arXiv subjects

Luke Lippstreu

Publications and source records attributed to Luke Lippstreu.

12 recordsLinked to original sources

arXiv2026

New Tools in the Landau Bootstrap

We describe recent advances in our understanding of the analytic structure of Feynman integrals. In particular, we describe two new classes of constraints on such integrals, that identify discontinuities that either cannot be repeated, or that always give rise to the same result (no matter which other discontinuities are computed first). These new constraints hold at all orders in dimensional regularization, and provide us with new input for the Landau bootstrap, where information about the singularities and discontinuities of individual Feynman integrals is used to construct their functional form.

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arXiv2025

Steinmann Violation and Minimal Cuts

The Steinmann relations are known to be violated with respect to some -- but not all -- two-particle momentum channels in massless Feynman integrals. We trace the source of this Steinmann violation to a special class of singularities, which arise from partially-overlapping minimal cuts. This allows us to propose an efficient graphical test for predicting which Steinmann relations will be violated by massless Feynman integrals of a given topology, which can be applied at any loop order. We provide evidence for this test by correctly predicting all instances of Steinmann violation in the complete set of known two-loop integrals that contribute to five-particle scattering with one or two external masses.

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arXiv2025

Analytic Properties of Infrared-Finite Amplitudes in Theories with Long-Range Forces

Infrared divergences obscure important analytic properties of scattering amplitudes, indicating gaps in our understanding of unitarity, causality, and crossing symmetry in theories with long-range forces. Using the exactly solvable model of a charged scalar particle in a fixed Coulomb background, we demonstrate that novel analytic properties arise and can be systematically studied when long-range interactions are properly incorporated. We first canonically quantize a scalar particle in a Coulomb potential, confirming that basic conditions for unitarity and causality hold. We then examine the necessary modifications to the LSZ reduction formula, the general optical theorem, and the treatment of the disconnected components of scattering amplitudes. Next, we show that the Coulomb phase divergence is analytically related to real radiative divergences via crossing symmetry, implying that a well-defined treatment of the Coulomb phase divergence provides constraints on the real radiative divergence. In contrast to the Faddeev-Kulish approach, we propose that an effective way to eliminate infrared divergences and study these analytic properties is to fully solve the quantum theory associated with the asymptotic Hamiltonian.

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arXiv2024

Minimal Cuts and Genealogical Constraints on Feynman Integrals

We introduce an efficient method for deriving hierarchical constraints on the discontinuities of individual Feynman integrals. This method can be applied at any loop order and particle multiplicity, and to any configuration of massive or massless virtual particles. The resulting constraints hold to all orders in dimensional regularization, and complement the extended Steinmann relations -- which restrict adjacent sequential discontinuities -- by disallowing ordered pairs of discontinuities from appearing even when separated by (any number of) other discontinuities. We focus on a preferred class of hierarchical constraints, which we refer to as \emph{genealogical constraints}, that govern what singularities can follow from certain \emph{minimal cuts} that act as the primogenitors of the discontinuities that appear in Feynman integrals. While deriving the full set of hierarchical constraints on a given Feynman integral generally requires identifying all solutions to the (blown up) Landau equations, these genealogical constraints can be worked out with only minimal information about what singularities may appear. We illustrate the power of this new method in examples at one, two, and three loops, and provide evidence that genealogical constraints restrict the analytic structure of Feynman integrals significantly more than the extended Steinmann relations.

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arXiv2023

A perturbation theory for the Coulomb-phase infrared divergence

We construct a perturbation theory which we conjecture to be free of the Coulomb-phase infrared divergence. This perturbation theory is developed for one of the simplest yet prototypical scattering amplitudes which would otherwise exhibit this divergence: the semiclassical scattering of a spinless boson on a background Coulomb field. The perturbation theory is based upon replacing plane waves with Coulomb wavefunctions, and the free-field propagator with the Coulomb propagator, in order to appropriately match the asymptotics of the exact in/out states. We compute the leading-order (LO) and next-to-leading-order (NLO) infrared-finite scattering amplitudes in this framework, which include effects to all orders in the coupling, and demonstrate that these amplitudes are in agreement with the known exact amplitude at these orders. We comment on the Runge-Lenz symmetry of the LO amplitude, under which the states furnish a principal-series representation of the Euclidean conformal group on the 2-sphere.

