Equivalence of three-particle scattering formalisms

Jackura, A.; Dawid, Sebastian M.; Fernández-Ramírez, C.; Mathieu, V.; Mikhasenko, M.; Pilloni, A.; Sharpe, Stephen R.; Szczepaniak, Adam P.

doi:10.1103/physrevd.100.034508

Cited by 78 publications

(88 citation statements)

References 30 publications

(105 reference statements)

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“…[5,7] has been determined in Ref. [68]. We also think that it will be worthwhile investigating the use of the K df;3 parametrization of M 3 in analyses of experimental data.…”

Section: Discussionmentioning

confidence: 91%

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Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism

et al. 2019

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Hansen and Sharpe [Phys. Rev. D 92, 114509 (2015)] derived a relation between the scattering amplitude of three identical bosons, M 3 , and a real function referred to as the divergence-free K matrix and denoted K df;3. The result arose in the context of a relation between finite-volume energies and K df;3 , derived to all orders in the perturbative expansion of a generic low-energy effective field theory. In this work we set aside the role of the finite volume and focus on the infinite-volume relation between K df;3 and M 3. We show that, for any real choice of K df;3 , M 3 satisfies the three-particle unitarity constraint to all orders. Given that K df;3 is also free of a class of kinematic divergences, the function may provide a useful tool for parametrizing three-body scattering data. Applications include the phenomenological analysis of experimental data (where the connection to the finite volume is irrelevant) as well as calculations in lattice quantum chromodynamics (where the volume plays a key role).

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“…[5,7] has been determined in Ref. [68]. We also think that it will be worthwhile investigating the use of the K df;3 parametrization of M 3 in analyses of experimental data.…”

Section: Discussionmentioning

confidence: 91%

“…where we have made use of the definition of R, given in Eq. (68). The result (83) can be rewritten as…”

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confidence: 99%

Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism

et al. 2019

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“…Similar work has also been done in the ϕ 4 theory[31] 3. It is worth emphasizing that efforts to constrain infinite-volume three-particle amplitudes from finitevolume LQCD results has partially motivated several infinite-volume studies[43][44][45][46][47].…”

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confidence: 80%

Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states

Romero-López

Sharpe

Blanton

et al. 2019

J. High Energ. Phys.

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In this work, we use an extension of the quantization condition, given in ref. [1], to numerically explore the finite-volume spectrum of three relativistic particles, in the case that two-particle subsets are either resonant or bound. The original form of the relativistic three-particle quantization condition was derived under a technical assumption on the twoparticle K matrix that required the absence of two-particle bound states or narrow twoparticle resonances. Here we describe how this restriction can be lifted in a simple way using the freedom in the definition of the K-matrix-like quantity that enters the quantization condition. With this in hand, we extend previous numerical studies of the quantization condition to explore the finite-volume signature for a variety of two-and three-particle interactions. We determine the spectrum for parameters such that the system contains both dimers (two-particle bound states) and one or more trimers (in which all three particles are bound), and also for cases where the two-particle subchannel is resonant. We also show how the quantization condition provides a tool for determining infinite-volume dimerparticle scattering amplitudes for energies below the dimer breakup. We illustrate this for a series of examples, including one that parallels physical deuteron-nucleon scattering. All calculations presented here are restricted to the case of three identical scalar particles.

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“…Furthermore, the formalism of Ref. [135] provides a parametrization of the infinite-volume three-particle scattering amplitude that is unitary [151], and has been shown to be equivalent to parametrizations used to analyze experimental scattering data [152]. Using simple parametrizations of the two-and three-particle amplitudes, as well as other well-motivated approximations, the quantization condition has been solved in simple examples [147,150,[153][154][155][156].…”

Section: Multihadron Physicsmentioning

confidence: 99%

Opportunities for Lattice QCD in quark and lepton flavor physics

et al. 2019

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This document is one of a series of whitepapers from the USQCD collaboration. Here, we discuss opportunities for lattice QCD in quark and lepton flavor physics. New data generated at Belle II, LHCb, BES III, NA62, KOTO, and Fermilab E989, combined with precise calculations of the relevant hadronic physics, may reveal what lies beyond the Standard Model. We outline a path toward improvements of the precision of existing lattice-QCD calculations and discuss groundbreaking new methods that allow lattice QCD to access new observables.

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Equivalence of three-particle scattering formalisms

Cited by 78 publications

References 30 publications

Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism

Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism

Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states

Opportunities for Lattice QCD in quark and lepton flavor physics

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