Positivity Constraints on EFT’s and Geometric Function Theory

Abstract: In this talk, we shall look at the implications of crossing symmetry, locality, and unitarity in the UV on low-energy EFT’s. We will begin by looking at 2-2scattering amplitudes with identical external particles and introduce a crossing symmetric dispersive representation (CSDR) of the amplitude that makes full (s,t,u)-crossing symmetry manifest, unlike the usual fixed-t dispersion relations. Though the CSDR makes crossing symmetry manifest, locality is lost and has to be restored by demanding that certain spurious singularities cancel in the low energy expansion of the amplitude leading to locality constraints.

For massive external particles, the CSDR and unitarity make a certain analytic property of the amplitude called typically-realness manifest and enables us to use techniques from the geometric function theory of typically-real functions to show that the low energy Wilson coefficients have to be o(1) numbers and that the space of these Wilson coefficients is finite. For massless external particles with massive exchanges we look at the celestial amplitude (CA) corresponding to our original 2-2 scattering amplitude and show that the locality constraints imply an infinite linear system of equations that the partial wave moments of any local theory need to satisfy. By additionally imposing linear unitarity (positivity of partial wave moments), we show that these naturally lead to the phenomenon of low-spin dominance (LSD). Finally, we show that the crossing symmetric partial waves with spurious singularities removed, dubbed as Feynman blocks are typically-real and using this we obtain two-sided bounds on low-energy Wilson coefficients for this case. This is based on work with Sudip Ghosh and Aninda Sinha.

HEP - theorymathematical physicsquantum physics

Audience: researchers in the topic

( video )

Comments: Host: Martin Kruczenski

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Purdue HET

Series comments: The recorded talks will be available on YouTube here: www.youtube.com/playlist?list=PLxU3vHZccQj64m9zsQR74D5WP1z1g4t1J

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