Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude

Hansen, Maxwell T.; Sharpe, Stephen R.

doi:10.1103/physrevd.92.114509

Cited by 223 publications

(495 citation statements)

References 13 publications

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“…We summarized the result of Refs. [17] and [18], where the quantization condition was derived for a system of identical scalar particles. This result has two key assumptions:…”

Section: Discussionmentioning

confidence: 99%

“…4, we described a test of the formalism published in Refs. [17] and [18]. We outlined how the result was used to reproduce, and extend, the known finite-volume shift to a threeparticle bound state.…”

Section: Discussionmentioning

confidence: 99%

“…This was derived by two of us in Refs. [17] and [18]. In these references we restrict attention to a system of identical scalar particles, with mass m, and with interactions that satisfy a Z 2 symmetry so that the even-and odd-particle-number sectors are decoupled.…”

Section: Three-particle Formalismmentioning

confidence: 99%

“…[18]. Finally, the u superscripts indicate that these quantities are unsymmetrized, meaning that they are not invariant under interchange of external momenta.…”

Section: Three-particle Formalismmentioning

confidence: 99%

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Progress in three-particle scattering from LQCD

2017

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Abstract. We present the status of our formalism for extracting three-particle scattering observables from lattice QCD (LQCD). The method relies on relating the discrete finitevolume energy spectrum of a quantum field theory with its scattering amplitudes. As the finite-volume spectrum can be directly determined in LQCD, this provides a method for determining scattering observables, and associated resonance properties, from the underlying theory. In a pair of papers published over the last two years, two of us have extended this approach to apply to relativistic three-particle scattering states. In this talk we summarize recent progress in checking and further extending this result. We describe an extension of the formalism to include systems in which two-to-three transitions can occur. We then present a check of the previously published formalism, in which we reproduce the known finite-volume energy shift of a three-particle bound state.

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“…We summarized the result of Refs. [17] and [18], where the quantization condition was derived for a system of identical scalar particles. This result has two key assumptions:…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Three-particle Formalismmentioning

confidence: 99%

“…[18]. Finally, the u superscripts indicate that these quantities are unsymmetrized, meaning that they are not invariant under interchange of external momenta.…”

Section: Three-particle Formalismmentioning

confidence: 99%

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Progress in three-particle scattering from LQCD

2017

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“…The extension of this connection to the threeparticle sector is the subject of ongoing research (see, for example, Refs. [4][5][6][7]). As a consequence, the scattering parameters, such as the scattering length and effective range, can be extracted from finite-volume energy levels obtained from lattice QCD.…”

Section: Introductionmentioning

confidence: 99%

Quantum Monte Carlo calculations of two neutrons in finite volume

Klos¹,

Lynn²,

Tews³

et al. 2016

Phys. Rev. C

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Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliary-field diffusion Monte Carlo calculations of the ground and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effective field theory interactions. We compare the results against exact diagonalizations and present a detailed analysis of the finite-volume effects, whose understanding is crucial for determining observables from the calculated energies. Using the Lüscher formula, we extract the low-energy S-wave scattering parameters from ground-and excited-state energies for different box sizes.

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Thomas¹

2018

Light Cone 2016

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Some recent progress in using lattice QCD to perform first-principles calculations of the spectra of mesons is discussed. In particular, I highlight some new results on resonances, near-threshold states and related scattering phenomena-this is a theoretically and experimentally interesting area where we have made significant advances in the last few years.This article belongs to the Topical Collection "Light Cone 2016".

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Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude

Cited by 223 publications

References 13 publications

Progress in three-particle scattering from LQCD

Progress in three-particle scattering from LQCD

Quantum Monte Carlo calculations of two neutrons in finite volume

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