Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds

TL;DR

This work develops crossing-symmetric dispersion relations for 2-2 scattering of identical spinning particles, enabling two-sided bounds on low-energy Wilson coefficients via Geometric Function Theory. By constructing crossing-symmetric helicity amplitudes for photons, gravitons, and Majorana fermions and implementing locality constraints, the authors connect positivity to low-spin dominance and derive Bieberbach-Rogosinski bounds that constrain EFT parameters. They provide explicit scalar, photon, and graviton bounds, including LSD evidence and numerical coefficient ranges, and demonstrate the framework's compatibility with known results while outlining avenues for S-matrix bootstrap extensions. The approach offers a systematic, crossing-symmetric route to EFT bounds, with clear pathways to incorporate non-linear constraints and AdS/CFT generalizations in future work.

Abstract

We develop crossing symmetric dispersion relations for describing 2-2 scattering of identical external particles carrying spin. This enables us to import techniques from Geometric Function Theory and study two sided bounds on low energy Wilson coefficients. We consider scattering of photons, gravitons in weakly coupled effective field theories. We provide general expressions for the locality/null constraints. Consideration of the positivity of the absorptive part leads to an interesting connection with the recently conjectured weak low spin dominance. We also construct the crossing symmetric amplitudes and locality constraints for the massive neutral Majorana fermions and parity violating photon and graviton theories. The techniques developed in this paper will be useful for considering numerical S-matrix bootstrap in the future.

Figures (9)

• Figure 1: The above flowchart shows the steps involved in the GFT approach.
• Figure 2: The allowed regions in the $\left(\frac{g_3}{g_2},\frac{f_3}{f_2}\right)$ vs $\frac{f_2}{g_2}$ space with scalar,axion,graviton,QED,scalar QED, $W^{\pm}$ sector benchmarked.
• Figure 3: The space of allowed regions in the $\left(\frac{f_3}{f_2},\frac{g_3}{f_2}\right)$for $f_2=k g_2$ with $k=0,0.25.0.5,1$ corresponding to blue, purple,yellow,green and red respectively.
• Figure 4: Plots for $(w_{11}$ and $w_{02})$ vs $w_{01}$ for $TR^\gamma_U$ upto $n=3$ .
• Figure 5: A comparative plot of changing regions of positivity in $\xi$ with spin for $f^{(3)}$.