Crossing Symmetric Dispersion Relations in Quantum Field Theories

Sinha, A and Zahed, A (2021) Crossing Symmetric Dispersion Relations in Quantum Field Theories. In: Physical Review Letters, 126 (18).

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Abstract

For 2-2 scattering in quantum field theories, the usual fixed t dispersion relation exhibits only two-channel symmetry. This Letter considers a crossing symmetric dispersion relation, reviving certain old ideas from the 1970s. Rather than the fixed t dispersion relation, this needs a dispersion relation in a different variable z, which is related to the Mandelstam invariants s, t, u via a parametric cubic relation making the crossing symmetry in the complex z plane a geometric rotation. The resulting dispersion is manifestly three-channel crossing symmetric. We give simple derivations of certain known positivity conditions for effective field theories, including the null constraints, which lead to two sided bounds and derive a general set of new nonperturbative inequalities. We show how these inequalities enable us to locate the first massive string state from a low energy expansion of the four dilaton amplitude in type II string theory. We also show how a generalized (numerical) Froissart bound, valid for all energies, is obtained from this approach. © 2021 authors. Published by the American Physical Society.

Item Type:	Journal Article
Publication:	Physical Review Letters
Publisher:	American Physical Society
Additional Information:	The copyright for this article belongs to the Authors.
Keywords:	Dispersions, Dispersion relations; Effective field theory; Energy expansion; Nonperturbative; Positivity conditions; Quantum field theory; Simple derivations; Three channel, Quantum theory, article
Department/Centre:	Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited:	27 Apr 2023 05:24
Last Modified:	27 Apr 2023 05:24
URI:	https://eprints.iisc.ac.in/id/eprint/81453

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