New positivity bounds from full crossing symmetry

Andrew Tolley (Theoretical Physics, Blackett Laboratory, Imperial College, London, SW7 2AZ, U.K.; CERCA, Department of Physics, Case Western Reserve University, 10900 Euclid Ave, Cleveland, OH, 44106, USA) ; Zi-Yue Wang (School of Gifted Young, University of Science and Technology of China, Hefei, Anhui, 230026, China) ; Shuang-Yong Zhou (Interdisciplinary Center for Theoretical Study, University of Science and Technology of China, Hefei, Anhui, 230026, China; Peng Huanwu Center for Fundamental Theory, Hefei, Anhui, 230026, China)

Positivity bounds are powerful tools to constrain effective field theories. Utilizing the partial wave expansion in the dispersion relation and the full crossing symmetry of the scattering amplitude, we derive several sets of generically nonlinear positivity bounds for a generic scalar effective field theory: we refer to these as the P Q, D su, D stu and D ¯ stu $$ {\overline{D}}^{\mathrm{stu}} $$ bounds. While the PQ bounds and D su bounds only make use of the s ↔ u dispersion relation, the D stu and D ¯ stu $$ {\overline{D}}^{\mathrm{stu}} $$ bounds are obtained by further imposing the s ↔ t crossing symmetry. In contradistinction to the linear positivity for scalars, these inequalities can be applied to put upper and lower bounds on Wilson coefficients, and are much more constraining as shown in the lowest orders. In particular we are able to exclude theories with soft amplitude behaviour such as weakly broken Galileon theories from admitting a standard UV completion. We also apply these bounds to chiral perturbation theory and we find these bounds are stronger than the previous bounds in constraining its Wilson coefficients.

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      "source": "Springer", 
      "value": "Positivity bounds are powerful tools to constrain effective field theories. Utilizing the partial wave expansion in the dispersion relation and the full crossing symmetry of the scattering amplitude, we derive several sets of generically nonlinear positivity bounds for a generic scalar effective field theory: we refer to these as the P Q, D su, D stu and   <math> <msup> <mover> <mi>D</mi> <mo>\u00af</mo> </mover> <mi>stu</mi> </msup> </math>  $$ {\\overline{D}}^{\\mathrm{stu}} $$  bounds. While the PQ bounds and D su bounds only make use of the s \u2194 u dispersion relation, the D stu and   <math> <msup> <mover> <mi>D</mi> <mo>\u00af</mo> </mover> <mi>stu</mi> </msup> </math>  $$ {\\overline{D}}^{\\mathrm{stu}} $$  bounds are obtained by further imposing the s \u2194 t crossing symmetry. In contradistinction to the linear positivity for scalars, these inequalities can be applied to put upper and lower bounds on Wilson coefficients, and are much more constraining as shown in the lowest orders. In particular we are able to exclude theories with soft amplitude behaviour such as weakly broken Galileon theories from admitting a standard UV completion. We also apply these bounds to chiral perturbation theory and we find these bounds are stronger than the previous bounds in constraining its Wilson coefficients."
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Published on:
27 May 2021
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2021 (2021)
Issue 5
Pages 1-42
DOI:
https://doi.org/10.1007/JHEP05(2021)255
arXiv:
2011.02400
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: