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Bounds on scattering of neutral Goldstones
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abstract
We study the space of $2\to 2$ scattering amplitudes of neutral Goldstone bosons in four space-time dimensions. We establish universal bounds on the first two non-universal Wilson coefficients of the low energy Effective Field Theory (EFT) for such particles. We reconstruct the analytic, crossing-symmetric, and unitary amplitudes saturating our bounds, and we study their physical content. We uncover non-perturbative Regge trajectories by continuing our numerical amplitudes to complex spins. We then explore the consequence of additional constraints arising when we impose the knowledge about the EFT up to the cut-off scale. In the process, we improve on some aspects of the numerical $S$-matrix bootstrap technology for massless particles.
Forward citations
Cited by 9 Pith papers
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For three particle flavors, the positivity cone C_W has exactly three families of extremal rays, one of which yields genuinely new inelastic constraints not implied by elastic bounds.
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For a shift-symmetric scalar EFT with gravity, unitarity and dispersion relations imply Λ/M_P < 2.38 \tilde{g}_2^{1/5} and, in an improved smeared version, Λ^2/M_P^2 < 0.0115 |\tilde{g}_2|.
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The EFT Bootstrap at Finite $M_{PL}$
One-loop gravity effects make forward-limit positivity bounds ill-defined for massless scalar-gravity EFTs, forcing non-forward dispersion relations that shift the tree-level bounds by order-one factors.
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Running EFT-hedron with null constraints at loop level
One-loop massless corrections modify the null constraints of shift-symmetric scalar EFTs, and IR-finite combinations of them reproduce tree-level bounds in the weak-coupling limit while deforming bounds in five and si...
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