arXiv subjects

Sid Smith

Publications and source records attributed to Sid Smith.

13 recordsLinked to original sources

arXiv2026

Gravitational Compton scattering at the fifth post-Minkowskian order

Working in the Worldline Quantum Field Theory framework, we obtain the classical gravitational Compton amplitude through the fifth post-Minkowskian order, $\mathcal{O}(G^5)$. At this order, the point-particle description must be supplemented by the leading static tidal operators. After removing lower-order iterations, we extract the corresponding $N$-matrix element and match it to black-hole perturbation theory. The matching fixes the static tidal Wilson coefficients to zero, providing confirmation of the vanishing static Love numbers of a Schwarzschild black hole.

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arXiv2026

Gravitational Compton scattering at the fourth post-Minkowskian order

We compute the classical gravitational Compton amplitude at the fourth post-Minkowskian order, $\mathcal{O}(G^4)$, within the Worldline Quantum Field Theory framework. We derive the associated $N$-matrix element, which provides the gravitational-wave scattering phase shift at the same order. As a nontrivial check, we show that our result agrees with black-hole perturbation theory.

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arXiv2026

Magic Relations and Critical Varieties of Feynman Integrals

Magic relations are a class of integration-by-parts identities where all integrals in the generating sector drop out. Since their presence causes several otherwise successful methods in the Feynman-integral computational pipeline to break down, they are important to detect and understand. In this paper, we take a first step toward a systematic characterization of such identities. Specifically, we observe and argue that the occurrence of magic relations always coincides with the presence of higher-dimensional critical varieties in the generating sector. This provides a practical computational test to check if a family of Feynman integrals can contain magic relations and to find them, which we implement in the ancillary Mathematica file Magic-Test.m. Additionally, we discuss how to count the number of master integrals in the presence of higher-dimensional critical varieties, classify the behavior of magic relations under symmetries, and we discuss their interplay with cuts.

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arXiv2026

All-order structure of static gravitational interactions and the seventh post-Newtonian potential

We present a closed formula for the computation of static post-Newtonian corrections to the two-body gravitational dynamics at any odd order, assuming the lower-order results are known. The formula is derived within a correlation function framework and exploits the $\mathbb{Z}_2$ symmetry of the static sector, leading to a novel theoretical interpretation of the factorization theorem. As an application, we compute the gravitational interaction of two compact coalescing objects at the seventh post-Newtonian order in the static limit, which receives contributions from seven-loop graphs at order $\mathcal{O}(G_N^8 v^0)$, and find complete agreement with the results obtained using the diagrammatic approach of the factorization theorem.

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arXiv2026

Symbolic syzygy-constrained reduction rules for Feynman integrals and the LoopIn framework

We present a new algorithm for integration-by-parts (IBP) reduction of Feynman integrals with high powers of numerators or propagators, a demanding computational step in evaluating multi-loop scattering amplitudes. The algorithm allows us to avoid a large intermediate system of equations and instead focus on applying direct reduction rules to the integrals. We demonstrate the application of our algorithm with some highly non-trivial examples, namely rank-20 integrals for the double box with an external mass and the massless pentabox. We also achieve much faster IBP reduction for an example of scattering amplitudes for spinning black hole binary systems. Finally, we present LoopIn, a modular framework for automating multi-loop calculations, where the IBP techniques described here can be interfaced.

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arXiv2026

Three-loop helicity amplitudes of four-lepton scattering in QED

We present the analytic expressions of the three-loop virtual corrections to the helicity amplitudes of 2 -> 2 four-fermion scattering processes in massless QED. The contributing Feynman diagrams are grouped into integrand families characterised by independent Symanzik polynomials and decomposed in terms of master integrals using an optimised integration-by-parts strategy. Upon the renormalisation of the ultraviolet divergences and the extraction of the universal infrared pole structure, the finite results are expressed in terms of generalised polylogarithms up to transcendental weight six. Amplitudes for dimuon production in electron-positron annihilations, electron-muon scattering, and Bhabha scattering are explicitly derived.

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arXiv2025

Scattering Amplitudes and Conservative Binary Dynamics at $O(G^5)$ without Self-Force Truncation

We compute the complete potential-graviton contributions to the conservative radial action and scattering angle for two non-spinning bodies in general relativity, accurate through fifth order in Newton's constant and including second-order self-force (2SF) effects. The calculation is carried out in the scattering-amplitude framework, combining the double copy, effective field theory, and multi-loop integration techniques based on integration by parts and differential equations. To address a major computational bottleneck, we develop improved integration-by-parts algorithms that render calculations at this order tractable. The post-Minkowskian amplitude is presented as a series expansion, following the strategy used earlier in maximal supergravity. For the first self-force sector, which involves only polylogarithmic functions, we also provide a closed-form analytic expression. For the second self-force sector, as in earlier supergravity work, we find nontrivial cancellations among contributions related to integrals supported on Calabi-Yau geometry.

