arXiv subjects

Ekta Chaubey

Publications and source records attributed to Ekta Chaubey.

At least 19 recordsLinked to original sources

arXiv2026

How to choose a good rational basis for elliptic Feynman integrals?

Representing multi-loop scattering amplitudes as linear combinations of multivalued transcendental functions with process-dependent rational coefficients has long been understood to be advantageous. In general, these transcendental functions satisfy a system of differential equations with coupled homogeneous blocks. When these coupled blocks can be removed through algebraic basis transformations, the relation between the rational and algebraic bases is universal and minimal. Here, we ask whether an analogous universal and minimal relation exists when decoupling requires transformations involving complete elliptic integrals. We elaborate on the method proposed in ref. arXiv:2504.20897, in which we suggested that a basis constructed using an elliptic generalization of leading singularities may provide an answer to this question. We extend this analysis to the off-diagonal blocks of the rational differential equations satisfied by the bases obtained through this construction. We find that the $ε$ dependence of these blocks can be organized into a universal structure that is preserved under the decoupling transformation used to express the solutions in terms of iterated integrals.

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arXiv2026

Light-by-light scattering: asymptotic expansions, Coulomb resummation and NLO corrections

Light-by-light (LbL) scattering is one of the earliest predictions of quantum electrodynamics (QED). Interest in this process has been renewed following its experimental observation at the LHC and the prospects of future measurements at free-electron laser facilities. In this paper, we refine theoretical predictions for LbL scattering by improving the full fermion-mass-dependent two-loop QCD and QED helicity amplitudes using high- and low-energy asymptotic expansions, and by performing Coulomb resummation in the threshold region. We present state-of-the-art predictions for LbL cross sections in the Standard Model and provide a new event generator, LbLatNLO, for Monte Carlo simulations of LbL scattering.

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arXiv2026

A comprehensive analysis of Drell-Yan production uncertainties and mass effects at moderate and low dilepton masses

We present a thorough investigation of the sources of uncertainties to the Drell-Yan production using state-of-the-art predictions for both neutral and charged current channels, focusing on the low invariant mass region. Differential predictions for the invariant mass spectrum are provided at N$^3$LO supplemented with exact charm and bottom quark mass effects calculated at $\mathcal{O}(α_s^2)$. The impact of PDF choices (including approximate N$^3$LO), scale variations, the variation of the strong coupling constant, and impact heavy quark mass effects on the distributions is studied in detail. We also comment on the correlation of high-energy astrophysical processes with the low-mass DY region.

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arXiv2026

Estimating power corrections for the Drell-Yan Process

We study power corrections in the Drell-Yan (DY) process using state-of-the-art predictions for both neutral and charged current production. For both types of DY processes, we account for power corrections arising from bottom and charm quark effects within a variable flavor number scheme. Our results show that these corrections become significant in the low-$Q$ region. We also ensure proper treatment of overlapping contributions by carefully applying matching procedures to eliminate any double counting.

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arXiv2025

Elliptic leading singularities and canonical integrands

In the well-studied genus zero case, bases of $\mathrm{d}\log$ integrands with integer leading singularities define Feynman integrals that automatically satisfy differential equations in canonical form. Such integrand bases can be constructed without input from the differential equations and without explicit involvement of dimensional regularization parameter $ε$. We propose a generalization of this construction to genus one geometry arising from the appearance of elliptic curves. We argue that a particular choice of algebraic one-forms of the second kind that avoids derivatives is crucial. We observe that the corresponding Feynman integrals satisfy a special form of differential equations that has not been previously reported, and that their solutions order by order in $ε$ yield pure functions. We conjecture that our integrand-level construction universally leads to such differential equations.

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arXiv2025

Two-loop helicity amplitudes for diphoton production with massive quark loop

We compute two-loop helicity amplitudes in QCD for diphoton production through quark- and gluon-initiated channels, accounting for a massive internal quark loop by keeping its full mass dependence. Using physical projectors, we directly decompose the amplitude into its helicity components. By renormalising the heavy quark mass in on-shell, and other quantities in $\overline{\rm MS}$ schemes, we obtain finite remainders. This work paves the way for calculating the cross-section for diphoton production at higher orders in QCD with a massive quark loop, employing different subtraction schemes. The effect of a heavy quark is expected to play a crucial role in high-luminosity LHC.

