2020
DOI: 10.1007/jhep07(2020)047
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Generalizing the relativistic quantization condition to include all three-pion isospin channels

Abstract: We present a generalization of the relativistic, finite-volume, three-particle quantization condition for non-identical pions in isosymmetric QCD. The resulting formalism allows one to use discrete finite-volume energies, determined using lattice QCD, to constrain scattering amplitudes for all possible values of two-and three-pion isospin. As for the case of identical pions considered previously, the result splits into two steps: the first defines a non-perturbative function with roots equal to the allowed ene… Show more

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Cited by 78 publications
(89 citation statements)
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“…The study of resonant three-particle systems using lattice QCD (LQCD) is becoming feasible, due to advances in the underlying theoretical formalism [1][2][3][4][5][6][7][8][9][10][11][12][13] and its practical application [4,[14][15][16], as well as in algorithmic and computational methods necessary to extract three-particle spectra (see, for example, the recent results presented in Refs. [17][18][19]).…”
Section: Introductionmentioning
confidence: 99%
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“…The study of resonant three-particle systems using lattice QCD (LQCD) is becoming feasible, due to advances in the underlying theoretical formalism [1][2][3][4][5][6][7][8][9][10][11][12][13] and its practical application [4,[14][15][16], as well as in algorithmic and computational methods necessary to extract three-particle spectra (see, for example, the recent results presented in Refs. [17][18][19]).…”
Section: Introductionmentioning
confidence: 99%
“…The first is based on an all-orders diagrammatic analysis in a generic relativistic field theory and is usually denoted the RFT approach. It was initially developed for identical scalar particles with a G-parity-like Z 2 symmetry [1,2], and subsequently extended to allow 2 → 3 processes [6], the inclusion of poles in the two-particle K matrix [9,11], and nonidentical but degenerate scalars [12]. In all cases, the formalism allows arbitrary interactions in two-particle subsystems (which we henceforth refer to as "dimers").…”
Section: Introductionmentioning
confidence: 99%
“…This is a complementary generalization to that achieved recently in Ref. [42], which considers degenerate, but potentially distinguishable, spinless particles. We expect it to be profitable to combine the two approaches.…”
Section: Discussionmentioning
confidence: 59%
“…We stress that these and similar steps have been repeatedly used in previous RFT papers, i.e., in HS1, HS2, and Refs. [39][40][41][42]. As a first step, we define d 23 as m 2 þ m 3 evaluated when c 3 → 0:…”
Section: Appendix C: Algebraic Matrix Manipulationsmentioning
confidence: 99%
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