Causal Bounds on EFTs with anomalies with a Pseudoscalar, Photons, and Gravitons

TL;DR

The work tackles the problem of constraining EFTs with a pseudoscalar coupled to photons and gravitons through anomalies by applying the S-matrix bootstrap. It develops smeared dispersion relations to bound anomaly coefficients $\kappa$ and $\kappa_g$ and non-minimal couplings $\kappa_1$, $\kappa_3$ from 2→2 amplitudes involving $\eta$, $\gamma$, and $h$, relating low-energy Wilson coefficients to the UV spectrum, including the lightest $J\ge 2$ and $J\ge 3$ states. The main results yield explicit causal bounds such as $M_{J\ge 2}\lesssim \sqrt{c_{4\gamma}/G_N}\, F_\pi^2 /(\kappa\kappa_g)$ and $e^2|\kappa_1| M_{J\ge 3}^2 \lesssim 226 \ln(M_{J\ge 3}/M_{\rm IR})$, with significant implications for 5D holographic models (CS terms) and strongly-coupled gauge theories; astrophysical constraints on $\kappa_1$ imply new physics at extremely low energies, $\sim 10^{-10}$ eV, to affect current observables. Overall, the results provide model-independent, causality-driven limits on anomaly-driven EFTs and connect 4D bounds to 5D holographic realizations.

Abstract

Theories with pseudoscalars that couple through anomalies (such as axion models) are of particular phenomenological interest. We carry out a comprehensive analysis of all bounds obtainable from bootstrapping the amplitudes when a pseudoscalar couples to photons and gravitons. This allows us to find new cutoff scales of theories with anomalies that are more restrictive than those obtained from naive perturbative analysis. Our results are especially relevant for holographic models, as the bounds determine the allowed region of the five-dimensional EFTs, for example, by imposing strong bounds on Chern-Simons terms. We also consider modifications of General Relativity in photon--graviton couplings and show that current experiments are sensitive to these effects only if new physics appears at $\sim 10^{-10}$ eV.

Figures (6)

• Figure 1: Contours in the complex $s$-plane used to obtain dispersion relations. The red crosses mark the poles from massless exchanges in the amplitudes at low-energies, while the purple crosses indicate poles associated with the heavy states of the UV completion.
• Figure 2: Contributions to the process $\gamma^+\gamma^+\rightarrow h^+h^+$. All helicities are indicated in the all-incoming convention. The red diamond and circle represent resprectively the anomaly couplings $\kappa$ and $\kappa_g$, while the blue diamond and circle correspond to the non-minimal couplings $\kappa_1$ and $\kappa_3$.
• Figure 3: Contributions to the three elastic processes $\gamma^+\gamma^+\rightarrow \gamma^+\gamma^+$, $h^+h^+\rightarrow h^+h^+$, and $\gamma^+h^- \rightarrow \gamma^+ h^-$. The red and blue markers correspond to the couplings introduced in Fig. \ref{['fig:4pt_kappa']}. The black circle represents the gravitational minimal coupling.
• Figure 4: Contributions to the process $\gamma^+ h^+\rightarrow \gamma^-h^+$.
• Figure 5: Bounds on the cutoff scale of the 5D model Eq. (\ref{['lagrangian5']}). The black lines corresponds to the perturbative bounds Eq. (\ref{['pertcut']}), while the red (blue) corresponds to the bound from causality Eq. (\ref{['flat2']}) (Eq. (\ref{['flat3']})).