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Roman N. Lee

Publications and source records attributed to Roman N. Lee.

At least 19 recordsLinked to original sources
arXiv2026

Five legs @ three loops: slightly off-shell dual conformal integrals

We calculate the three-loop master integrals contributing to the three-loop five-point amplitude on the special Coulomb branch of $\mathcal{N}=4$ SYM theory. For the genuine pentagon integrals, we follow the approach of Ref. [JHEP 12 (2025) 107], which includes a regularization preserving dual conformal invariance (DCI). As a new ingredient, we introduce a simple method, allowing to factor out the dependence on the DCI cross ratios from the contribution of each region. The remaining integrals are then essentially simplified by taking successive limits of vanishing external invariants. For 3 out of 82 regions contributing to the most complicated integral $\mathcal{I}_5^{(3)}$ we were not able to perform the integration even after these simplifications. For these three regions, we perform the integration-by-parts (IBP) reduction in parametric representation and evaluate the resulting locally finite integrals using HyperInt.

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arXiv2026

Five legs @ three loops: N=4 sYM amplitude near mass-shell

We present a three-loop analysis of the scattering amplitude of five nearly massless W-bosons in planar maximally supersymmetric Yang-Mills theory. The basis of the master integrals is established, making use of the unitarity-cut sewing technique in six-dimensional N=(1,1) super-Yang-Mills theory. Its dimensional reduction down to four allows us to generate masses for internal and external states. We descend on the special Coulomb branch of maximally supersymmetric Yang-Mills theory by setting all propagator masses to zero. Employing explicit expressions for all integrals that we calculated in a companion paper, we find a concise representation for this infrared-sensitive observable. We confirm its exponentiation, both for infrared and finite terms. The infrared double logarithm manifests the anticipated universality through the octagon anomalous dimension as its governing coefficient. Unlike our previous two-loop result, this consideration reveals that each of the three independent kinematic structures furnishing the amplitude possesses its own function of 't Hooft coupling.

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arXiv2026

Radiative correction to the charge asymmetry in $e^{+}e^{-}\toμ^{+}μ^{-}$ process

We calculate the next-to-next-to-leading order (NNLO) QED corrections to the $C$-odd part of the differential cross section of the $e^+e^-\toμ^+μ^-$ process. This part contributes to the angular and forward-backward asymmetry. Together with our earlier paper [10.1007/JHEP08(2025)118], this work completes the analytical calculation of $e^+e^-\toμ^+μ^-$ differential cross section at NNLO.

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arXiv2026

Method of regions for dual conformal integrals

In this contribution, we present a recently introduced approach [BorkLeeOnishchenko2025] to the calculation of slightly off-shell dual conformal integrals based on the method of regions with regularization preserving dual conformal invariance (DCI). Unlike conventional dimensional regularization, which breaks DCI, our approach uses a combination of dimensional and analytic regularizations specifically designed to retain DCI throughout the calculation. Our approach drastically simplifies the computation of slightly off-shell dual conformal integrals. For the two-loop five-point DCI integrals we find that with DCI-preserving regularization, the contributions of all regions can be expressed in terms of $Γ$-functions, resulting in a remarkably compact final expression in terms of logarithms of cross-ratios only. This is in sharp contrast to conventional approach which yields complex polylogarithmic expressions [Belitsky&Smirnov2025]. We argue that a similar approach might be useful also for non-DCI integrals.

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arXiv2025

NNLO QCD corrections to unpolarized and polarized SIDIS

The semi-inclusive deep-inelastic scattering (SIDIS) process requires the presence of an identified hadron H$'$ in the final state, which arises from the scattering of a lepton with an initial hadron P. By employing factorization in quantum chromodynamics (QCD), SIDIS provides essential knowledge on the hadron structure, enabling the exploration of parton distribution functions (PDFs) and fragmentation functions (FFs). The coefficient functions for SIDIS can be calculated in perturbative QCD and are currently known to the next-to-next-to-leading order (NNLO) for the cases, where the incoming lepton and the hadron P are either both polarized or unpolarized. We present a detailed description of these NNLO computations, including a thorough discussion of all the partonic channels, the calculation of the amplitudes and master integrals for the phase-space integration as well as the renormalization of ultraviolet divergences and mass factorization of infrared divergences in dimensional regularization through NNLO. We provide an extensive phenomenological analysis of the effects of NNLO corrections on SIDIS cross sections for different PDFs and FFs and various kinematics, including those of the future Electron-Ion Collider (EIC). We find that these corrections are not only significant but also crucial for reducing the dependence on the renormalization and factorization scales $μ_R$ and $μ_F$ to obtain stable predictions.

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arXiv2025

Next-to-Next-to-Leading Order QCD Corrections to Polarized Semi-Inclusive Deep-Inelastic Scattering

Polarized semi-inclusive deep-inelastic scattering (SIDIS) is a key process in the quest for a resolution of the proton spin puzzle. We present the complete results for the polarized SIDIS process at next-to-next-to-leading order (NNLO) in perturbative quantum chromodynamics. Our analytical results include all partonic channels for the scattering of polarized leptons off hadrons and a spin-averaged hadron identified in the final state. A numerical analysis of the NNLO corrections illustrates their significance and the reduced residual scale dependence in the kinematic range probed by the future Electron-Ion-Collider EIC.

