Bounds on scattering amplitudes of non-identical scalar particles in 4d
Abstract
We initiate the study of two-to-two scattering amplitudes involving two distinct scalar particles in d = 4 spacetime dimensions using the primal S-matrix bootstrap. We impose a ℤ2 × ℤ2 global symmetry under which the two particles are the lightest ones carrying charges (−,+) and (+,−), guaranteeing their absolute stability and absence of triangular anomalous thresholds. For unequal masses, the presence of a pseudo-physical cut whose discontinuity is not directly constrained by physical unitarity qualitatively changes the bootstrap problem. We find several observables to be unbounded, while others obey non-trivial one-sided bounds or become bounded once another observable is fixed. In the equal-mass limit, where the pseudo-physical region disappears, two-sided bounds are recovered. As a proof of concept, we show that supplying information about the pseudo-physical discontinuity through an Omnès parametrisation also restores boundedness. Our results provide a starting point for future studies of physical processes such as pion-kaon and pion-nucleon scattering.
Related
- Six Particles, Infinite Optimism: Towards Positivity Bounds for Six-Point Amplitudes
- Elastic Scattering of Dirac Dark Matter with Charged Leptons through a Scalar Mediator: Analytical Framework, Numerical Stability, and Direct-Detection Bounds
- Colloquium: Quantum information processing with ensembles of identical particles
- Indistinguishability Theory for Identical Particles with Invariant Degrees of Freedom
- Capillary forces between two identical spherical particles
BibTeX
@misc{ferretti2026bounds,
title = {{Bounds on scattering amplitudes of non-identical scalar particles in 4d}},
author = {Gabriele Ferretti and Denis Karateev and Alessandro Piazza and Marco Serone},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09282},
eprint = {2609.09282},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09282},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bounds on scattering amplitudes of non-identical scalar particles in 4d
AU - Gabriele Ferretti
AU - Denis Karateev
AU - Alessandro Piazza
AU - Marco Serone
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09282
UR - https://arxiv.org/abs/2609.09282
AB - We initiate the study of two-to-two scattering amplitudes involving two distinct scalar particles in d = 4 spacetime dimensions using the primal S-matrix bootstrap. We impose a ℤ_2 × ℤ_2 global symmetry under which the two particles are the lightest ones carrying charges (−,+) and (+,−), guaranteeing their absolute stability and absence of triangular anomalous thresholds. For unequal masses, the presence of a pseudo-physical cut whose discontinuity is not directly constrained by physical unitarity qualitatively changes the bootstrap problem. We find several observables to be unbounded, while others obey non-trivial one-sided bounds or become bounded once another observable is fixed. In the equal-mass limit, where the pseudo-physical region disappears, two-sided bounds are recovered. As a proof of concept, we show that supplying information about the pseudo-physical discontinuity through an Omnès parametrisation also restores boundedness. Our results provide a starting point for future studies of physical processes such as pion-kaon and pion-nucleon scattering.
ER -