S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem

Journal Article · 23 August 2021 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep08(2021)125 · OSTI ID:1842921

He, Yifei  ^[1]; Kruczenski, Martin ^[2]

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1. Univ. PSL, Paris (France); Univ. Paris-Saclay, Gif-sur-Yvette (France); Purdue University
2. Purdue Univ., West Lafayette, IN (United States)

The S-matrix bootstrap maps out the space of S-matrices allowed by analyticity, crossing, unitarity, and other constraints. For the 2 → 2 scattering matrix S_2→2 such space is an infinite dimensional convex space whose boundary can be determined by maximizing linear functionals. On the boundary interesting theories can be found, many times at vertices of the space. Here we consider 3 + 1 dimensional theories and focus on the equivalent dual convex minimization problem that provides strict upper bounds for the regularized primal problem and has interesting practical and physical advantages over the primal problem. Its variables are dual partial waves k_ℓ(s) that are free variables, namely they do not have to obey any crossing, unitarity or other constraints. Nevertheless they are directly related to the partial waves f_ℓ(s), for which all crossing, unitarity and symmetry properties result from the minimization. Numerically, it requires only a few dual partial waves, much as one wants to possibly match experimental results. We consider the case of scalar fields which is related to pion physics.

• Research Organization: Purdue Univ., West Lafayette, IN (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: SC0019202
• OSTI ID: 1842921
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 8 Vol. 2021; ISSN 1029-8479
• Publisher: Springer NatureCopyright Statement
• Country of Publication: United States
• Language: English