arXiv subjects

Yingxuan Xu

Publications and source records attributed to Yingxuan Xu.

11 recordsLinked to original sources

arXiv2026

On the spanning cuts consistency problem in the IBP reductions of Feynman integrals

The spanning cuts method is a powerful approach to reduce the cost of IBP reduction while computing Feynman integrals. However, its usage is limited due to the so-called consistency problem. It was unclear why the IBP reduction coefficients can be inconsistent with each other between different cuts. In this paper, we report a mechanism behind this inconsistency. We found that the IBP relations can be violated under the cuts, if we blindly erase the hidden terms that are proportional to the ``vanishing'' Feynman prescription parameters in the relations. In some cases, the cut introduces pinch singularities, which cancel the vanishing Feynman prescription parameters, making the hidden terms finite. In various cases, the error comes from omitting such finite hidden terms. We also claimed that the pinch singularity under the cuts are related to some hidden relations between the propagators. In this paper, we provide an algorithm and its implementation to find the linear hidden relations.

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arXiv2026

Two-loop Six-point Planar Massless Feynman Integrals to Higher $ε$ Orders

In this work, we calculate two-loop six-point planar massless Feynman integrals at higher orders in the dimensional regulator $ε$, corresponding to higher transcendental weights. In previous works, these integrals were calculated up to weight four for the purpose of two-loop gauge theory amplitudes. Using modern rational reconstruction methods, we identify the complete alphabet with $269$ letters relevant to all weights, derive the analytic canonical differential equation and obtain the symbols up to weight six. As a proof of concept, using a new method with Chebyshev pseudospectral transport, we show that the corresponding pure basis can be efficiently evaluated up to weight six, i.e., to $ \mathcal{O}(ε^2)$ in a physical scattering region. The results of this work can be applied to future three-loop amplitudes and provide new data for the formal study of symbols and cluster algebras.

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arXiv2026

Perturbative bootstrap of the Wilson-line defect CFT: Bulk-defect-defect correlators

We study the correlators of bulk and defect half-BPS operators in $\mathcal{N}=4$ Super Yang-Mills theory with a Maldacena-Wilson line defect, focusing on the case involving one bulk and two defect local operators. We analyze the non-perturbative constraints on these correlators, which include a topological sector, pinching and splitting limits, and we compute a variety of bulk-defect-defect correlators up to next-to-leading order at weak coupling, surprisingly observing that transcendental terms cancel. Additionally, we provide results in the strong-coupling regime for the first two leading orders using a mixture of Witten diagrams and non-perturbative constraints.

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arXiv2025

Uncovering Singularities in Feynman Integrals via Machine Learning

We introduce a machine-learning framework based on symbolic regression to extract the full symbol alphabet of multi-loop Feynman integrals. By targeting the analytic structure rather than reduction, the method is broadly applicable and interpretable across different families of integrals. It successfully reconstructs complete symbol alphabets in nontrivial examples, demonstrating both robustness and generality. Beyond accelerating computations case by case, it uncovers the analytic structure universally. This framework opens new avenues for multi-loop amplitude analysis and provides a versatile tool for exploring scattering amplitudes.

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arXiv2025

Performing integration-by-parts reductions using NeatIBP 1.1 + Kira

We introduce a new version v1.1 of NeatIBP. In this new version, a Kira interface is included. It allows the user to reduce the integration-by-parts (IBP) identity systems generated by NeatIBP using Kira in a highly automated way. This new version also implements the so-called spanning cuts method. It helps to reduce the total computational complexity of IBP reduction for certain hard problems. Another important feature of this new version is an algorithm to simplify the solution module of the syzygy equations hinted by the idea of maximal cuts.

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arXiv2025

Complete function space for planar two-loop six-particle scattering amplitudes

We derive the full system of canonical differential equations for all planar two-loop massless six-particle master integrals, and determine analytically the boundary conditions. This fully specifies the solutions, which may be written as Chen iterated integrals. We argue that this is sufficient information for evaluating any scattering amplitude in four dimensions up to the finite part. We support this claim by reducing, for the most complicated integral topologies, integrals with typical Yang-Mills numerators. We use the analytic solutions to the differential equations, together with dihedral symmetry, to provide the full solution space relevant for two-loop six-particle computations. This includes the relevant function alphabet, as well as the independent set of iterated integrals up to weight four. We also provide the answer for all master integrals in terms of iterated integrals that can be readily evaluated numerically. As a proof of concept, we provide a numerical implementation that evaluates the integrals in part of the Euclidean region, and validate this against numerical evaluation of the Feynman integrals. Our result removes the bottleneck of Feynman integral evaluation, paving the way to future analytic evaluations of six-particle scattering amplitudes.

