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-...

We study charmonium correlators in pseudoscalar and vector channels at finite temperature using lattice QCD simulation in the quenched approximation. Anisotropic lattices are used in order to have sufficient numbers of degrees of freedom in the Euclidean temporal direction. We focus on the low energy structure of the spectral function, corresponding to the ground state in the hadron phase, by applying the smearing technique to enhance the contribution to the correlator from this region. We employ two analysis procedures: the maximum entropy method (MEM) for the extraction of the spectral function without assuming a specific form, to estimate the shape of the spectral function, and the standard χ 2 fit analysis using typical forms in accordance with the result of MEM, for a more quantitative evaluation. To verify the applicability of the procedures, we first analyze the smeared correlators as well as the point correlators at zero temperature. We find that by shortening the t-interval used for the analysis (a situation inevitable at T > 0) the reliability of MEM for point correlators is lost, while it subsists for smeared correlators. Then the smeared correlators at T ≃ 0.9Tc and 1.1Tc are analyzed. At T ≃ 0.9Tc, the spectral function exhibits a strong peak, well approximated by a delta function corresponding to the ground state with almost the same mass as at T = 0. At T ≃ 1.1Tc, we find that the strong peak structure still persists at almost the same place as below Tc, but with a finite width of a few hundred MeV. This result indicates that the correlators possess a nontrivial structure even in the deconfined phase.

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We present the first results of our spatially axisymmetric core-collapse supernova simulations with full Boltzmann neutrino transport, which amount to a time-dependent 5-dimensional (2 in space and 3 in momentum space) problem in fact. Special relativistic effects are fully taken into account with a two-energy-grid technique. We performed two simulations for a progenitor of 11.2M ⊙ , employing different nuclear equations-of-state (EOS's): Lattimer and Swesty's EOS with the incompressibility of K = 220MeV (LS EOS) and Furusawa's EOS based on the relativistic mean field theory with the TM1 parameter set (FS EOS). In the LS EOS the shock wave reaches ∼ 700km at 300ms after bounce and is still expanding whereas in the FS EOS it stalled at ∼ 200km and has started to recede by the same time. This seems to be due to more vigorous turbulent motions in the former during the entire post-bounce phase, which leads to higher neutrino-heating efficiency in the neutrino-driven convection. We also look into the neutrino distributions in momentum space, which is the advantage of the Boltzmann transport over other approximate methods. We find non-axisymmetric angular distributions with respect to the local radial direction, which also generate off-diagonal components of the Eddington tensor. We find that the rθ-component reaches ∼ 10% of the dominant rr-component and, more importantly, it dictates the evolution of lateral neutrino fluxes, dominating over the θθ-component, in the semi-transparent region. These data will be useful to further test and possibly improve the prescriptions used in the approximate methods.