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arXiv2024

Two-loop massive QCD and QED helicity amplitudes for light-by-light scattering

We present the analytic and compact two-loop helicity amplitudes for QCD and QED corrections to the light-by-light scattering process with massive internal fermions. We express the master integrals either in terms of multiple polylogarithms or in terms of iterated integrals with dlog one-forms. We also elaborate on optimizing the analytic results for each phase-space region. This makes the numerical evaluation of the scattering amplitudes fast, stable and suitable for phenomenological applications.

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arXiv2024

Light-by-Light Scattering at Next-to-Leading Order in QCD and QED

The recent experimental observation of Light-by-Light (LbL) scattering at the Large Hadron Collider has revived interest in this fundamental process, and especially of the accurate prediction of its cross-section, which we present here for the first time at Next-to-Leading Order (NLO) in both QCD and QED. We compare two radically different computational approaches, both exact in the fermion mass dependence, thus offering a strong cross-check of our results. The first approach is a fully analytic method to calculate compact and well-organized two-loop helicity amplitudes. The second one is entirely numerical and leverages the Local Unitarity construction. Our two calculations agree with each other and conclude that including the exact fermion mass contribution typically increases the size of the NLO corrections. Moreover, we find that the exact result converges slowly to the massless limit of the high-energy regime, thus emphasizing the importance of including the full mass dependence at NLO. We also compare our results with the ATLAS measurement of LbL in ultra-peripheral lead-lead collisions, and find that the inclusion of exact NLO corrections reduces, but does not eliminate, the existing tension with theoretical predictions.

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arXiv2024

Two-loop non-planar four-point topology with massive internal loop

We study a set of two-loop non-planar master integrals needed for the NNLO QCD corrections to diphoton and dijet production at hadron colliders. The top-sector topology contains an internal massive fermion loop and is known to contain elliptic curves. Leveraging the method of differential equations, we provide a comprehensive discussion for deriving an $ε$-factorized differential equation related to the most intricate sector within the Feynman integral family. Despite the dependence on multiple scales and the presence of two elliptic sectors, we demonstrate how to leverage the properties of their maximal cuts and the factorization of the Picard-Fuchs operator to deal with the complexity of the analytic computation. In particular, we construct a transformation matrix that brings the differential equations into a format enabling the convenient expression of analytic results in terms of Chen's iterated integrals.

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arXiv2023

Two-loop master integrals for a planar topology contributing to $pp \rightarrow t\bar{t}j$

We consider the case of a two-loop five-point pentagon-box integral configuration with one internal massive propagator that contributes to top-quark pair production in association with a jet at hadron colliders. We construct the system of differential equations for all the master integrals in a canonical form where the analytic form is reconstructed from numerical evaluations over finite fields. We find that the system can be represented as a sum of d-logarithmic forms using an alphabet of 71 letters. Using high precision boundary values obtained via the auxiliary mass flow method, a numerical solution to the master integrals is provided using generalised power series expansions.

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arXiv2022

Three-loop master integrals for the Higgs boson self-energy with internal top-quarks and W-bosons

We consider the full set of master integrals with internal top-and $W$-propagators contributing to the three-loop Higgs self-energy diagrams of order ${\mathcal O}(α^2 α_s)$. We split the master integrals into a system relevant to the Feynman diagrams proportional to the product of Yukawa couplings $y_b y_t$ and the complement. For both systems we define master integrals of uniform weight, such that the associated differential equation is in $\varepsilon$-factorised form. The occurring square roots are rationalised and all master integrals are expressible in multiple polylogarithms.

