arXiv subjects

Narayan Rana

Publications and source records attributed to Narayan Rana.

At least 19 recordsLinked to original sources

arXiv2026

Renormalization of axial anomaly in SU(N)$\times$U(1)

Defining $\gamma_5$ within dimensional regularization remains a fundamental challenge. Larin's prescription addresses this by introducing additional renormalization constants to restore standard and chiral Ward identities. While these constants are known up to four loops in pure quantum chromodynamics, current precision Standard Model phenomenology requires extending these corrections to mixed gauge sectors. In this article, we propose a novel technique utilizing form factors and the universality of infrared divergences to compute these constants. Applying this framework, we present the new three-loop results for the renormalization constants, as well as the pure-singlet contributions to the quark axial-vector form factor, for a mixed $SU(N) \times U(1)$ gauge group.

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arXiv2026

Three loop QCD corrections to electroweak radiative parameters

We reevaluate the vacuum polarization functions for electroweak gauge bosons at three loops in QCD, employing state-of-the-art perturbative techniques. We apply these results to determine the ${\mathcal{O}}(\alpha \alpha_s^2)$ corrections to the electroweak radiative parameters $\Delta\rho$, $\Delta r$ and $\Delta \kappa$. We improve the accuracy of the calculation at this perturbative order, compared to the existing literature, and present some phenomenological implications of these results. We find a shift in the prediction of the $W$ boson mass, significant in view of the FCC precision targets. We improve the prediction of the $\overline{\mathrm{MS}}$ electric charge at $q^2=m_Z^2$ with the inclusion of these ${\mathcal{O}}(\alpha \alpha_s^2)$ corrections.

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arXiv2025

${\mathcal{O}(\alpha_s^2 \alpha)}$ corrections to quark form factor

We present the analytic results for the non-singlet contributions to the three-loop mixed strong-electroweak ${\mathcal{O}}(\alpha_s^2\alpha)$ virtual corrections to the quark form factors. The primary challenge of this computation arises from the presence of massive vector bosons within the loops. This significantly increases the complexity of the integration-by-parts reduction of the scalar integrals and complicates their evaluation via the method of differential equations. To obtain the physical results, we perform the appropriate ultraviolet renormalization and subtract the universal infrared divergences. The resulting finite remainders are expressed in terms of Harmonic Polylogarithms and Generalized Polylogarithms.

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arXiv2025

Soft and virtual corrections to semi-inclusive DIS up to four loops in QCD

We apply the threshold resummation formalism for semi-inclusive deep-inelastic scattering (SIDIS) to derive the soft and virtual corrections for the SIDIS cross section up to four loops in QCD. Using the recently computed next-to-next-to-leading order QCD corrections for the SIDIS cross section together with known results for the form factor and splitting functions in QCD up to four loops, we derive the complete soft and collinear contributions to the SIDIS coefficient functions at four-loop order. We also include systematically the next-to-leading power corrections, which are suppressed near threshold. The numerical analysis of the new four-loop corrections shows a small effect on the cross section underpinning the very good perturbative stability of the SIDIS process at that order in perturbation theory, including the reduced dependence on the renormalization and factorization scales $\mu_R$ and $\mu_F$.

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arXiv2025

Three loop master integrals for ${\mathcal{O}} (\alpha \alpha_s^2)$ corrections to quark form factor

We consider the three-loop mixed strong-electroweak (${\mathcal{O}}(\alpha \alpha_s^2)$) corrections to the quark form factor. We compute the master integrals which are appearing in the Feynman diagrams containing a single massive boson in the loop. We use the state-of-the-art method of differential equations to compute all 303 of them, expressing the results in terms of generalized polylogarithms. We encounter multiple square roots that cannot be simultaneously rationalized using a single transformation. Applying concurrent transformations allows us to express the results through generalized polylogarithms with a simple alphabet, but with multiple interdependent arguments.

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arXiv2024

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 $\mu_R$ and $\mu_F$ to obtain stable predictions.

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arXiv2024

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

Mixed QCD-EW corrections to the neutral-current Drell-Yan process

We report on the complete computation of the mixed QCD-electroweak corrections to the neutral-current Drell-Yan process. Our calculation holds in the entire range of dilepton invariant masses. We present phenomenological results for several kinematical distributions in the case of bare muons both in the resonant region and for high invariant masses. We also consider the forward-backward asymmetry, which is a key observable to measure the weak mixing angle. We finally extend our calculation to dressed leptons and compare our results in the massless limit to those available in the literature.

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arXiv2024

Three loop QCD corrections to the heavy-light form factors: fermionic contributions

We present analytic results for three-loop fermionic corrections to the heavy-light form factors in perturbative quantum chromodynamics. Specifically, we present all light quark contributions and contributions from two heavy quark loops. We use the method of differential equations to compute all relevant three-loop master integrals. The results for all these contributions are expressed in terms of harmonic polylogarithms and generalized harmonic polylogarithms.

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arXiv2024

Two-loop mixed QCD-EW corrections to charged current Drell-Yan

We present the two-loop mixed strong-electroweak virtual corrections to the charged current Drell-Yan process. The final-state collinear singularities are regularised by the lepton mass. The evaluation of all the relevant Feynman integrals, including those with up to two different internal massive lines, has been worked out relying on semi-analytical techniques, using complex-valued masses. We can provide, at any arbitrary phase-space point, the solution as a power series in the $W$-boson mass, around a reference value. Starting from these expansions, we can prepare a numerical grid for any value of the $W$-boson mass within their radius of convergence in a negligible amount of time.