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arXiv2023

Landau Singularities of the 7-Point Ziggurat II

We solve the Landau equations to find the singularities of nine three-loop 7-point graphs that arise as relaxations of the graph studied in arXiv:2211.16425. Along the way we establish that $Y{-}\Delta$ equivalence fails for certain branches of solutions to the Landau equations. We find two graphs with singularities outside the heptagon symbol alphabet; in particular they are not cluster variables of ${\rm Gr}(4,7)$. We compare maximal residues of scalar graphs exhibiting these singularities to those in $\mathcal{N}=4$ super-Yang-Mills theory in order to probe their cancellation from its amplitudes.

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arXiv2022

Landau Singularities of the 7-Point Ziggurat I

We compute the leading (first-type Landau) singularities of a certain four-loop 7-point graph that is related to the 7-point ``ziggurat'' graph by the graphical moves familiar from equivalent circuit theory. We find perfect agreement with a subset of the ``heptagon symbol alphabet'' that has appeared in the context of planar $\mathcal{N}=4$ super-Yang-Mills theory. The remaining heptagon symbol letters are found in its subleading Landau singularities, which we address in a companion paper.

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arXiv2022

Angular momentum of the asymptotic electromagnetic field in the classical scattering of charged particles

We compute the angular momentum of the electromagnetic field on a late time Cauchy surface with an arbitrary constant normal vector relevant for the classical scattering of charged particles. We find a time independent contribution to the angular momentum. This demonstrates that every charged particle scattering event is accompanied by a net shift in the angular momentum of the electromagnetic field. We speculate that this shift is related to a subleading electromagnetic memory effect. We argue that this asymptotic angular momentum should be included in the description of the asymptotic states in quantum theories containing infrared divergences. We demonstrate that the Lorentz covariance of the asymptotic electromagnetic angular momentum can only be exhibited upon making reference to the Cauchy slice's normal vector.

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arXiv2022

Loop-level gluon OPEs in celestial holography

We compute one-loop corrections to the OPE of gluons in the celestial conformal field theory corresponding to Yang-Mills coupled to arbitrary matter. We exploit universal hard/soft factorization to derive an IR finite OPE for the hard gluon operators. This OPE involves logarithms and operators that resemble logarithmic partners of primary operators. We derive an exact all-loop OPE in a limit of the Higgs-regulated planar $\mathcal{N}=4$ super Yang-Mills theory.

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arXiv2022

Four-point correlators of light-ray operators in CCFT

We compute the four-point correlator of two gluon light-ray operators and two gluon primaries from the four-gluon celestial amplitude in $(2,2)$ signature spacetime. The correlator is non-distributional and allows us to verify that light-ray operators appear in the OPE of two gluon primaries. We also carry out a conformal block decomposition of the terms involving the exchange of gluon operators.

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arXiv2021

Zwanziger's pairwise little group on the celestial sphere

We generalize Zwanziger's pairwise little group to include a boost subgroup. We do so by working in the celestial sphere representation of scattering amplitudes. We propose that due to late time soft photon and graviton exchanges, matter particles in the asymptotic states in massless QED and gravity transform under the Poincare group with an additional pair of pairwise celestial representations for each pair of matter particles. We demonstrate that the massless abelian and gravitational exponentiation theorems are consistent with the proposed pairwise Poincare transformation properties. For massless QED we demonstrate that our results are consistent with the effects of the Faddeev-Kulish dressing and the abelian exponentiation theorem for celestial amplitudes found in [2012.04208]. We discuss electric and magnetic charges simultaneously as it is especially natural to do so in this formalism.

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arXiv2019

Weak Separation, Positivity and Extremal Yangian Invariants

We classify all positive n-particle N^kMHV Yangian invariants in N=4 Yang-Mills theory with n=5k, which we call extremal because none exist for n>5k. We show that this problem is equivalent to that of enumerating plane cactus graphs with k pentagons. We use the known solution of that problem to provide an exact expression for the number of cyclic classes of such invariants for any k, and a simple rule for writing them down explicitly. As a byproduct, we provide an alternative (but equivalent) classification by showing that a product of k five-brackets with disjoint sets of indices is a positive Yangian invariant if and only if the sets are all weakly separated.

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