S-Matrix Marathon - Daily Workshop Schedules

Tuesday, March 12, 2024

Title: Scattering on periodic lattices

Speaker: Max Hansen

Abstract: Lattice regularization of quantum field theories is a powerful tool for understanding such theories when analytic methods are not applicable. However, the utility of numerical results can be affected by two issues: (i) calculations are necessarily performed in a finite-volume spacetime, and (ii) imaginary-time correlation functions are estimated. Both aspects play a particularly important role for multiparticle observables, including scattering and decay amplitudes.

In these lectures I will give an overview, together with various detailed examples, on the topic of extracting scattering amplitudes using numerical lattice field theory. I will focus on the strategy of using the finite volume as a tool rather than an unwanted artifact, and of applying generic field-theoretic relations between finite-volume quantities and infinite-volume amplitudes. Specific topics include the challenges of two-to-three and three-to-three amplitudes, and the role of anomalous thresholds and left-hand cuts. The lectures will include an overview of how the relations are derived and their limitations, as well as numerical results.

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