$S$ -Matrix for massless particles

Journal Article · Fri May 01 00:00:00 EDT 2020 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.101.105001· OSTI ID:1616788

Hannesdottir, Holmfridur ; Schwartz, Matthew D.

The traditional $$\textit{S}$$-matrix does not exist for theories with massless particles, such as quantum electrodynamics. The difficulty in isolating asymptotic states manifests itself as infrared divergences at each order in perturbation theory. Building on insights from the literature on coherent states and factorization, we construct an $$\textit{S}$$-matrix that is free of singularities order-by-order in perturbation theory. Factorization guarantees that the asymptotic evolution in gauge theories is universal, i.e., independent of the hard process. Although the hard $$\textit{S}$$-matrix element is computed between well-defined few particle Fock states, dressed/coherent states can be seen to form as intermediate states in the calculation of hard $$\textit{S}$$-matrix elements. We present a framework for the perturbative calculation of hard $$\textit{S}$$-matrix elements combining Lorentz-covariant Feynman rules for the dressed-state scattering with time-ordered perturbation theory for the asymptotic evolution. With hard cutoffs on the asymptotic Hamiltonian, the cancellation of divergences can be seen explicitly. In dimensional regularization, where the hard cutoffs are replaced by a renormalization scale, the contribution from the asymptotic evolution produces scaleless integrals that vanish. A number of illustrative examples are given in QED, QCD, and $$\mathcal{N}$$ = 4 super-Yang-Mills theory.

• Research Organization: Harvard Univ., Cambridge, MA (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: SC0013607
• OSTI ID: 1616788
• Alternate ID(s): OSTI ID: 1802515
• Journal Information: Physical Review D, Journal Name: Physical Review D Vol. 101 Journal Issue: 10; ISSN 2470-0010
• Publisher: American Physical Society
• Country of Publication: United States
• Language: English

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