Heavy-hadron interactions from Lattice QCD

Mohler, Daniel

doi:10.1051/epjconf/201818101027

Cited by 2 publications

(3 citation statements)

References 57 publications

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“…frame, â * 2,k . Decomposing the latter in spherical harmonics leads to the indices k, , m, which we abbreviate to k m. 6 We turn now to the 2 state, built from a particle of mass m and the resonance of mass M . In the overall c.m.…”

Section: A Kinematicsmentioning

confidence: 99%

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Three-particle systems with resonant subprocesses in a finite volume

2019

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1 For recent reviews, see . 2 In practice, this requires truncation of the quantization condition by assuming that higher partial waves are negligible. Such truncation schemes for the three-particle case have been discussed in Refs. [1,3,11,12,[14][15][16]. We do not consider these further in the present work. 3 In addition the particles were taken to be identical and spinless. Based on experience with the two-particle case, we expect the extensions to multiple channels of non-identical and non-degenerate particles, as well as particles with intrinsic spin, will be relatively straightforward. arXiv:1810.01429v1 [hep-lat] 2 Oct 2018package The NCAlgebra Suite is used to check the key results by algebraically manipulating matrices of unspecified size as generic non-commuting objects [32].This article is organized as follows. We begin in Sec. II by presenting the final result and defining all of the objects appearing in it. This section is meant to stand alone so that the lattice practitioner does not need to look elsewhere in order to make use of the result. In Sec. III we present the derivation of the quantization condition, with technical details given in Appendix B. The quantization condition is written in terms of the three-body K matrix, which we relate to the physical scattering amplitude in Sec. IV. We summarize, compare to previous work, and give an outlook in Sec. V.The framework presented here relies heavily on two facts: First, that the off-shell version of K 2 has the same poles as its on-shell limit and second, that at the residues of the poles of the off-shell K 2 can be written as a product of functions separately describing the incoming and outgoing two-particle states. In Appendix A we demonstrate these two results using constraints from unitarity and all-orders perturbation theory. II. SUMMARY OF THE FINAL RESULTThe main result of this article is a quantization condition with solutions equal to the energies of finite-volume three-particle states in a generic, relativistic quantum field theory. In contrast to earlier work, this result also holds for systems with a two-particle resonant subchannel. The particles are assumed to be identical, of physical mass m, and to have a G-parity-like symmetry that restricts interactions to those involving an even number of fields.We assume that K 2 diverges only for a single angular momentum, denoted J, in the energy range of interest, specified below. We further assume that there is only one pole in K (J) 2

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Section: A Kinematicsmentioning

confidence: 99%

“…We stress that the index pair m plays a very different role in the 3 and 2 states. This causes no problems, however, as these two sets of indices are never contracted 6. As mentioned above, the quantization condition depends only on the allowed finite-volume spectator momenta, k = 2π n/L with n a 3-vector of integers.…”

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confidence: 99%

Three-particle systems with resonant subprocesses in a finite volume

2019

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“…Using the formalism described above, there have been many calculations of a variety of charmonium-like resonances in lattice QCD. In view of the vast literature, we refer the reader to several recent reviews of the subject [321][322][323].…”

Section: Hadron Spectroscopymentioning

confidence: 99%

QCD on the Lattice

Wittig¹

2020

Particle Physics Reference Library

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Since Wilson’s seminal papers of the mid-1970s, the lattice approach to Quantum Chromodynamics has become increasingly important for the study of the strong interaction at low energies, and has now turned into a mature and established technique. In spite of the fact that the lattice formulation of Quantum Field Theory has been applied to virtually all fundamental interactions, it is appropriate to discuss this topic in a chapter devoted to QCD, since by far the largest part of activity is focused on the strong interaction. Lattice QCD is, in fact, the only known method which allows ab initio investigations of hadronic properties, starting from the QCD Lagrangian formulated in terms of quarks and gluons.

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Heavy-hadron interactions from Lattice QCD

Cited by 2 publications

References 57 publications

Three-particle systems with resonant subprocesses in a finite volume

Three-particle systems with resonant subprocesses in a finite volume

QCD on the Lattice

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