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arXiv2025

NNLO QCD$\otimes$QED corrections to unpolarized and polarized SIDIS

We present the first computation of next-to-next-to-leading order (NNLO) pure QED and mixed QCD$\otimes$QED corrections to unpolarized and polarized semi-inclusive deep-inelastic scattering (SIDIS). Building on our previous NNLO QCD results, these corrections are crucial for improving the theoretical precision. The coefficient functions are derived within the QCD factorization framework using dimensional regularization, with consistent renormalization and mass factorization. A detailed phenomenological analysis shows that the NNLO QED and QCD$\otimes$QED terms enhance perturbative stability and reduce scale uncertainties. These results are essential for high-precision SIDIS predictions at future facilities such as the Electron-Ion Collider.

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arXiv2025

Method of regions for dual conformal integrals

We apply the method of regions to the evaluation of dual conformal integrals with small off-shellness. In contrast to conventional approach, where the separation of regions is performed via dimensional regularization breaking the dual conformal invariance (DCI), we use a sufficiently generic combination of dimensional and analytic regularizations which preserves the DCI. Within this regularization (dubbed as DCI regularization), the contribution of each region becomes DCI. We show that our method dramatically simplifies the calculations. As a demonstration, we calculate the slightly off-shell DCI pentabox integral up to power corrections. The contributions of all 32 regions appear to be expressible in terms of products/ratios of $Γ$-functions multiplied by some powers of DCI cross-ratios. Therefore, after removing the regularization, we obtain the final expression in terms of cross-ratios logarithms only. We have checked that our result for pentabox integral numerically agrees with the result of the recent Belitsky\&Smirnov paper [arXiv:2508.14298] which has essentially more complicated form.

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arXiv2025

Monodromy of multiloop integrals in $d$ dimensions

We consider the monodromy group of the differential systems for multiloop integrals. We describe a simple heuristic method to obtain the monodromy matrices as functions of space-time dimension $d$. We observe that in a special basis the elements of these matrices are Laurent polynomials in $z=\exp(iπd)$ with integer coefficients, i.e., the monodromy group is a subgroup of $GL(n,\mathbb{Z}[z,1/z])$. We derive bilinear relations for monodromies in $d$ and $-d$ dimensions which follow from the twisted Riemann bilinear relations and check that the found monodromy matrices satisfy them.

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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

Master integrals for $e^{+}e^{-}\rightarrow2γ$ process at large energies and angles

We calculate two-loop massive master integrals for $e^{+}e^{-}\rightarrow2γ$ in terms of generalized power series with respect to electron mass. The coefficients of this series are expressed via Goncharov's polylogarithms. Our approach exploits a number of modern multiloop methods: IBP reduction, differential equations for master integrals, Frobenius method, reduction to $ε$-form, and DRA method.

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arXiv2024

Polylogarithmic functions with prescribed branching locus and linear relations between them

We consider the problem of finding the set of classical polylogarithmic functions $\text{Li}_n$ with branching locus determined by the solution of $p_1\cdot p_2\cdot \ldots \cdot p_n=0$, where $p_1,\ldots, p_n$ are irreducible polynomials of several variables. We present an algorithm of constructing a complete set of possible arguments of $\text{Li}_n$ functions. The corresponding Mathematica code is included as ancillary file. Using this algorithm and the symbol map, we provide some examples of polylogarithmic identities.

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arXiv2023

Total Born cross section of $e^+e^-$-pair production by an electron in the Coulomb field of a nucleus

We calculate the total Born cross section of the $e^+e^-$-pair production by an electron in the field of a nucleus (trident process) using the modern multiloop methods. For general energies we obtain the cross section in terms of converging power series. The threshold asymptotics and the high-energy asymptotics are obtained analytically. In particular, we obtain additional contribution to the Racah formula due to the identity of the final electrons. Besides, our result for the leading term of the high-energy asymptotics reveals a typo in an old Racah paper [Racah1937].

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arXiv2023

Master Integrals for Four-Loop Massless Form Factors

We present analytical results for all master integrals for massless three-point functions, with one off-shell leg, at four loops. Our solutions were obtained using differential equations and direct integration techniques. We review the methods and provide additional details.

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arXiv2023

Two-loop corrections to Lamb shift and hyperfine splitting in hydrogen via multi-loop methods

We revisit the contributions of order $α^2(Zα)^5m$ and $α^2(Zα)E_F$, respectively, to the Lamb shift and to the hyperfine splitting from mixed self-energy-vacuum-polarization diagrams, involving fermionic loop. We use modern multi-loop calculation techniques based on IBP reduction and differential equations. We construct the $ε$-regular basis [LeeOnishchenko2019] and explicitly demonstrate that it is compatible with the renormalization. We obtain analytic results in terms of one-fold integral involving elliptic function and dilogarithm. As a by-product, we obtain the analogous contribution for the limiting cases of heavy and light fermionic loop.

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