arXiv subjects

David A. Kosower

Publications and source records attributed to David A. Kosower.

At least 19 recordsLinked to original sources

arXiv2026

Analytic One-loop Scattering Waveform in General Relativity

Leveraging the computational framework presented in reference [JHEP 07, 062 (2024)], we evaluate the analytic scattering waveform in General Relativity to second order, $G^3 M^3 /r b^2$ and to all orders in velocity. This new representation of the next-to-leading order waveform is well-suited for numerical evaluation. Integrating the [modulus square of the] waveform over the angles on the celestial sphere, we also compute the power spectrum of the radiation to order $G^4$ numerically.

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arXiv2026

Finite Massless Pentaboxes

We characterize the integrand numerators that give rise to locally finite or evanescent Feynman integrals for the massless pentabox. We provide compact expressions for the generators of the corresponding ideal in terms of an adapted momentum basis and also in terms of Gram determinants. We also compute the integrals corresponding to the lowest-rank numerators in terms of polylogarithms using the HyperInt package, and in terms of pentagon functions.

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arXiv2026

Seedless Reduction of Feynman Integrals

We show how to construct a complete set of lowering operators, whose successive application reduces an arbitrary Fenyman integral to a combination of master integrals. The construction builds systems of equations for generic integral indices using IBP-generating vectors. The solution to each system is a lowering operator.

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arXiv2025

Singularity-Free Feynman Integral Bases

Standard integration-by-parts (IBP) reduction methods typically yield Feynman integral bases where the reduction of some integrals gives rise to coefficients singular as the dimensional regulator $ε\rightarrow 0$. These singular coefficients can also appear in scattering amplitudes, obscuring their structure, and rendering their evaluation more complicated. We investigate the use of bases in which the reduction of any integral is free of singular coefficients. We present two general algorithms for constructing such bases. The first is based on sequential $D=4$ IBP reduction. It constructs a basis iteratively by projecting onto the finite part of the set of IBP relations. The second algorithm performs Gaussian elimination within a local ring forbidding division by $ε$ while permitting division by polynomials in $ε$ finite at $ε=0$. We study the application of both algorithms to a pair of two-loop examples, the planar and nonplanar double-box families of integrals. We also explore the incorporation of finite Feynman integrals into these bases. In one example, the resulting basis provides a simpler and more compact representation of a scattering amplitude.

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arXiv2025

Serendipitous Syzygies of Scattering Amplitudes

We study linear relations between color-ordered all-plus amplitudes at one loop in Yang--Mills theory. We show that on general grounds, there are $(n-1)!/2-2$ relations for $n\ge 5$, leaving only two independent color-ordered amplitudes. We present two complementary approaches to finding such relations: one using numerical linear algebra and the other using syzygies in computational algebraic geometry. We obtain explicit forms for all relations through $n=7$. We also study relations for the tree-level MHV amplitudes through $n=8$. The latter relations include the well-known color and Bern--Carrasco--Johansson identities.

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arXiv2025

Two-Loop Maximal Unitarity with External Masses

We extend the maximal unitarity method at two loops to double-box basis integrals with up to three external massive legs. We use consistency equations based on the requirement that integrals of total derivatives vanish. We obtain unique formulae for the coefficients of the master double-box integrals. These formulae can be used either analytically or numerically.

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arXiv2025

Maximal Unitarity for the Four-Mass Double Box

We extend the maximal-unitarity formalism at two loops to double-box integrals with four massive external legs. These are relevant for higher-point processes, as well as for heavy vector rescattering, VV -> VV. In this formalism, the two-loop amplitude is expanded over a basis of integrals. We obtain formulas for the coefficients of the double-box integrals, expressing them as products of tree-level amplitudes integrated over specific complex multidimensional contours. The contours are subject to the consistency condition that integrals over them annihilate any integrand whose integral over real Minkowski space vanishes. These include integrals over parity-odd integrands and total derivatives arising from integration-by-parts (IBP) identities. We find that, unlike the zero- through three-mass cases, the IBP identities impose no constraints on the contours in the four-mass case. We also discuss the algebraic varieties connected with various double-box integrals, and show how discrete symmetries of these varieties largely determine the constraints.

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arXiv2024

Finite Integrals from Feynman Polytopes

We investigate a geometric approach to determining the complete set of numerators giving rise to finite Feynman integrals. Our approach proceeds graph by graph, and makes use of the Newton polytope associated to the integral's Symanzik polynomials. It relies on a theorem by Berkesch, Forsgård, and Passare on the convergence of Euler--Mellin integrals, which include Feynman integrals. We conjecture that a necessary in addition to a sufficient condition is that all parameter-space monomials lie in the interior of the polytope. We present an algorithm for finding all finite numerators based on this conjecture. In a variety of examples, we find agreement between the results obtained using the geometric approach, and a Landau-analysis approach developed by Gambuti, Tancredi, and two of the authors.

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arXiv2023

Finite Feynman Integrals

We describe an algorithm to organize Feynman integrals in terms of their infrared properties. Our approach builds upon the theory of Landau singularities, which we use to classify all configurations of loop momenta that can give rise to infrared divergences. We then construct bases of numerators for arbitrary Feynman integrals, which cancel all singularities and render the integrals finite. Through the same analysis, one can also classify so-called evanescent and evanescently finite Feynman integrals. These are integrals whose vanishing or finiteness relies on properties of dimensional regularization. To illustrate the use of these integrals, we display how to obtain a simpler form for the leading-color two-loop four-gluon scattering amplitude through the choice of a suitable basis of finite integrals. In particular, when all gluon helicities are equal, we show that with our basis the most complicated double-box integrals do not contribute to the finite remainder of the scattering amplitude.

