Precise determination of the three-quark potential in SU(3) lattice gauge theory

Koma, Yoshiaki; Koma, Miho

doi:10.1103/physrevd.95.094513

Cited by 27 publications

(49 citation statements)

References 51 publications

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“…1 contain strikingly different shapes: whereas most of Ref. [5] points (triangle shapes) lie outside of the three straight lines in Fig. 1, defined by the right-triangle configurations, most of Ref.…”

Section: Hyper-spherical Coordinatesmentioning

confidence: 96%

“…The lattice data from Refs. [4,5] were converted into permutation-adapted hyper-spherical coordinates by the above equations. We plotted those data points in the x-y projection of the shape sphere.…”

Section: Hyper-spherical Coordinatesmentioning

confidence: 99%

“…Two older calculations of the effective static three-quark potential on the lattice are the one by Alexandrou et al [3], who proposed the ∆-string form, and the one by Takahashi et al [4], who strongly claimed the Y-string. The recent calculation of the three-quark potential by Koma and Koma [5], on a larger (24 4 ) lattice, has re-ignited interest in this question. These authors did not test the potential for the O(2) dynamical symmetry, however, so their work cannot be conclusive with regard to the Y versus ∆ dilemma.…”

Section: Introductionmentioning

confidence: 99%

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Application of Hyper-spherical Three-body Variables to Lattice QCD Data

Leech¹,

Šuvakov²,

Dmitrašinović³

2018

Acta Phys. Pol. B Proc. Suppl.

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Is the three-quark confinement potential better described by the Y-string or the ∆-string form? We have re-analysed the recent lattice QCD calculations and the older results using hyper-spherical three-body variables. The presently available lattice data do not give a conclusive answer to the above question. We briefly discuss sources of uncertainties in these calculations, the ways to reduce them, and how to avoid them.

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Section: Hyper-spherical Coordinatesmentioning

confidence: 96%

Section: Hyper-spherical Coordinatesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Application of Hyper-spherical Three-body Variables to Lattice QCD Data

Leech¹,

Šuvakov²,

Dmitrašinović³

2018

Acta Phys. Pol. B Proc. Suppl.

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show abstract

“…[23] "finds support for the ∆ Ansatz", whereas the most recent Ref. [24] finds that "The potentials of triangle geometries are clearly different from the half of the sum of the two-body quark-antiquark potential", i.e., suggesting that is not the ∆ Ansatz. All of which indicates that the lattice QCD potential is neither pure Y Ansatz, nor a pure ∆ Ansatz.…”

Section: Three-body Spin-independent Potentialsmentioning

confidence: 98%

O(6) algebraic theory of three nonrelativistic quarks bound by spin-independent interactions

Dmitrašinović

Salom

2018

Phys. Rev. D

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We apply the newly developed theory of permutation-symmetric O(6) hyperspherical harmonics to the quantum-mechanical problem of three non-relativistic quarks confined by a spin-independent 3-quark potential. We use our previously derived results to reduce the three-body Schrödinger equation to a set of coupled ordinary differential equations in the hyper-radius R with coupling coefficients expressed entirely in terms of (i) a few interaction-dependent O(6) expansion coefficients and (ii) O(6) hyperspherical harmonics matrix elements, that have been evaluated in our previous paper. This system of equations allows a solution to the eigenvalue problem with homogeneous 3-quark potentials, which class includes a number of standard Ansätze for the confining potentials, such as the Y-and ∆-string ones. We present analytic formulae for the K = 2, 3, 4, 5 shell states' eigen-energies in homogeneous three-body potentials, which formulae we then apply to the Y-and ∆-string, as well as the logarithmic confining potentials. We also present numerical results for power-law pair-wise potentials with the exponent ranging between -1 and +2. In the process we resolve the 25 year-old Taxil & Richard vs. Bowler et al. controversy regarding the ordering of states in the K = 3 shell, in favor of the former. Finally, we show the first clear difference between the spectra of ∆-and Y-string potentials, which appears in K ≥ 3 shells. Our results are generally valid, not just for confining potentials, but also for many momentum-independent permutation-symmetric homogenous potentials, that need not be pairwise sums of two-body terms. The potentials that can be treated in this way must be square-integrable under the O(6) hyperangular integral, however, which class does not include the Dirac δ-function.

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“…for heavy sources has been addressed on the lattice in several works [41][42][43], where it has actually been found that up to numerical uncertainties the potential is linearly rising, and the corresponding string tension is numerically identical to the one of the qq system (see specifically Ref. [43]). In this section we show analytically that under very specific assumptions this must actually be true.…”

Section: Quark-diquark Potential From Polyakov Loop Correlatorsmentioning

confidence: 99%

Baryonic susceptibilities, quark-diquark models, and quark-hadron duality at finite temperature

2019

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Fluctuations of conserved charges such as baryon number, electric charge and strangeness may provide a test for completeness of states in lattice QCD for three light flavors. We elaborate on the idea that the corresponding susceptibilities can be saturated with excited baryonic states with an underlying quark-diquark structure with a linearly confining interaction. Using Polyakov-loop correlators we show that in the static limit, the quark-diquark potential coincides with the quark-antiquark potential in marked agreement with recent lattice studies. We thus study in a quark-diquark model the baryonic fluctuations of electric charge, baryon number and strangeness: χ BQ , χ BB and χ BS ; by considering a realization of the hadron resonance gas model in the light flavor sector of QCD. These results have been obtained by using the baryon spectrum computed within a relativistic quark-diquark model, leading to an overall good agreement with the spectrum obtained with other quark models and with lattice data for the fluctuations.

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Precise determination of the three-quark potential in SU(3) lattice gauge theory

Cited by 27 publications

References 51 publications

Application of Hyper-spherical Three-body Variables to Lattice QCD Data

Application of Hyper-spherical Three-body Variables to Lattice QCD Data

O(6) algebraic theory of three nonrelativistic quarks bound by spin-independent interactions

Baryonic susceptibilities, quark-diquark models, and quark-hadron duality at finite temperature

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