The three-pion $K$-matrix at NLO in ChPT

Birmingham U.); CPT; Fernando Romero-L\'opez (MIT); Johan Bijnens (Lund U.); Jorge Baeza-Ballesteros (IFIC; Marseille); Mattias Sj\"o (Lund U.; Stephen R. Sharpe (Washington U.); Tom\'a\v{s} Husek (Charles U.; Valencia)

The three-pion $K$-matrix at NLO in ChPT

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arxiv 2401.14293 v1 pith:RHPBIWEV submitted 2024-01-25 hep-ph hep-latnucl-th

Jorge Baeza-Ballesteros (IFIC , Valencia) , Johan Bijnens (Lund U.) , Tomáš Husek (Charles U. , Birmingham U.) , Fernando Romero-López (MIT) , Stephen R. Sharpe (Washington U.) , Mattias Sjö (Lund U.

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keywords isospinorderthree-particlematrixthree-pionworkanalyticcase

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abstract

The three-particle $K$-matrix, $\mathcal{K}_{\mathrm{df},3}$, is a scheme-dependent quantity that parametrizes short-range three-particle interactions in the relativistic-field-theory three-particle finite-volume formalism. In this work, we compute its value for systems of three pions in all isospin channels through next-to-leading order in Chiral Perturbation Theory, generalizing previous work done at maximum isospin. We obtain analytic expressions through quadratic order (or cubic order, in the case of zero isospin) in the expansion about the three-pion threshold.

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Implementing the RFT finite-volume formalism for three pions across all non-maximal isospins
hep-lat 2024-12 conditional novelty 5.0 of 10

A numerical implementation of the RFT quantization condition yields finite-volume three-pion spectra for isospins 0, 1, and 2 with three-particle interactions turned off.

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