Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data

Self Cite

172

213

Using non-relativistic effective Lagrangians in the particle-dimer picture, we rederive the expression for the energy shift of a loosely bound three-particle bound state of identical bosons in the unitary limit. The effective field theory formalism allows us to explicitly investigate the role of the three-particle force. Moreover, we discuss relaxing the unitary limit of infinite scattering length and demonstrate a smooth transition from the weakly bound three-particle state to a two-particle bound state of a particle and a deeply bound dimer.

“…The particle-dimer language allow one to achieve most of the above goals with an impressive ease. However, we relegate the proof of this statement to our forthcoming publication [37].…”

Section: Jhep09(2017)109mentioning

confidence: 95%

Section: Jhep09(2017)109mentioning

confidence: 99%

“…[37]). Hence, the treatment of the finite-volume effects with the use of the particle-dimer approach is as general as the one based on a three-particle Lagrangian without a dimer field.…”

Section: Jhep09(2017)109mentioning

confidence: 99%

Section: Jhep09(2017)109mentioning

confidence: 99%

See 2 more Smart Citations

Three-particle quantization condition in a finite volume: 1. The role of the three-particle force

Hammer

Pang²,

Rusetsky³

2017

Self Cite

172

213

“…Ω = 0.3593(7) [62], and the experimental mass, m exp. Ω = 1672.45 (29) MeV [63], we obtain the inverse temporal spacing via a…”

Section: Jhep07(2018)043mentioning

confidence: 99%

Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD

Woss

Thomas

Dudek

et al. 2018

We present the first determination of ρπ scattering, incorporating dynamicallycoupled partial-waves, using lattice QCD, a first-principles numerical approach to QCD. Considering the case of isospin-2 ρπ, we calculate partial-wave amplitudes with J ≤ 3 and determine the degree of dynamical mixing between the coupled S and D-wave channels with J P = 1 + . The analysis makes use of the relationship between scattering amplitudes and the discrete spectrum of states in the finite volume lattice. Constraints on the scattering amplitudes are provided by over one hundred energy levels computed on two lattice volumes at various overall momenta and in several irreducible representations of the relevant symmetry groups. The spectra follow from variational analyses of matrices of correlations functions computed with large bases of meson-meson operators. Calculations are performed with degenerate light and strange quarks tuned to the physical strange quark mass so that m π ∼ 700 MeV, ensuring that the ρ is stable against strong decay. This work demonstrates the successful application of techniques, opening the door to calculations of scattering processes that incorporate the effects of dynamically-coupled partial-waves, including those involving resonances or bound states.

Erratum to: Generalizing the relativistic quantization condition to include all three-pion isospin channels

Hansen

Romero-López

Sharpe

2021

We have found an error in a statement following eq. (2.5) of our paper, concerning the function f (a, b, k) that first appears in that equation. The issue arises in the statement that it is convenient to take the function f (a, b, k) to be exchange symmetric with respect to its three arguments. This has the unwanted consequence of making six of the seven operators in the column vector of eq. (2.4) identically equal. This, in turn, implies that many operators are identically zero in the definite isospin basis, considered in section 2.4. To repair this, the last sentence of the paragraph containing eq. (2.4), starting “It is convenient for the subsequent…”, should be removed, as should footnote 3 and the next paragraph, beginning with “At this point, the reader may wonder why…”.