Three-particle scattering amplitudes from lattice QCD

Abstract

Lattice QCD already offers the possibility of extracting three-hadron scattering quantities from first principles. In the last few years, significant progress has been achieved in developing and applying the finite-volume three-body formalism. The formalism is now able to treat physically relevant systems of three mesons, including those with resonances, as well as three-body decays. In this talk, I will review the state of the art, and comment on recent applications to lattice QCD data for systems of three pions and kaons.

Multi-hadron interactions from lattice QCD

“…Additionally, three-particle amplitudes contain twoto-two subprocesses, and so, they depend on two-particle interactions. Nevertheless, significant progress has been made in understanding the three-particle problem in finite volume, as can be seen in recent reviews [94][95][96][97]. These advances include theoretical developments , as well as the first applications to lattice QCD data [39,42,116,[134][135][136][137][138][139][140][141][142] boosted by technical developments in the extractions of the lattice spectrum [67,143,144].…”

Three relativistic neutrons in a finite volume

“…For recent reviews see refs. [66][67][68][69][70]. Other finite-volume approaches, which we do not discuss, include formulating EFTs in finite volume [71][72][73][74][75], the finite-volume Hamiltonian method (see, e.g., ref.…”

The isospin-3 three-particle $K$-matrix at NLO in ChPT

“…Here, b pk ≡ P − p − k, and H(x) is a smooth cutoff function that is 0 when x ≤ 0 and 1 when x ≥ 1, with x k ≡ (P − k) 2 /(4M 2 π ) and similarly for x p . 9 Note that k * p refers to the 7 An alternative notation involving two variables and an adjustment of factors of the energy, 2ω, has been used in some subsequent works, e.g., ref. [32].…”

“…The extraction of scattering amplitudes from lattice QCD is a very active topic of research (see refs. [1][2][3][4][5][6][7][8] for recent reviews), and, in particular, three-particle processes have recently received a lot of attention. The formalism to extract these amplitudes from the three-particle finite-volume spectrum computed on the lattice has been developed over the last decade , using three main approaches, and has been applied to results from lattice simulations for a number of scattering amplitudes [40][41][42][43][44][45][46][47][48][49][50][51][52][53].…”