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arXiv2024

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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arXiv2024

NNLO QCD corrections to semi-inclusive DIS

We present the first results for the next-to-next-to leading order (NNLO) corrections to the semi-inclusive deep-inelastic scattering process in perturbative quantum chromodynamics. We consider the quark initiated flavor non-singlet process and obtain the complete contributions analytically at leading color. All relevant virtual and real emission Feynman diagrams have been computed using integration-by-parts reduction to master integrals and two approaches for their subsequent evaluation (parametric phase-space integration and method of differential equations). The numerical analysis demonstrates the significance of the NNLO corrections and their great impact on the reduction of the residual scale dependence.

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arXiv2023

Three loop QCD corrections to the heavy-light form factors in the color-planar limit

We present the analytic expressions for the color-planar contributions to the heavy-light form factors at three loops in perturbative QCD. These form factors play an important role in the precision predictions of various observables in top quark and flavour physics. We compute the master integrals using the method of differential equations. We perform the ultraviolet renormalization for all the appearing fields and parameters. The analytic results for the renormalized form factors are expressed in terms of generalized harmonic polylogarithms. We also study the Sudakov behaviour of these form factors in the asymptotic limit, which enables us to obtain the complete logarithmic three-loop and partial four-loop contributions.

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arXiv2023

Analytic results on the massive three-loop form factors: quarkonic contributions

The quarkonic contributions to the three-loop heavy-quark form factors for vector, axial-vector, scalar and pseudoscalar currents are described by closed form difference equations for the expansion coefficients in the limit of small virtualities $q^2/m^2$. A part of the contributions can be solved analytically and expressed in terms of harmonic and cyclotomic harmonic polylogarithms and square-root valued iterated integrals. Other contributions obey equations which are not first-order factorizable. For them still infinite series expansions around the singularities of the form factors can be obtained by matching the expansions at intermediate points and using differential equations which are obeyed directly by the form factors and are derived by guessing algorithms. One may determine all expansion coefficients for $q^2 /m^2 \to \infty$ analytically in terms of multiple zeta values. By expanding around the threshold and pseudo-threshold, the corresponding constants are multiple zeta values supplemented by a finite amount of new constants, which can be computed at high precision. For a part of these coefficients, the infinite series in front of these constants may be even resummed into harmonic polylogarithms. In this way, one obtains a deeper analytic description of the massive form factors, beyond their pure numerical evaluation. The calculations of these analytic results are based on sophisticated computer algebra techniques. We also compare our results with numerical results in the literature.

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arXiv2022

Evaluation of Feynman integrals with arbitrary complex masses via series expansions

We present an algorithm to evaluate multiloop Feynman integrals with an arbitrary number of internal massive lines, with the masses being in general complex-valued, and its implementation in the \textsc{Mathematica} package \textsc{SeaSyde}. The implementation solves by series expansions the system of differential equations satisfied by the Master Integrals. At variance with respect to other existing codes, the analytical continuation of the solution is performed in the complex plane associated to each kinematical invariant. We present the results of the evaluation of the Master Integrals relevant for the NNLO QCD-EW corrections to the neutral-current Drell-Yan processes.

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arXiv2022

Two-loop mixed QCD-EW corrections to neutral current Drell-Yan

We present the two-loop mixed strong-electroweak virtual corrections to the neutral current Drell-Yan process and we provide, in ancillary files, the explicit formulae of the infrared-subtracted finite remainder. The final state collinear singularities are regularised by the lepton mass. The evaluation of all the relevant Feynman integrals, including those with up to two internal massive lines, has been worked out relying on analytical and semi-analytical techniques, in the case of complex-valued masses.

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arXiv2021

On-shell Z boson production through ${\cal O}(αα_s)$

The analytical expressions of the mixed QCD-EW corrections to on-shell Z boson inclusive production cross section at hadron colliders are presented, together with computational details. The results are given in terms of polylogarithmic functions and elliptic integrals. The impact on the prediction of the Z boson production total cross section is discussed, comparing different proton parton density sets.

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arXiv2021

Mixed strong$-$electroweak corrections to the Drell$-$Yan process

We report on the first complete computation of the mixed QCD$-$electroweak (EW) corrections to the neutral-current Drell$-$Yan process. Superseding previously applied approximations, our calculation provides the first result at this order that is valid in the entire range of dilepton invariant masses. The two-loop virtual contribution is computed by using semi-analytical techniques, overcoming the technical problems in the evaluation of the relevant master integrals. The cancellation of soft and collinear singularities is achieved by a formulation of the $q_T$ subtraction formalism valid in presence of charged massive particles in the final state. We present numerical results for the fiducial cross section and selected kinematical distributions. At large values of the lepton $p_T$ the mixed QCD$-$EW corrections are negative and increase in size, to about $-15\%$ with respect to the next-to-leading-order QCD result at $p_T=500\,$GeV. Up to dilepton invariant masses of 1 TeV the computed corrections amount to about $-1.5\%$ with respect to the next-to-leading-order QCD result.

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