Roman N. Lee

A bstract: We calculate the next-to-next-to-leading order (NNLO) QED virtual and soft corrections to the C -odd part of the differential cross section of the e ⁺ e ⁻ → μ ⁺ μ ⁻ process. This part contributes to the angular and forward-backward asymmetry. Together with our earlier paper [1], this work completes the analytical calculation of e ⁺ e ⁻ → μ ⁺ μ ⁻ differential cross section at NNLO.

We present the first computation of next-to-next-to-leading order (NNLO) pure QED and mixed QCD ⊗ 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 ⊗ 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.

We study a five-leg scattering amplitude on the special Coulomb branch of planar N = 4 super Yang-Mills theory. We reach this point of the moduli space of scalar vacuum expectation values by considering six-dimensional N = ( 1 , 1 ) super Yang-Mills theory and reducing it down to four space-time dimensions with extradimensional momenta being nonvanishing. This branch is characterized by massive external W-bosons and massless internal gluons propagating in loops. We analyze the five W-boson amplitude in the kinematics when their masses are much smaller than all Mandelstam-like invariants. This is what we dub the near mass-shell limit. We perform calculations to two-loop order in ’t Hooft coupling, making use of recent advances in analytic calculations of required Feynman integrals. Our findings confirm exponentiation of infrared logarithms and enable us to conjecture a concise all-order expression for the amplitude in question. We further analyze its duality to the square root of a five-point correlation function of infinitely heavy half-BPS (Bogomol’nyi–Prasad–Sommerfield) operators, known as the decagon. By considering the near-null limit for inter-operators distances, we verify that the two objects coincide. This observation corroborates the novel Coulomb amplitudes/heavy correlator duality previously observed for four W-boson amplitudes and Sudakov form factors.

A bstract: 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 [1] which has essentially more complicated form.

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.

A bstract: 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 , 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.

We calculate the NNLO QED corrections to the C-even part of differential cross section of e ⁺ e ⁻ → μ ⁺ μ ⁻ process. We neglect power corrections in the electron mass and obtain the result in terms of Goncharov’s polylogarithms.

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 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.

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.

We calculate a subset of two-loop master integrals relevant for the differential cross section of e ⁺ e ⁻ → μ ⁺ μ ⁻ process. We consider only those families for which the account of the electron mass m is necessary. Our results have the form of the Frobenius series in m with coefficients expressed via Goncharov’s polylogarithms.