Quartet of spin-3/2 baryons in chiral multiplet (1,1/2)⊕(1/2,1)(1, 1/2) \oplus (1/2, 1) with mirror assignment

We study the possible existence of chiral partners in the spin-\thalf sector of the baryon spectrum. We consider a quartet scheme where four spin-3/2 baryons, $P_{33}$, $D_{33}$, $D_{13}$ and $P_{13}$, group into higher-dimensional chiral multiplets (1, \half)\oplus (\half,1) with a mirror assignment. With an effective $SU(2)_R\times SU(2)_L$ Lagrangian, we derive constraints imposed by chiral symmetry together with the mirror assignment on the masses and coupling constants of the quartet. Using the effective Lagrangian, we try to find a set of baryons suitable for the chiral quartet. It turns out that two cases reasonably agree with the mass pattern of the quartet: ($\Delta(1600)$, $\Delta(1940)$, $N(1520)$, $N(1720)$) and ($\Delta(1920)$, $\Delta(1940)$, $N(2080)$, $N(1900)$).Comment: 23 pages, 1figures, 6tables. Published in Phys.Rev.D82:034007,201

Imaginary Chemical Potential Approach for the Pseudo-Critical Line in the QCD Phase Diagram with Clover-Improved Wilson Fermions

The QCD phase diagram is studied in the lattice QCD simulation with the imaginary chemical potential approach. We employ a clover-improved Wilson fermion action of two-flavors and a renormalization-group improved gauge action, and perform the simulation at an intermediate quark mass on a $8^3\times 4$ lattice. The QCD phase diagram in the imaginary chemical potential $\mu_I$ region is investigated by performing the simulation for more than 150 points on the $(\beta,\mu_I)$ plane. We find that the Roberge-Weiss phase transition at $\mu_I/T=\pi/3$ is first order and its endpoint is second order, which are identified by the phase of the Polyakov loop. We determine the pseudo-critical line from the susceptibility of the Polyakov loop modulus. We find a clear deviation from a linear dependence of the pseudo-critical line on $\mu_I^2$.Comment: 10 pages, 20 figures, 3 tables. Revtex4. References are added and, discussions are sharpene

Wilson Fermion Determinant in Lattice QCD

We present a formula for reducing the rank of Wilson fermions from $4 N_c N_x N_y N_z N_t$ to $4 N_c N_x N_y N_z$ keeping the value of its determinant. We analyse eigenvalues of a reduced matrix and coefficients $C_n$ in the fugacity expansion of the fermion determinant $\sum_n C_n (\exp(\mu/T))^n$, which play an important role in the canonical formulation, using lattice QCD configurations on a $4^4$ lattice. Numerically, $\log |C_n|$ varies as $N_x N_y N_z$, and goes easily over the standard numerical range; We give a simple cure for that. The phase of $C_n$ correlates with the distribution of the Polyakov loop in the complex plain. These results lay the groundwork for future finite density calculations in lattice QCD.Comment: 20 pages, 2 tables, 32 figure

Test for a universal behavior of Dirac eigenvalues in the complex Langevin method

We apply the complex Langevin (CL) method to a chiral random matrix theory (ChRMT) at non-zero chemical potential and study the nearest neighbor spacing (NNS) distribution of the Dirac eigenvalues. The NNS distribution is extracted using an unfolding procedure for the Dirac eigenvalues obtained in the CL method. For large quark mass, we find that the NNS distribution obeys the Ginibre ensemble as expected. For small quark mass, the NNS distribution follows the Wigner surmise for correct convergence case, while it follows the Ginibre ensemble for wrong convergence case. The Wigner surmise is physically reasonable from the chemical potential independence of the ChRMT. The Ginibre ensemble is known to be favored in a phase quenched QCD at finite chemical potential. Our result suggests a possibility that the originally universal behavior of the NNS distribution is preserved even in the CL method for correct convergence case.Comment: 11 pages, 14 figure