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arXiv · 2011.05520

Relativistic three-particle quantization condition for nondegenerate scalars

Tyler D. Blanton·Stephen R. Sharpe
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Abstract

The formalism relating the relativistic three-particle infinite-volume scattering amplitude to the finite-volume spectrum has been developed thus far only for identical or degenerate particles. We provide the generalization to the case of three nondegenerate scalar particles with arbitrary masses. A key quantity in this formalism is the quantization condition, which relates the spectrum to an intermediate K matrix. We derive three versions of this quantization condition, each a natural generalization of the corresponding results for identical particles. In each case we also determine the integral equations relating the intermediate K matrix to the three-particle scattering amplitude, $\mathcal M_3$. The version that is likely to be most practical involves a single Lorentz-invariant intermediate K matrix, $\widetilde{\mathcal K}_{\rm df,3}$. The other versions involve a matrix of K matrices, with elements distinguished by the choice of which initial and final particles are the spectators. Our approach should allow a straightforward generalization of the relativistic approach to all other three-particle systems of interest.

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Tyler D. Blanton, Stephen R. Sharpe. 2020-11-11. Relativistic three-particle quantization condition for nondegenerate scalars. https://doi.org/10.1103/physrevd.103.054503

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