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SU(3) Lattice QCD Study for Static Three-Quark Potential

T. T. Takahashi·H. Suganuma·H. Matsufuru·Y. Nemoto
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Abstract

We study the static three-quark (3Q) potential in detail using SU(3) lattice QCD with $12^3 \times 24$ at $β=5.7$ and $16^3 \times 32$ at $β=5.8, 6.0$ at the quenched level. For more than 200 patterns of the 3Q systems, we numerically derive 3Q ground-state potential $V_{3Q}$ from the 3Q Wilson loop with the smearing technique, which reduces excited-state contaminations. The lattice QCD data of $V_{3Q}$ are well reproduced within a few % deviation by a sum of a constant, the two-body Coulomb term and the three-body linear confinement term $σ_{3Q} L_{min}$, with $L_{min}$ the minimal value of total length of color flux tubes linking the three quarks. From the comparison with the Q-$\bar {Q}$ potential, we find a universality of the string tension as $σ_{3Q} \simeq σ_{\rm Q \bar Q}$ and the one-gluon-exchange result for Coulomb coefficients, $A_{3Q} \simeq \frac12 A_{\rm Q \bar Q}$.

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T. T. Takahashi, H. Suganuma, H. Matsufuru, Y. Nemoto. 2001-07-11. SU(3) Lattice QCD Study for Static Three-Quark Potential. https://doi.org/10.1063/1.1425520

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