Three-particle bound states in a finite volume: Unequal masses and higher partial waves

Meng, Yu; Liu, Chuan; Meißner, Ulf‐G.; Rusetsky, Akaki

doi:10.1103/physrevd.98.014508

Cited by 36 publications

(15 citation statements)

References 41 publications

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“…Eqs. (29) and (22). Knowing that the interference between two ρπ decay channels must be present, we now focus on systematic studies of SYMM-DISP, keeping QTB-DISP for a mere comparison.…”

Section: Systematic Uncertaintiesmentioning

confidence: 99%

Pole position of the a1(1260) from τ -decay

et al. 2018

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We perform an analysis of the three-pion system with quantum numbers J P C = 1 ++ produced in the weak decay of τ leptons. The interaction is known to be dominated by the axial meson a1(1260). We build a model based on approximate three-body unitary and fix the free parameters by fitting it to the ALEPH data on τ − → π − π + π − ντ decay. We then perform the analytic continuation of the amplitude to the complex energy plane. The singularity structures related to the ππ subchannel resonances are carefully addressed. Finally, we extract the a1(1260) pole position m (a 1 (1260)) p − iΓ (a 1 (1260)) p /2 with m (a 1 (1260)) p = (1209 ± 4 +12 −9 ) MeV, Γ (a 1 (1260)) p = (576 ± 11 +89 −20 ) MeV.

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“…Eqs. (29) and (22). Knowing that the interference between two ρπ decay channels must be present, we now focus on systematic studies of SYMM-DISP, keeping QTB-DISP for a mere comparison.…”

Section: Systematic Uncertaintiesmentioning

confidence: 99%

Pole position of the a1(1260) from τ -decay

et al. 2018

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“…Apart from the general formulation, important applications have also been considered in the literature. From these, one may single out the study of the binding energy of a shallow three-body bound state [13,30,31], as well as the calculation of the (perturbative) shift of the three-particle ground state in a finite volume; see, e.g., Refs. [32,33].…”

Section: Introductionmentioning

confidence: 99%

Three-body spectrum in a finite volume: The role of cubic symmetry

et al. 2018

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The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the BetheSalpeter equation for particle-dimer scattering is expanded in the basis functions of different irreducible representations of the octahedral group. Such a projection is of particular importance for the three-body problem in the finite volume due to the occurrence of three-body singularities above breakup. Additionally, we study the numerical solution and properties of such a projected quantization condition in a simple model. It is shown that, for large volumes, these solutions allow for an instructive interpretation of the energy eigenvalues in terms of bound and scattering states.

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“…There has been comparison and cross-checks of existing forms [59]. Other approaches include building in to some extent additional symmetries or constraints on the scattering system that then can lead to a three-body relation to the finite-volume energies that can be extracted from a lattice calculation [60,61,62]. What is needed are calculations in three-body systems to drive this development.…”

Section: Pos(lattice2019)253mentioning

confidence: 99%

Hadron Spectroscopy

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2020

Proceedings of 37th International Symposium on Lattice Field Theory — PoS(LATTICE2019)

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Three-particle bound states in a finite volume: Unequal masses and higher partial waves

Cited by 36 publications

References 41 publications

Pole position of the a1(1260) from τ -decay

Pole position of the a1(1260) from τ -decay

Three-body spectrum in a finite volume: The role of cubic symmetry

Hadron Spectroscopy

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