QCD sum rules for hyperon-nucleon interactions

We investigate the hyperon-nucleon interactions in the QCD sum rule starting from the nucleon matrix element of the hyperon correlation function. Through the dispersion relation, the correlation function in the operator product expansion (OPE) is related with its integral over the physical energy region. The dispersion integral around the hyperon-nucleon ($YN$) threshold is identified as a measure of the interaction strength in the $YN$ channel. The Wilson coefficients of the OPE for the hyperon correlation function are calculated. The obtained sum rules relate $YN$ interaction strengths to the nucleon matrix elements of the quark-gluon composite operators, which include strange quark operators as well as up and down quark operators. It is found that the $YN$ interaction strengths are smaller than the $NN$ interaction strength since the nucleon matrix elements of strange quark operators are smaller than those of up and down quark operators. Among $YN$ channels $\Lambda N$ channel has stronger interaction than $\Sigma N$ and $\Xi N$ channels. Also found is that the interaction strength is greater in the $\Sigma^+N$ ($\Xi^0 N$) channel than in the $\Sigma^-N$ ($\Xi^-N$) channel since the nucleon matrix elements of up quark operators are greater than those of down quark operators. The spin-dependent part is much smaller than the spin-independent part in the $YN$ and $NN$ channels. The results of the sum rules are compared with those of the phenomenological meson-exchange models.Comment: number of pages:28, number of figures:

A projected correlation function approach to the pi NN coupling constant in QCD sum rules

We propose a new approach to construct QCD sum rules for the pi NN coupling constant, g, starting from the vacuum-to-pion correlation function of the interpolating fields of two nucleons and taking its matrix element with respect to nucleon spinors. The new approach with the projected correlation function is advantageous because even in the chiral limit the dispersion integral can be parametrized with well-defined physical parameters. Another advantage of the new approach is that unwanted pole contribution is projected out. Calculating the Wilson coefficients of the operator product expansion of the correlation function up to O(M_B^{-4}) and O(m_pi) where M_B and m_pi are the Borel mass and the pion mass, respectively, we construct new QCD sum rules for the pi NN coupling constant from the projected correlation function with consistently including O(m_pi) corrections. By numerically analyzing the obtained four sum rules we identified the most prominent one. After roughly estimating errors we obtaind, g=10 +/- 3, as a result of this sum rule, which is in reasonable agreement with the empirical value. It is also found that the O(m_pi) correction is about 5%.Comment: 24 pages, 4 figure

A Study of Degenerate Two-Body and Three-Body Coupled-Channel Systems -Renormalized Effective AGS Equations and Near-Threshold Resonances-

Motivated by the existence of candidates for exotic hadrons whose masses are close to both of two-body and three-body hadronic thresholds lying close to each other, we study degenerate two-body and three-body coupled-channel systems. We first formulate the scattering problem of non-degenerate two-body and three-body coupled-channels as an effective three-body problem, i.e.\ effective Alt-Grassberger-Sandhas (AGS) equations. We next investigate the behavior of $S$-matrix poles near the threshold when two-body and three-body thresholds are degenerate. We solve the eigenvalue equations of the kernel of AGS equations instead of AGS equations themselves to obtain the $S$-matrix pole energy. We then face a problem of unphysical singularity: though the physical transition amplitudes have physical singularities only, the kernel of AGS equations have unphysical singularities. We show, however, that these unphysical singularities can be removed by appropriate reorganization of the scattering equations and mass renormalization. The behavior of $S$-matrix poles near the degenerate threshold is found to be universal in the sense that the complex pole energy, $E$, is determined by a real parameter, $c$, as $c - E \log{\left( - E \right)} = 0$, or equivalently, ${\rm Im} E = - \pi {\rm Re} E / \log{\mid {\rm Re} E \mid}$. This behavior is different from that of either two-body or three-body system and is characteristic in the degenerate two-body and three-body coupled-channel system. We expect that this new class of universal behavior might play a key role in understanding exotic hadrons.Comment: 26 pages, 12 figure

Renormalization group equations in a model of generalized hidden local symmetry and restoration of chiral symmetry

