Quantum Chromodynamics with Many Flavors

We investigate the phase structure of lattice QCD for general number of flavors $N_F$. Based on numerical data combined with the results of the perturbation theory we propose the following picture: When $N_F \ge 17$, there is only one IR fixed point at vanishing gauge coupling, i.e., the theory in the continuum limit is trivial. On the other hand, when $16 \ge N_F \ge 7$, there is a non-trivial fixed point. Therefore, the theory is non-trivial with anomalous dimensions, however, without quark confinement. Theories which satisfy both quark confinement and spontaneous chiral symmetry breaking in the continuum limit exist only for $N_F \le 6$.Comment: Talk presented by K. Kanaya at the 1997 Yukawa International Seminar (YKIS'97) on ``Non-Perturbative QCD --- Structure of the QCD Vacuum ---'', YITP, Kyoto, Japan, 2--12 Dec. 1997. To be published in the proceedings [Prog. Theor. Phys. Suppl.

Towards the QCD equation of state at the physical point using Wilson fermion

We study the (2+1)-flavor QCD at nonzero temperatures using nonperturbatively improved Wilson quarks of the physical masses by the fixed scale approach. We perform physical point simulations at finite temperatures with the coupling parameters which were adopted by the PACS-CS Collaboration in their studies using the reweighting technique. Zero temperature values are obtained on the PACS-CS configurations which are open to the public on the ILDG/JLDG. Finite temperature configurations are generated with the RHMC algorithm. The lattice sizes are $32^3 \times N_t$ with $N_t=14$, 13, $\cdots$, 4 which correspond to $T \approx 160$--550 MeV. We present results of some basic observables at these temperatures and the status of our calculation of the equation of state.Comment: 7 pages, 3 figures, proceedings of the 33rd International Symposium on Lattice Field Theory, July 14-18, 2015, Kobe, Japa

Phase structure of QCD for general number of flavors

We investigate and elucidate the phase structure of QCD for general number of flavors $N_F$ with Wilson quarks, varying $N_F$ from 2 up to 300. Based on numerical results combined with the result of the perturbation theory we propose the following picture: When $N_F \ge 17$, there is only a trivial fixed point and therefore the theory in the continuum limit is trivial. On the other hand, when $16 \ge N_F \ge 7$, there is a non-trivial fixed point and therefore the theory is non-trivial with anomalous dimensions, however, without quark confinement. Theories which satisfy both quark confinement and spontaneous chiral symmetry breaking in the continuum limit exist only for $N_F \le 6$. We also discuss the structure of the deconfining phase at finite temperatures for the small number of flavors such as $N_F=2$ and 3, through a systematic study of it for general number of flavors.Comment: LaTeX, 7 pages, 10 PS figures, Talk presented at LATTICE96(poster) and LATTICE96(finite temperature

Equation of state in 2+1 flavor QCD with improved Wilson quarks by the fixed scale approach

We study the equation of state in 2+1 flavor QCD with nonperturbatively improved Wilson quarks coupled with the RG-improved Iwasaki glue. We apply the $T$-integration method to nonperturbatively calculate the equation of state by the fixed-scale approach. With the fixed-scale approach, we can purely vary the temperature on a line of constant physics without changing the system size and renormalization constants. Unlike the conventional fixed-$N_t$ approach, it is easy to keep scaling violations small at low temperature in the fixed scale approach. We study 2+1 flavor QCD at light quark mass corresponding to $m_\pi/m_\rho \simeq 0.63$, while the strange quark mass is chosen around the physical point. Although the light quark masses are heavier than the physical values yet, our equation of state is roughly consistent with recent results with highly improved staggered quarks at large $N_t$.Comment: 14 pages, 12 figures, v2: Table I and Figure 3 are corrected, reference updated. Main discussions and conclusions are unchanged, v3: version to appear in PRD, v4: reference adde

Finite Temperature QCD with Wilson Quarks: A Study with a Renormalization Group Improved Gauge Action

Finite temperature transition in lattice QCD with degenerate Wilson quarks is investigated on an $N_t=4$ lattice, using a renormalization group improved gauge action. We find the following for the $N_F=2$ case: 1) The transition is smooth for a wide range of the quark mass. 2) The chiral transition is continuous. 3) The chiral condensation well satisfies a scaling relation with the critical exponents of the 3 dimensional $O(4)$ spin model. For $N_F=3$, we find that the chiral transition is of first order.Comment: 4 pages (6 figures), Postscript file, Contribution to Lattice 95 proceeding

Finite-temperature chiral transitions in QCD with the Wilson quark action

We investigate the finite-temperature phase structure and the scaling of the chiral condensate in lattice QCD with two degenerate light quarks, using a renormalization group improved gauge action and the Wilson quark action. We obtain a phase diagram which is consistent with that from the parity-flavor breaking scenario. The scaling relation for the chiral condensate assuming the critical exponents and the scaling function of the three dimensional O(4) model is remarkably satisfied for a wide range of parameters. This indicates that the chiral transition in two flavor QCD is of second order in the continuum limit.Comment: LaTeX, 3 pages, 4 EPS figures, Talk presented at LATTICE97 (finite temperature

Finite temperature phase transition of two-flavor QCD with an improved Wilson quark action

We study the phase structure of QCD at finite temperatures with two flavors of dynamical quarks on a lattice with the size $N_s^3 \times N_t=16^3 \times 4$, using a renormalization group improved gauge action and a clover improved Wilson quark action. The simulations are made along the lines of constant physics determined in terms of $m_{\rm PS}/m_{\rm V}$ at zero-temperature. We show preliminary results for the spatial string tension in the high temperature phase.Comment: 7 pages, 7 figures, talk presented at Lattice 2006 (high temperature and density