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arXiv2025

An Analytic Computation of Three-Loop Five-Point Feynman Integrals

We evaluate the three-loop five-point pentagon-box-box massless integral family in the dimensional regularization scheme, via canonical differential equation. We use tools from computational algebraic geometry to enable the necessary integral reductions. The boundary values of the differential equation are determined analytically in the Euclidean region. To express the final result, we introduce a new representation of weight six functions in terms of one-fold integrals over the product of weight-three functions with weight-two kernels that are derived from the differential equation. Our work paves the way to the analytic computation of three-loop multi-leg Feynman integrals.

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arXiv2024

A computation of two-loop six-point Feynman integrals in dimensional regularization

We compute three families of two-loop six-point massless Feynman integrals in dimensional regularization, namely the double-box, the pentagon-triangle, and the hegaxon-bubble family. This constitutes the first analytic computation of two-loop master integrals with eight scales. We use the method of canonical differential equations. We describe the corresponding integral basis with uniform transcendentality, the relevant function alphabet, and analytic boundary values at a particular point in the Euclidean region up to the fourth order in the regularization parameter $ε$. The results are expressed as one-fold integrals over classical polylogarithms suitable for fast and high-precision evaluation.

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arXiv2023

Conservative scattering of spinning black holes at fourth post-Minkowskian order

Using the ${\mathcal N}=1$ supersymmetric, spinning worldline quantum field theory formalism we compute the conservative spin-orbit part of the momentum impulse $Δp_i^μ$, spin kick $ΔS_i^μ$ and scattering angle $θ$ from the scattering of two spinning massive bodies (black holes or neutron stars) up to fourth post-Minkowskian (PM) order. These three-loop results extend the state-of-the-art for generically spinning binaries from 3PM to 4PM. They are obtained by employing recursion relations for the integrand construction and advanced multi-loop Feynman integral technology in the causal (in-in) worldline quantum field theory framework to directly produce classical observables. We focus on the conservative contribution (including tail effects) and outline the computations for the dissipative contributions as well. Our spin-orbit results agree with N$^3$LO post-Newtonian and test-body data in the respective limits. We also re-confirm the conservative 4PM non-spinning results.

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arXiv2022

A first look at the function space for planar two-loop six-particle Feynman integrals

Two-loop corrections to scattering amplitudes are crucial theoretical input for collider physics. Recent years have seen tremendous advances in computing Feynman integrals, scattering amplitudes, and cross sections for five-particle processes. In this paper, we initiate the study of the function space for planar two-loop six-particle processes. We study all genuine six-particle Feynman integrals, and derive the differential equations they satisfy on maximal cuts. Performing a leading singularity analysis in momentum space, and in Baikov representation, we find an integral basis that puts the differential equations into canonical form. The corresponding differential equation in the eight independent kinematic variables is derived with the finite-field reconstruction method and the symbol letters are identified. We identify the dual conformally invariant hexagon alphabet known from maximally supersymmetric Yang-Mills theory as a subset of our alphabet. This paper constitutes an important step in the analytic calculation of planar two-loop six-particle Feynman integrals.

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arXiv2020

IBP reduction coefficients made simple

We present an efficient method to shorten the analytic integration-by-parts (IBP) reduction coefficients of multi-loop Feynman integrals. For our approach, we develop an improved version of Leinartas' multivariate partial fraction algorithm, and provide a modern implementation based on the computer algebra system Singular. Furthermore, We observe that for an integral basis with uniform transcendental (UT) weights, the denominators of IBP reduction coefficients with respect to the UT basis are either symbol letters or polynomials purely in the spacetime dimension $D$. With a UT basis, the partial fraction algorithm is more efficient both with respect to its performance and the size reduction. We show that in complicated examples with existence of a UT basis, the IBP reduction coefficients size can be reduced by a factor of as large as $\sim 100$. We observe that our algorithm also works well for settings without a UT basis.

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