Positivity bounds for scalar field theories

By Claudia de Rham, S. Melville, A. Tolley, Shuang-Yong Zhou. 2017

169 citations recorded by the source corpus.

Assuming the existence of a local, analytic, unitary UV completion in a Poincar\'{e} invariant scalar field theory with a mass gap, we derive an infinite number of positivity requirements using the known properties of the amplitude at and away from the forward scattering limit. These take the form of bounds on combinations of the pole subtracted scattering amplitude and its derivatives. In turn, these positivity requirements act as constraints on the operator coefficients in the low energy effective theory. For certain theories these constraints can be used to place an upper bound on the mass of the next lightest state that must lie beyond the low energy effective theory if such a UV completion is to ever exist.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ec9db8b98811facbc7f42cc5a08483727d429325

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In Astronomy and Astrophysics

In Nuclear and High Energy Physics

Citations in the corpus

The cosmological bootstrap: inflationary correlators from symmetries and singularities (2018, unknown): “For amplitudes, this has led to powerful dispersion relations, which in turn result in nontrivial positivity constraints on the coefficients of higher-dimension operators in the low-energy effective field theory expansion [88] (see also [126–132]).”
New positivity bounds from full crossing symmetry (2020, methodology): “These positivity constraints are different from the positivity bounds defined in [9] in that these positivity bounds are nonlinear in the amplitude and its s and t derivatives, while the Y positivity bounds are linear in them.”
Positive moments for scattering amplitudes (2020, background): “[8] Claudia de Rham, Scott Melville, Andrew J.”