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arXiv2023

Universal Decomposition of Phase-Space Integrands

One-loop integrands can be written in terms of a simple, process-independent basis. We show that a similar basis exists for integrands of phase-space integrals for the real-emission contribution at next-to-leading order. Our demonstration deploys techniques from computational algebraic geometry to partial-fraction integrands in a systematic way. This takes the first step towards a decomposition of phase-space integrals in terms of a basis of master integrals.

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arXiv2023

The SAGEX Review on Scattering Amplitudes

This is an introduction to, and invitation to read, a series of review articles on scattering amplitudes in gauge theory, gravity, and superstring theory. Our aim is to provide an overview of the field, from basic aspects to a selection of current (2022) research and developments.

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arXiv2022

The SAGEX Review on Scattering Amplitudes, Chapter 14: Classical Gravity from Scattering Amplitudes

Scattering amplitudes have their origin in quantum field theory, but have wide-ranging applications extending to classical physics. We review a formalism to connect certain classical observables to scattering amplitudes. An advantage of this formalism is that it enables us to study implications of the double copy in classical gravity. We discuss examples of observables including the total change of a particle's momentum, and the gravitational waveform, during a scattering encounter. The double copy also allows direct access to classical solutions in gravity. We review this classical double copy starting from its linearised level, where it originates in the double copy of three-point amplitudes. The classical double copy extends elegantly to exact solutions, making a connection between scattering amplitudes and the geometric formulation of General Relativity.

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arXiv2022

Yang-Mills All-Plus: Two Loops for the Price of One

We present work on two-loop amplitudes in pure Yang-Mills theory with all gluons of identical helicity. We show how to obtain their rational terms -- the hardest parts to compute -- via well-understood one-loop unitarity techniques.

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arXiv2022

A Unitarity Approach to Two-Loop All-Plus Rational Terms

We present a calculation of the rational terms in two-loop all-plus gluon amplitudes using $D$-dimensional unitarity. We use a conjecture of separability of the two loops, and then a simple generalization of one-loop $D$-dimensional unitarity to perform calculations. We compute the four- and five-point rational terms analytically, and the six- and seven-point ones numerically. We find agreement with previous calculations of Dalgleish, Dunbar, Godwin, Jehu, Perkins, and Strong. For a special subleading-color amplitude, we compute the eight- and nine-point results numerically, and find agreement with an all-$n$ conjecture of Dunbar, Perkins, and Strong.

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arXiv2021

Waveforms from Amplitudes

We show how to compute classical wave observables using quantum scattering amplitudes. We discuss observables both with incoming and with outgoing waves. The required classical limits are naturally described by coherent states of massless bosons. We recompute the classic gravitational deflection of light, and also show how to rederive Thomson scattering. We introduce a new class of local observables, which includes the asymptotic electromagnetic and gravitational Newman--Penrose scalars. As an example, we compute a simple radiated waveform: the expectation of the electromagnetic field in charged-particle scattering. At leading order, the waveform is trivially related to the five-point scattering amplitude.

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arXiv2021

Fishnet four-point integrals: integrable representations and thermodynamic limits

We consider four-point integrals arising in the planar limit of the conformal "fishnet" theory in four dimensions. They define a two-parameter family of higher-loop Feynman integrals, which extend the series of ladder integrals and were argued, based on integrability and analyticity, to admit matrix-model-like integral and determinantal representations. In this paper, we prove the equivalence of all these representations using exact summation and integration techniques. We then analyze the large-order behaviour, corresponding to the thermodynamic limit of a large fishnet graph. The saddle-point equations are found to match known two-cut singular equations arising in matrix models, enabling us to obtain a concise parametric expression for the free-energy density in terms of complete elliptic integrals. Interestingly, the latter depends non-trivially on the fishnet aspect ratio and differs from a scaling formula due to Zamolodchikov for large periodic fishnets, suggesting a strong sensitivity to the boundary conditions. We also find an intriguing connection between the saddle-point equation and the equation describing the Frolov-Tseytlin spinning string in $AdS_{3}\times S^{1}$, in a generalized scaling combining the thermodynamic and short-distance limits.

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arXiv2018

Amplitudes, Observables, and Classical Scattering

We present a formalism for computing classically measurable quantities directly from on-shell quantum scattering amplitudes. We discuss the ingredients needed for obtaining the classical result, and show how to set up the calculation to derive the result efficiently. We do this without specializing to a specific theory. We study in detail two examples in electrodynamics: the momentum transfer in spinless scattering to next-to-leading order, and the momentum radiated to leading order.

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arXiv2018

Direct Solution of Integration-by-Parts Systems

Systems of integration-by-parts identities play an important role in simplifying the higher-loop Feynman integrals that arise in quantum field theory. Solving these systems is equivalent to reducing integrals containing numerator products of irreducible invariants to a small set of master integrals. I present a new approach to solving these systems that finds direct reduction equations for numerator terms of a given Feynman integral. As a particular example of its power, I show how to obtain reduction equations for arbitrary powers of irreducible invariants, along with their solutions.

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