Triple crossing positivity bounds for multi-field theories

Nov 1, 2021
28 pages
Published in:
  • JHEP 12 (2021) 115
  • Published: Dec 17, 2021
e-Print:
Report number:
  • USTC-ICTS/PCFT-21-42

Citations per year

20212022202320242025051015
Abstract: (Springer)
We develop a formalism to extract triple crossing symmetric positivity bounds for effective field theories with multiple degrees of freedom, by making use of su symmetric dispersion relations supplemented with positivity of the partial waves, st null constraints and the generalized optical theorem. This generalizes the convex cone approach to constrain the s2^{2} coefficient space to higher orders. Optimal positive bounds can be extracted by semi-definite programs with a continuous decision variable, compared with linear programs for the case of a single field. As an example, we explicitly compute the positivity constraints on bi-scalar theories, and find all the Wilson coefficients can be constrained in a finite region, including the coefficients with odd powers of s, which are absent in the single scalar case.
Note:
  • 28 pages, 4 figures, 1 table; corrected error about upper bounds on s^2 coefficients, conclusions remain unchanged
  • Effective Field Theories
  • Nonperturbative Effects
  • crossing
  • partial wave
  • optical theorem
  • dispersion relation
  • higher-order
  • effective field theory