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arXiv2022

Master integrals for ${\cal O}(αα_s)$ corrections to $H \to ZZ^*$

We present analytic results for all the Feynman integrals relevant for ${\mathcal O}(αα_s)$ virtual corrections to $H \rightarrow ZZ^*$ decay. We use the method of differential equations to solve the master integrals while keeping the full dependence on the masses of all the particles including internal propagators. Due to the presence of four mass scales we encounter multiple square roots. We argue that all the occurring square roots can not be rationalized at the same time as a simultaneous rationalization brings us to integrals over $CY_3$ manifolds. Hence we rationalize only three square roots simultaneously and construct suitable ansätze to obtain dlog-forms containing the square root, after obtaining an epsilon-factorised form for the differential equations. We present the alphabet and the analytic form of all the boundary constants that appear in the solutions of the differential equations. The results for master integrals are expressed in terms of Chen's iterated integrals with dlog one-forms.

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arXiv2022

Analytic representations of two-loop scattering amplitudes with internal masses

We highlight the latest developments in computing higher-order scattering amplitudes with massive internal propagators. The contributing Feynman integrals often lead to special classes of functions, for example, functions associated with elliptic curves. With the presence of more scales in the amplitudes, it becomes imperative to have a better understanding of the contributing Feynman integrals and using current cutting-edge technologies to tackle the growth in analytic and algebraic complexities. In particular, we start with discussing two-loop scattering amplitudes for top-quark pair production and conclude with motivating important steps towards obtaining next-to-next-to leading-order corrections for five-point processes.

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arXiv2022

One-loop QCD helicity amplitudes for $pp\to t\bar{t} j$ to $O(ε^2)$

We compute helicity amplitudes for the one-loop QCD corrections to top-quark pair production analytically in terms of a set of uniformly transcendental master integrals. We provide corrections up to $O(ε^2)$ in the dimensional regulator for the first time which are relevant at NNLO. Four independent pentagon integral topologies appear in the complete description of the colour structure for which we provide numerical solutions using canonical form differential equations and the method of generalised power series expansions. Analytic forms of the boundary values are obtained in all cases except one where we find a one-dimensional integral representation.

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arXiv2022

Functions Beyond Multiple Polylogarithms for Precision Collider Physics

Feynman diagrams constitute one of the essential ingredients for making precision predictions for collider experiments. Yet, while the simplest Feynman diagrams can be evaluated in terms of multiple polylogarithms -- whose properties as special functions are well understood -- more complex diagrams often involve integrals over complicated algebraic manifolds. Such diagrams already contribute at NNLO to the self-energy of the electron, $t \bar{t}$ production, $γγ$ production, and Higgs decay, and appear at two loops in the planar limit of maximally supersymmetric Yang-Mills theory. This makes the study of these more complicated types of integrals of phenomenological as well as conceptual importance. In this white paper contribution to the Snowmass community planning exercise, we provide an overview of the state of research on Feynman diagrams that involve special functions beyond multiple polylogarithms, and highlight a number of research directions that constitute essential avenues for future investigation.

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arXiv2021

Master integrals contributing to two-loop leading colour QCD helicity amplitudes for top-quark pair production in the gluon fusion channel

We present the master integrals relevant for computing the complete set of leading-colour analytic helicity amplitudes for top-quark pair production via gluon fusion at two-loops in QCD. We include corrections due to massive fermion loops which give rise to integrals involving elliptic curves. We also elaborate on the structure of singularities that play an important role in the numerical evaluation of the iterated integrals and their analytic continuation.

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arXiv2021

Two-loop leading colour QCD helicity amplitudes for top quark pair production in the gluon fusion channel

We present a complete set of analytic helicity amplitudes for top quark pair production via gluon fusion at two-loops in QCD. For the first time, we include corrections due to massive fermion loops which give rise to integrals over elliptic curves. We present the results of the missing master integrals needed to compute the amplitude and obtain an analytic form for the finite remainders in terms of iterated integrals using rationalised kinematics and finite field sampling. We also study the numerical evaluation of the iterated integrals.

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arXiv2019

Two-loop master integrals for the mixed QCD-electroweak corrections for $H \rightarrow b\bar{b}$ through a $H t \bar{t}$-coupling

We present the two-loop master integrals relevant to the ${\mathcal O}(αα_s)$-corrections to the decay $H \rightarrow b \bar{b}$ through a $H t \bar{t}$-coupling. We keep the full dependence on the heavy particle masses, but neglect the $b$-quark mass. The occurring square roots can be rationalised and the result is expressed in terms of multiple polylogarithms.

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