3Q Potential Research Articles

Three Quark Static Potential in the Thick Center Vortex Model

We study the baryonic potential between three static sources in the S U(3) gauge group through the thick center vortex model. We consider different open configurations where the line-like center vortex penetrates the Wilson loop in the Y, T and L ansatze. Our calculation shows that using uncorrelated center vortices, the data obtained from Y, L and T-shaped Wilson loops lie very close to each other at very large separations. Investigations on these three sets of data, one might conclude that the 3Q potential shows a little dependence on the flux tube meeting point only at intermediate distances. Comparing the slope of the three-quark potential in the Y, T and L form with the $Q\bar Q$ potential, we find $\sigma _{3Q} \simeq \sigma _{Q\bar Q}$ at very large distances. In fact, the point to point ratio of the 3Q potential to the $Q\bar Q$ one varies from 1 -at small quark seperations- to 1.7 -at large distances.

Confining potential of Y-string on the lattice at finite T

The potential due to a system of three static quark (3Q) is studied using SU(3) lattice QCD at finite temperature with Polyakov loops operators. We focused our analysis on the large distance properties of the 3Q potential and found a good fit behavior to the Y-string model formula. In addition to the linearly confining term proportional to the minimal length of the Y-string, we observed that the subleading logarithmic term, which is proportional to Dedekind eta function and accounts for the Y-string's quantum fluctuations, is necessary to reproduce the quark anti-quark string tension of the corresponding mesonic system at finite temperature.

Three-quark potential and Abelian dominance of confinement in SU(3) QCD

We study the baryonic three-quark (3Q) potential and its Abelian projection in terms of the dual-superconductor picture in SU(3) quenched lattice QCD. The non-Abelian SU(3) gauge theory is projected onto Abelian U(1)$^2$ gauge theory in the maximal Abelian gauge. We investigate the 3Q potential and its Abelian part for more than 300 different patterns of static 3Q systems in total at $\beta=5.8$ on $16^332$ and at $\beta=6.0$ on $20^332$ with 1000-2000 gauge configurations. For all the distances, both the 3Q potential and Abelian part are found to be well described by the Y ansatz, i.e., two-body Coulomb term plus three-body Y-type linear term $\sigma_{3\mathrm{Q}} L_{\mathrm{min}}$, where $L_{\mathrm{min}}$ is the minimum flux-tube length connecting the three quarks. We find equivalence between the three-body string tension $\sigma_{3\mathrm{Q}}$ and its Abelian part $\sigma_{3\mathrm{Q}}^{\rm Abel}$ with an accuracy within a few percent deviation, i.e., $\sigma_{3\mathrm{Q}} \simeq \sigma_{3\mathrm{Q}}^{\rm Abel}$, which means Abelian dominance of the quark-confining force in 3Q systems.

Instantaneous interquark potential in generalized Landau gauge in SU(3) lattice QCD: A linkage between the Landau and the Coulomb gauges

We investigate in detail "instantaneous interquark potentials", interesting gauge-dependent quantities defined from the spatial correlators of the temporal link-variable $U_4$, in generalized Landau gauge using SU(3) quenched lattice QCD. The instantaneous Q$\bar{\rm Q}$ potential has no linear part in the Landau gauge, and it is expressed by the Coulomb plus linear potential in the Coulomb gauge, where the slope is 2-3 times larger than the physical string tension. Using the generalized Landau gauge, we find that the instantaneous potential can be continuously described between the Landau and the Coulomb gauges, and its linear part rapidly grows in the neighborhood of the Coulomb gauge. We also investigate the instantaneous 3Q potential in the generalized Landau gauge, and obtain similar results to the Q$\bar{\rm Q}$ case. $T$-length terminated Polyakov-line correlators and their corresponding "finite-time potentials" are also investigated in generalized Landau gauge.

