Higher order finite volume quantization conditions for two spinless particles

Lee, Frank; Alexandru, Andrei; Brett, Ruairí

doi:10.1103/physrevd.105.054517

Cited by 3 publications

(5 citation statements)

References 68 publications

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“…The question of how the value of E n (L) converges as a function of max has also recently been studied in ref. [42]. We comment in more detail on these items in our conclusion.…”

mentioning

confidence: 71%

Analytic expansions of multi-hadron finite-volume energies: I. Two-particle states

Grabowska¹,

Hansen²

2021

Preprint

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We derive analytic expansions for the finite-volume energies of weakly-interacting twoparticle systems, using the general relations between scattering amplitudes and energies derived by Lüscher and others. The relations hold for ground and excited states with both zero and non-zero total momentum in the finite-volume frame. A number of instructive aspects arise in the derivation, including the role of accidental degeneracies and the importance of defining a power-counting scheme in the expansions. The results give intuition concerning the imprint of weakly-interacting systems on the energy spectrum, while also providing a useful basis for the analogous results concerning three-particle excited states, to appear.

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“…The question of how the value of E n (L) converges as a function of max has also recently been studied in ref. [42]. We comment in more detail on these items in our conclusion.…”

mentioning

confidence: 71%

Analytic expansions of multi-hadron finite-volume energies: I. Two-particle states

Grabowska¹,

Hansen²

2021

Preprint

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“…We have confirmed the convergence of all 45 cases in the same manner, as summarized in Table 1. All 45 QCs can be found in Ref [21]. One point to emphasize is that to get agreement for certain cases we needed to consider QC all the way to order 5.…”

Section: Frank X Leementioning

confidence: 99%

“…In this work we derive and validate the quantization conditions for two spinless particles of unequal masses, rest and in moving frames, cubic and elongated geometries, and partial waves as high as ℓ = 5 (The full version is in Ref [21]).…”

Section: Introductionmentioning

confidence: 97%

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Higher order quantization conditions for two spinless particles

Lee¹,

Alexandru²,

Brett³

2022

Proceedings of the 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021)

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Lattice QCD calculations of scattering phaseshifts and resonance parameters in the two-body sector are becoming precision studies. Early calculations employed Lüscher's formula for extracting these quantities at lowest order. As the calculations become more ambitious, higher-order relations are required. In this study we derive higher-order quantization conditions and introduce a method to transparently cross-check our results. This is an important step given the involved derivations of these formulae. We derive quantization conditions up to ℓ = 5 partial waves in both cubic and elongated geometries, and for states with zero and non-zero total momentum. All 45 quantization conditions we include here (22 in cubic box, 23 in elongated box) pass our cross-check test.

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“…The sensitivity to the second lowest partial wave in Lüscher's quantization conditions was discussed in ref. [33].…”

Section: Introductionmentioning

confidence: 99%

Two-particle scattering from finite-volume quantization conditions using the plane wave basis

Meng,

Epelbaum

2021

Preprint

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We propose an alternative approach to Lüscher's formula for extracting two-body scattering phase shifts from finite volume spectra with no reliance on the partial wave expansion. We use an effective-field-theory-based Hamiltonian method in the plane wave basis and decompose the corresponding matrix elements of operators into irreducible representations of the relevant point groups. The proposed approach allows one to benefit from the knowledge of the long-range interaction and avoids complications from partial wave mixing in a finite volume. We consider spin-singlet channels in the two-nucleon system and pion-pion scattering in the ρ-meson channel in the rest and moving frames to illustrate the method for non-relativistic and relativistic systems, respectively. For the two-nucleon system, the long-range interaction due to the one-pion exchange is found to make the single-channel Lüscher formula unreliable at the physical pion mass. For S-wave dominated states, the Lüscher method suffers from significant finite-volume artifacts for a L = 3 fm box, but it works well for boxes with L > 5 fm. However, for P-wave dominated states, significant partial wave mixing effects prevent the application of the single-channel Lüscher formula regardless of the box size (except for the near-threshold region). Using a toy model to generate synthetic data for finite-volume energies, we show that our effective-field-theory-based approach in the plane wave basis is capable of a reliable extraction of the phase shifts. For pionpion scattering, we employ a phenomenological model to fit lattice QCD results at the physical pion mass. The extracted P-wave phase shifts are found to be in a good agreement with the experimental results.

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Higher order finite volume quantization conditions for two spinless particles

Cited by 3 publications

References 68 publications

Analytic expansions of multi-hadron finite-volume energies: I. Two-particle states

Analytic expansions of multi-hadron finite-volume energies: I. Two-particle states

Higher order quantization conditions for two spinless particles

Two-particle scattering from finite-volume quantization conditions using the plane wave basis

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