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arXiv2025

Six-loop gravitational interactions at the sixth post-Newtonian order

We compute the gravitational interaction of two coalescing compact objects at sixth post-Newtonian order in the static limit, employing the diagrammatic approach within the effective field theory framework of General Relativity. The calculation requires the evaluation of six-loop Feynman diagrams that are mapped onto two-point integrals with a gauge-theory-like structure, which are computed here for the first time. The resulting seventh-order contribution in Newton's constant is finite in three space dimensions. This result provides the most technically demanding missing ingredient for the determination of the conservative dynamics of the gravitational two-body system at sixth post-Newtonian order.

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arXiv2025

Gravitational waveforms from restriction theory and rapid-decay homology

We present a systematic framework for computing frequency-domain gravitational waveforms from relativistic binary scattering in different asymptotic regimes. The method yields a controlled series expansion that can in principle be extended to arbitrary order in the relevant kinematic parameter. By combining differential-equation techniques with restriction theory and algebraic-geometry methods for impact-parameter-space Fourier integrals, we derive recursion relations that generate the leading-order (tree-level) waveform in both the soft-emission and post-Newtonian regimes, establishing a proof of principle for extending the approach to higher-loop computations. Finally, following constraints from rapid-decay homology, we show that the Fourier integrals underlying the waveform satisfy epsilon-form differential equations mixing Bessel- and exponential-type kernels, marking a first step toward uncovering the analytic structure of the exact solution.

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arXiv2025

High-energy evolution in planar QCD to three loops: the non-conformal contribution

The Balitsky-Kovchegov (BK) equation offers a tractable description of the high-energy growth of gauge-theory scattering amplitudes and the nonlinear saturation effects that eventually tame it. Motivated by the upcoming Electron-Ion Collider (EIC), whose extended kinematic reach promises more decisive tests of saturation at high energies, we present a framework based on the spacelike-timelike correspondence that streamlines the computation of multi-loop corrections to the BK equation. We explicitly verify the correspondence at three loops in the large-flavor limit and predict the full nonconformal component of the three-loop BK Hamiltonian in the planar limit of a generic gauge theory, treating the numbers of fermions and scalars as free parameters.

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arXiv2025

Feynman Integral Reduction using Syzygy-Constrained Symbolic Reduction Rules

We present a new algorithm for integration-by-parts (IBP) reduction of Feynman integrals with high powers of numerators or propagators, a demanding computational step in evaluating multi-loop scattering amplitudes. The algorithm starts with solving syzygy equations in individual sectors to produce IBP operators that turn seed integrals into IBP equations without artificially raised propagator powers. The IBP operators are expressed in terms of index-shift operators and number operators. We perform row reduction to systematically reshuffle the IBP operators and expose reduction rules with symbolic dependence on the powers of propagators and numerators. When this is insufficient, we produce more symbolic reduction rules by directly solving the linear system of IBP equations in which some propagator/numerator powers are kept symbolic. This linear system is kept small, as the equations are generated from a small set of seed integrals in the neighborhood of the target integral. We stress-test our algorithm against two highly non-trivial examples, namely rank-20 integrals for the double box with an external mass and the massless pentabox. As an application, we revisit the IBP reduction in a calculation of scattering amplitudes for spinning black hole binary systems, which involves two-loop Feynman integrals with complexity greater than 20, and achieve much faster IBP reduction than that of the original calculation.

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arXiv2024

Feynman Integral Reductions by Intersection Theory with Orthogonal Bases and Closed Formulae

We present a prescription for choosing orthogonal bases of differential $n$-forms belonging to quadratic twisted period integrals, with respect to the intersection number inner product. To evaluate these inner products, we additionally propose a new closed formula for intersection numbers beyond $\mathrm{d} \log$ forms. These findings allow us to systematically construct orthonormal bases between twisted period integrals of this type. In the context of Feynman integrals, this represents all diagrams at one-loop.

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arXiv2023

Fourier Calculus from Intersection Theory

Building on recent advances in studying the co-homological properties of Feynman integrals, we apply intersection theory to the computation of Fourier integrals. We discuss applications pertinent to gravitational bremsstrahlung and deep inelastic scattering in the saturation regime. After identifying the bases of master integrals, the latter are evaluated by means of the differential equation method. Finally, new results with exact dependence on the spacetime dimension D are presented.

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