Elastic positivity vs extremal positivity bounds in SMEFT: a case study in transversal electroweak gauge-boson scatterings

A bstract The positivity bounds, derived from the axiomatic principles of quantum field theory (QFT), constrain the signs of Wilson coefficients and their linear combinations in the Standard Model Effective Field Theory (SMEFT). The precise determination of these bounds, however, can become increasi...

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Bibliographic Details
Published in:	The journal of high energy physics 2021-01, Vol.2021 (1), p.1-63, Article 95
Main Authors:	Yamashita, Kimiko, Zhang, Cen, Zhou, Shuang-Yong
Format:	Article
Language:	eng
Subjects:	Beyond Standard Model Bosons Classical and Quantum Gravitation Cones Constraining Couplings Effective Field Theories Elastic scattering Elementary Particles Field theory High energy physics Physics Physics and Astronomy Principles Quantum Field Theories Quantum Field Theory Quantum numbers Quantum Physics Quantum theory Regular Article - Theoretical Physics Relativity Theory String Theory
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Summary:	A bstract The positivity bounds, derived from the axiomatic principles of quantum field theory (QFT), constrain the signs of Wilson coefficients and their linear combinations in the Standard Model Effective Field Theory (SMEFT). The precise determination of these bounds, however, can become increasingly difficult as more and more SM modes and oper- ators are taken into account. We study two approaches that aim at obtaining the full set of bounds for a given set of SM fields: 1) the traditional elastic positivity approach, which exploits the elastic scattering amplitudes of states with arbitrarily superposed helicities as well as other quantum numbers, and 2) the newly proposed extremal positivity approach, which constructs the allowed coefficient space directly by using the extremal representation of convex cones. Considering the electroweak gauge-bosons as an example, we demonstrate how the best analytical and numerical positivity bounds can be obtained in several ways. We further compare the constraining power and the efficiency of various approaches, as well as their applicability to more complex problems. While the new extremal approach is more constraining by construction, we also find that it is analytically easier to use, nu- merically much faster than the elastic approach, and much more applicable when more SM particle states and operators are taken into account. As a byproduct, we provide the best positivity bounds on the transversal quartic-gauge-boson couplings, required by the axiomatic principles of QFT, and show that they exclude ≈ 99 . 3% of the parameter space currently being searched at the LHC.
ISSN:	1029-8479 1029-8479