Relativistic-invariant formulation of the NREFT three-particle quantization condition

Müller, Fabian; Pang, Jin-Yi; Rusetsky, Akaki; Wu, Jia-Jun

doi:10.48550/arxiv.2110.09351

Cited by 3 publications

(4 citation statements)

References 48 publications

(86 reference statements)

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“…The connection has been explicitly shown for FVU and RFT [34]. In addition, the equations in the FVU approach and the "relativized" formulation of the NREFT [54] have the same form. 2 Substantial numerical evidence also supports the equivalence [32,42].…”

Section: The Three-particle Finite-volume Formalismmentioning

confidence: 90%

Three-particle scattering amplitudes from lattice QCD

Romero-López¹

2021

Preprint

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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.

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Section: The Three-particle Finite-volume Formalismmentioning

confidence: 90%

Three-particle scattering amplitudes from lattice QCD

Romero-López¹

2021

Preprint

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“…[13]). We also note that a Lorentz-invariant extension of the NREFT formalism has recently been obtained [25], and this is expected to be equivalent to the other approaches [46]. In this work we follow the RFT approach.…”

Section: Jhep02(2022)098mentioning

confidence: 99%

“…It might be thought problematic that a lower cutoff is required for the nondegenerate theory -it certainly conflicts with the usual notion of a UV cutoff that one can send arbitrarily large, a point stressed recently in ref. [25]. This is why we have also called H (i) a "transition function," because, in all derivations in the RFT approach, it has the effect of transitioning the two-particle amplitude that appears in the expressions between the two-particle K matrix K 2 at threshold (where H (i) = 1) and the two-particle amplitude M 2 far below threshold (where H (i) = 0).…”

Section: Cutoff Functionmentioning

confidence: 99%

Implementing the three-particle quantization condition for π+π+K+ and related systems

Blanton

Romero-López

Sharpe

2022

J. High Energ. Phys.

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Recently, the formalism needed to relate the finite-volume spectrum of systems of nondegenerate spinless particles has been derived. In this work we discuss a range of issues that arise when implementing this formalism in practice, provide further theoretical results that can be used to check the implementation, and make available codes for implementing the three-particle quantization condition. Specifically, we discuss the need to modify the upper limit of the cutoff function due to the fact that the left-hand cut in the scattering amplitudes for two nondegenerate particles moves closer to threshold; we describe the decomposition of the three-particle amplitude $$ \mathcal{K} $$ K df,3 into the matrix basis used in the quantization condition, including both s and p waves, with the latter arising in the amplitude for two nondegenerate particles; we derive the threshold expansion for the lightest three-particle state in the rest frame up to $$ \mathcal{O} $$ O (1/L5); and we calculate the leading-order predictions in chiral perturbation theory for $$ \mathcal{K} $$ K df,3 in the π+π+K+ and π+K+K+ systems. We focus mainly on systems with two identical particles plus a third that is different (“2+1” systems). We describe the formalism in full detail, and present numerical explorations in toy models, in particular checking that the results agree with the threshold expansion, and making a prediction for the spectrum of π+π+K+ levels using the two- and three-particle interactions predicted by chiral perturbation theory.

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“…[146], three major approaches have been followed, commonly denoted the Relativistic Field Theory (RFT) [147,148], Non-Relativistic Effective Field Theory (NREFT) [149,150] and Finite Volume Unitarity (FVU) [151,152] approaches. The NREFT approach was recently generalized to a manifestly relativistic-invariant form [153]. Similarities and equivalences exist between these approaches [154][155][156][157].…”

Section: Resonances With Three-hadron Decay Channelsmentioning

confidence: 99%