The static three-quark (3Q) potential is studied in SU(3) lattice QCD with 12 3 × 24 and β = 5.7 at the quenched level. From the 3Q Wilson loop, 3Q ground-state potential V3Q is extracted using the smearing technique for ground-state enhancement. With accuracy better than a few %, V3Q is well described by a sum of a constant, the two-body Coulomb term and the three-body linear confinement term σ3QLmin, with Lmin the minimal value of total length of color flux tubes linking the three quarks. Comparing with the Q-Q potential, we find a universal feature of the string tension, σ3Q ≃ σ QQ , and the OGE result for Coulomb coefficients, A3Q ≃ 1 2In usual, the three-body force is regarded as a residual interaction in most fields of physics. In QCD, however, the three-body force among three quarks is expected to be a "primary" force reflecting the SU(3) c gauge symmetry. Indeed, the three quark (3Q) potential [1,2,3] is directly responsible to the structure and properties of baryons [4], similar to the relevant role of the Q-Q potential upon meson properties [5]. In contrast with a number of studies on the Q-Q potential using lattice QCD [6,7], there were only a few lattice QCD studies for the 3Q potential done mainly more than 13 years ago [8,9,10,11]. (In Ref.[11], the author only showed a preliminary result on the equilateral-triangle case without enough analyses.) In Refs. [8,10,11], the 3Q potential seemed to be expressed by a sum of twobody potentials, which supports the ∆-type flux tube picture [12]. On the other hand, Ref. [9] seemed to support the Y-type flux-tube picture [2,4] rather than the ∆-type one. These controversial results may be due to the difficulty of the accurate measurement of the 3Q ground-state potential in lattice QCD. For instance, in Refs. [8,10], the authors did not use the smearing for ground-state enhancement, and therefore their results may include serious contamination from the excited-state component.The 3Q static potential can be measured with the 3Q Wilson loop, where the 3Q gauge-invariant state is generated at t = 0 and is annihilated at t = T , as shown in Fig.1. Here, the three quarks are spatially fixed in R 3 for 0 < t < T . The 3Q Wilson loop W 3Q is defined in a gauge-invariant manner aswithHere, P denotes the path-ordered product along the path denoted by Γ k in Fig.1. Similar to the derivation of the Q-Q potential from the Wilson loop, the 3Q potential V 3Q is obtained asPhysically, the true ground state of the 3Q system, which is of interest here, is expected to be expressed by the flux tubes instead of the strings, and the 3Q state which is expressed by the three strings generally includes many excited-state components such as flux-tube vibrational modes. Of course, if the large T limit can be taken, the ground-state potential would be obtained. However, W 3Q decreases exponentially with T , and then the practical measurement of W 3Q becomes quite severe for large T in lattice QCD simulations. Therefore, for the accurate measurement of the 3Q ground-state potentia...

The static three-quark (3Q) potential is studied in detail using SU(3) lattice QCD with 12 3 × 24 at β = 5.7 and 16 3 × 32 at β = 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 V3Q. We perform the detailed fit analysis on V3Q 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 V3Q 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 σ3QLmin, with Lmin the minimal value of the total length of color flux tubes linking the three quarks. From the comparison with the Q-Q potential, we find a universality of the string tension as σ3Q ≃ σ QQ and the one-gluon-exchange result for the Coulomb coefficients as A3Q ≃ 1 2 A QQ . We investigate also the several fit analyses with the various ansätze: the Y-ansatz with the Yukawa potential, the ∆-ansatz and a more general ansatz including the Y and the ∆ ansätze in some limits. All these fit analyses support the Y-ansatz on the confinement part in the 3Q potential V3Q, although V3Q seems to be approximated by the ∆-ansatz with σ∆ ≃ 0.53σ.Even at present, the arguments on the 3Q potential seem to be rather controversial. In Refs. [24,26,27,28,29], the 3Q potential seemed to be expressed by a sum of two-body potentials, which supports the ∆-type flux tube picture [30]. On the other hand, Ref. [3,25,31,32,33] seemed to support the Y-type flux-tube picture [10,20] rather than the ∆-type one. These controversial results may be due to the difficulty of the accurate measurement of the 3Q ground-state potential in lattice QCD. For instance, in Refs.[24,26], the authors did not use the smearing for ground-state enhancement, and therefore their results may include serious contamination from the excited-state component. In Refs.[27,28,29], the author showed a preliminary result only on the equilateral-triangle case without the fit analysis.In this paper, for more than 300 different patterns of the 3Q system, we perform the accurate measurement of the static 3Q potential in SU(3) lattice QCD at β=5.7, 5.8 and 6.0, using the smearing method to remove the excited-state contaminations and to obtain the true ground-state potential. The contents are organized as follows. In Section 2, we make a brief theoretical consideration on the form of the inter-quark potential based on QCD. In Section 3, we explain the method of the lattice QCD measurement of the 3Q potential, referring the importance of the smearing technique and its physical meaning. In Section 4, we present the lattice QCD data of the 3Q potential, which are accurately measured from the smeared 3Q Wilson loop in a model-independent manner. In Section 5, we perform the fit analysis of the lattice data with the Y-...

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The static penta-quark (5Q) potential V5Q is studied in SU(3) lattice QCD with 16 3 × 32 and β=6.0 at the quenched level. From the 5Q Wilson loop, V5Q is calculated in a gauge-invariant manner, with the smearing method to enhance the ground-state component. V5Q is well described by the OGE plus multi-Y Ansatz: a sum of the OGE Coulomb term and the multi-Y-type linear term proportional to the minimal total length of the flux-tube linking the five quarks. Comparing with QQ and 3Q potentials, we find a universality of the string tension, σ QQ ≃ σ3Q ≃ σ5Q, and the OGE result for Coulomb coefficients.