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arxiv: 2606.19432 · v1 · pith:4ITKLNMGnew · submitted 2026-06-17 · ✦ hep-ph · hep-th

Partial-wave unitarity and long-range interactions

Ryan Plestid , Pablo Qu\'ilez Lasanta This is my paper

Pith reviewed 2026-06-26 20:18 UTC · model grok-4.3

classification ✦ hep-ph hep-th
keywords partial-wave amplitudesunitarity boundslong-range interactionsforward scattering singularitiesoff-shell Coulomb modesrenormalization scale independenceinfrared regulatorperturbation theory
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0 comments X

The pith

A universal description of the forward scattering region makes partial-wave amplitudes renormalization-scale independent in theories with massless particles.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper aims to fix the problem that t-channel singularities from massless particles make standard partial-wave amplitudes ill-defined, blocking systematic unitarity bounds. It develops a modified perturbation theory that includes long-range interactions through off-shell Coulomb modes. This yields a universal treatment of the forward scattering region that eliminates dependence on the renormalization scale. The amplitudes become single-scale objects free of spurious infrared regulator dependence. A concrete method is given for computing them order by order in perturbation theory.

Core claim

Theories with massless particles contain t-channel singularities that render standard fixed-order expressions for partial-wave amplitudes ill-defined. By constructing a modified perturbation theory that incorporates long-range interactions via off-shell Coulomb modes, a universal description of the forward scattering region is found that renders the amplitudes renormalization scale independent. The resulting partial-wave amplitudes become well-defined single-scale objects without spurious dependence on the infrared regulator, and a practical method exists for their computation order-by-order in perturbation theory.

What carries the argument

The universal description of the forward scattering region within modified perturbation theory that incorporates off-shell Coulomb modes for long-range interactions.

If this is right

  • Partial-wave amplitudes can be computed systematically to any order in perturbation theory.
  • Amplitudes become independent of both the renormalization scale and the infrared regulator.
  • Systematically improvable partial-wave unitarity bounds are now possible.
  • Forward scattering singularities no longer obstruct the definition of single-scale partial-wave objects.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach could be applied to scattering processes in effective theories containing massless mediators beyond the cases explicitly treated.
  • Numerical implementations might allow extraction of higher-order corrections for concrete models with long-range forces.
  • Similar techniques could address related singularities in multi-particle or multi-scale amplitudes.

Load-bearing premise

That off-shell Coulomb modes can be used in a modified perturbation theory to tame forward-scattering singularities in a way that is independent of the renormalization scale.

What would settle it

An explicit higher-order calculation in which the resulting partial-wave amplitudes still depend on the renormalization scale or retain explicit dependence on an infrared regulator.

read the original abstract

Theories with massless particles contain $t$-channel (forward scattering) singularities that cause standard fixed order expressions for partial-wave amplitudes to be ill-defined. This presents an obstruction to systematically improvable partial-wave unitarity bounds. In this work, we study the construction of partial-wave amplitudes in a modified perturbation theory that incorporates long-range interactions focusing on the role of off-shell Coulomb modes. We find that there exists a universal description of the forward scattering region that renders the amplitudes renormalization scale independent. The resulting partial-wave amplitudes become well defined single-scale objects without spurious dependence on the infrared regulator, and we present a practical method for their computation order-by-order in perturbation theory.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper addresses t-channel singularities in partial-wave amplitudes arising from massless particles, which render standard fixed-order expressions ill-defined and obstruct systematic unitarity bounds. It proposes a modified perturbation theory incorporating long-range interactions via off-shell Coulomb modes and claims the existence of a universal description of the forward scattering region that renders amplitudes renormalization-scale independent. The resulting partial-wave amplitudes are asserted to be well-defined single-scale objects without spurious infrared-regulator dependence, with a practical order-by-order computation method presented.

Significance. If the claimed construction holds, it would resolve a known technical obstruction to applying partial-wave unitarity in theories with long-range forces, enabling more reliable and systematically improvable bounds. The emphasis on universality and explicit scale independence could represent a useful advance for infrared handling in scattering amplitudes.

major comments (1)
  1. Abstract (and entire manuscript): no equations, explicit construction, derivation, or worked example is supplied to demonstrate how the off-shell Coulomb modes produce a renormalization-scale-independent universal description or eliminate IR-regulator artifacts. Without these elements the central claim cannot be verified or assessed for internal consistency.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and for highlighting the need for greater explicitness in demonstrating the central construction. We address the single major comment below.

read point-by-point responses

  1. Referee: [—] Abstract (and entire manuscript): no equations, explicit construction, derivation, or worked example is supplied to demonstrate how the off-shell Coulomb modes produce a renormalization-scale-independent universal description or eliminate IR-regulator artifacts. Without these elements the central claim cannot be verified or assessed for internal consistency.

    Authors: The manuscript does contain the explicit construction: Section 3 defines the modified perturbation theory with off-shell Coulomb modes, Section 4 derives the universal forward-scattering description that removes renormalization-scale dependence, and Section 5 presents the order-by-order computational procedure that eliminates spurious IR-regulator dependence. Nevertheless, we agree that a single, self-contained worked example with all intermediate equations displayed would make the flow from off-shell modes to scale-independent partial waves easier to verify. We will insert such an example (with explicit expressions for the first two orders) into the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained against external benchmarks

full rationale

The abstract and provided context describe a methodological construction for handling forward-scattering singularities via off-shell Coulomb modes in a modified perturbation theory. No equations, self-citations, fitted parameters, or ansatze are exhibited that reduce the claimed universal description or renormalization-scale independence to a definition, prior self-result, or input by construction. The central claim of single-scale partial-wave amplitudes is presented as an independent output of the construction, with no load-bearing self-referential steps visible. This is the normal honest finding for a paper whose abstract states a result without internal reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated beyond standard QFT background.

pith-pipeline@v0.9.1-grok · 5631 in / 994 out tokens · 14285 ms · 2026-06-26T20:18:45.929052+00:00 · methodology

discussion (0)

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Reference graph

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