at providing a novel determination of the leading order hadronic contribution to the muon anomalous magnetic moment through the study of elastic muon-electron scattering at relatively small momentum transfer. The anticipated accuracy of the order of 10ppm demands for high-precision predictions, including all the relevant radiative corrections. The theoretical formulation for the fixed-order NNLO photonic radiative corrections is described and the impact of the numerical results obtained with the corresponding Monte Carlo code is discussed for typical event selections of the MUonE experiment. In particular, the gauge-invariant subsets of corrections due to electron radiation as well as to muon radiation are treated exactly. The two-loop contribution due to diagrams where at least two virtual photons connect the electron and muon lines is approximated taking inspiration from the classical Yennie-Frautschi-Suura approach. The calculation and its Monte Carlo implementation pave the way towards the realization of a simulation code incorporating the full set of NNLO corrections matched to multiple photon radiation, that will be ultimately needed for data analysis.

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