Study of quark confinement in baryons with lattice QCD

In SU(3) lattice QCD, we perform the detailed study for the ground-state three-quark (3Q) potential $V_{\rm 3Q}^{\rm g.s.}$ and the 1st excited-state 3Q potential $V_{\rm 3Q}^{\rm e.s.}$, i.e., the energies of the ground state and the 1st excited state of the gluon field in the presence of the static three quarks. From the accurate calculation for more than 300 different patterns of 3Q systems, the static ground-state 3Q potential $V_{\rm 3Q}^{\rm g.s.}$ is found to be well described by the Coulomb plus Y-type linear potential (Y-Ansatz) within 1%-level deviation. As a clear evidence for Y-Ansatz, Y-type flux-tube formation is actually observed on the lattice in maximally-Abelian projected QCD. For about 100 patterns of 3Q systems, we calculate the 1st excited-state 3Q potential $V_{\rm 3Q}^{\rm e.s.}$, and find a large gluonic-excitation energy $\Delta E_{\rm 3Q} \equiv V_{\rm 3Q}^{\rm e.s.}-V_{\rm 3Q}^{\rm g.s.}$ of about 1 GeV, which gives a physical reason of the success of the quark model even without gluonic excitations. We present also the first study for the penta-quark potential $V_{\rm 5Q}$ in lattice QCD, and find that $V_{\rm 5Q}$ is well described by the sum of the OGE Coulomb plus multi-Y type linear potential.

Behind the success of the quark model

The ground-state three-quark (3Q) potential V 3Q g.s. and the excited-state 3Q potential V 3Q e.s. are studied using SU(3) lattice QCD at the quenched level. For more than 300 patterns of the 3Q systems, the ground-state potential V 3Q g.s. is investigated in detail in lattice QCD with 12 3 × 24 at β = 5.7 and with 16 3 × 32 at β = 5.8, 6.0. As a result, the ground-state potential V 3Q g.s. is found to be well described with Y-ansatz within the 1%-level deviation. From the comparison with the Q- Q potential, we find the universality of the string tension as σ 3 Q ≅ σ Q Q and the one-gluon-exchange result as A 3 Q ≅ 1 2 A Q Q . The excited-state potential V 3Q e.s. is also studied in lattice QCD with 16 3 × 32 at β = 5.8 for 24 patterns of the 3Q systems. The energy gap between V 3Q g.s. and V 3Q e.s., which physically means the gluonic excitation energy, is found to be about 1GeV in the typical hadronic scale, which is relatively large compared with the excitation energy of the quark origin. This large gluonic excitation energy justifies the great success of the simple quark model.

Detailed analysis of the three-quark potential in SU(3) lattice QCD

The static three-quark (3Q) potential is studied in detail using SU(3) lattice QCD with $12^3 \times 24$ at $\beta=5.7$ and $16^3 \times 32$ at $\beta=5.8$, 6.0 at the quenched level. For more than 300 different patterns of the 3Q systems, we perform the accurate measurement of the 3Q Wilson loop with the smearing method, which reduces excited-state contaminations, and present the lattice QCD data of the 3Q ground-state potential $V_{\rm 3Q}$. We perform the detailed fit analysis on $V_{\rm 3Q}$ in terms of the Y-ansatz both with the continuum Coulomb potential and with the lattice Coulomb potential, and find that the lattice QCD data of the 3Q potential $V_{\rm 3Q}$ are well reproduced within a few % deviation by the sum of a constant, the two-body Coulomb term and the three-body linear confinement term $\sigma_{\rm 3Q} L_{\rm min}$, with $L_{\rm min}$ the minimal value of the total length of color flux tubes linking the three quarks. From the comparison with the Q-$\bar {\rm Q}$ potential, we find a universality of the string tension as $\sigma_{\rm 3Q} \simeq \sigma_{\rm Q \bar Q}$ and the one-gluon-exchange result for the Coulomb coefficients as $A_{\rm 3Q} \simeq \frac12 A_{\rm Q \bar Q}$. We investigate also the several fit analyses with the various ans\"atze: the Y-ansatz with the Yukawa potential, the $\Delta$-ansatz and a more general ansatz including the Y and the $\Delta$ ans\"atze in some limits. All these fit analyses support the Y-ansatz on the confinement part in the 3Q potential $V_{\rm 3Q}$, although $V_{\rm 3Q}$ seems to be approximated by the $\Delta$-ansatz with $\sigma_\Delta \simeq 0.53 \sigma$.

Three-Quark Potential in SU(3) Lattice QCD.

The static three-quark ( 3Q) potential is studied in SU(3) lattice QCD with 12(3)x24 and beta = 5.7 at the quenched level. From the 3Q Wilson loop, 3Q ground-state potential V(3Q) is extracted using the smearing technique for ground-state enhancement. With accuracy better than a few percent, V(3Q) is well described by a sum of a constant, the two-body Coulomb term, and the three-body linear confinement term sigma(3Q)L(min), with L(min) the minimal value of total length of color flux tubes linking the three quarks. Comparing with the Q-&Qmacr; potential, we find a universal feature of the string tension, sigma(3Q) approximately sigma(Q&Qmacr;), and the OGE result for Coulomb coefficients, A(3Q) approximately 1 / 2A(Q&Qmacr;).