We study possible restoration patterns of chiral symmetry in a generalized hidden local symmetry model, which is a low energy effective theory of QCD including pseudo-scalar, vector and axial-vector mesons. We derive Wilsonian renormalization group equations and analyze the running couplings and their fixed points at the chiral restoration point. We find three types of the chiral restoration, which are classified as the standard, vector manifestation and intermediate scenarios, respectively. It turns out that the rho and A_1 meson become massless and their decay into pion is suppressed in all the restoration patterns. The each restoration scenario violates or fulfills the vector meson dominance at the critical point in a different manner, which may reflect on the contributions from the pion to the dilepton spectrum

New Universality for Near-Threshold Three-Body Resonances

In the three-body system with one resonantly interacting pair, we study the behavior of the $S$-matrix pole near the threshold in the fourth quadrant of the unphysical complex energy plane. Our study is essentially based on the unitarity and analyticity of the $S$-matrix and employs the Alt-Grassberger-Sandhas (AGS) equations specifically for the three-body scattering problem and the dispersion relation for the inverse $T$-matrix. We find that the trajectory of the complex energy, $E$, of the $S$-matrix pole near the threshold is uniquely given by $c_0 + E \log{\left( - E \right)} \approx 0$ or $c_0 + E_R \log E_R \approx 0$, $E_I \approx \pi E_R/\log E_R$ in the fourth quadrant of the unphysical complex energy plane, in contrast to the non-unique trajectories with no resonantly interacting pair, $c_0 + c_1 E + E^2 \log{\left( - E \right)} \approx 0$ or $E_R \approx -c_0/c_1$, $E_I \approx -\pi E_R^2/c_1$ where $E_R$ and $E_I$ are the real and imaginary parts of $E$, respectively, and $c_0$ and $c_1$ are real constants. This is a new universal behavior of the $S$-matrix near the threshold. Also, we briefly discuss implications to exotic hadron candidates.Comment: 7 pages, 2 figure

Momentum dependence of the spectral functions in the O(4) linear sigma model at finite temperature

The spatial momentum dependence of the spectral function for pi and sigma at finite temperature is studied by employing the O(4) linear sigma model and adopting a resummation technique called optimized perturbation theory (OPT).Comment: 25 pages,12 figure

Shear viscosity of a hadronic gas mixture

We discuss in detail the shear viscosity coefficient eta and the viscosity to entropy density ratio eta/s of a hadronic gas comprised of pions and nucleons. In particular, we study the effects of baryon chemical potential on eta and eta/s. We solve the relativistic quantum Boltzmann equations with binary collisions (pi pi, pi N, and NN) for a state slightly deviated from thermal equilibrium at temperature T and baryon chemical potential mu. The use of phenomenological amplitudes in the collision terms, which are constructed to reproduce experimental data, greatly helps to extend the validity region in the T-mu plane. The total viscosity coefficient eta(T,mu)=eta^pi + eta^N increases as a function of T and mu, indirectly reflecting energy dependences of binary cross sections. The increase in mu direction is due to enhancement of the nucleon contribution eta^N while the pion contribution eta^pi diminishes with increasing mu. On the other hand, due to rapid growth of entropy density, the ratio eta/s becomes a decreasing function of T and mu in a wide region of the T-mu plane. In the kinematical region we investigated T < 180MeV, mu < 1GeV, the smallest value of eta/s is about 0.3. Thus, it never violates the conjectured lower bound eta/s= 1/4pi ~ 0.1. The smallness of eta/s in the hadronic phase and its continuity at T ~ T_c (at least for crossover at small mu) implies that the ratio will be small enough in the deconfined phase T > T_c. There is a nontrivial structure at low temperature and at around normal nuclear density. We examine its possible interpretation as the liquid-gas phase transition.Comment: 19 pages, 13 figures, reference added, figure 8 updated, minor change in the tex

Axial Vector Tetraquark with Two s-quarks

Possibility of an axial vector isoscalar tetraquark $ud\bar{s}\bar{s}$ is discussed. If a $f_1$ meson in the mass region $1.4-1.5$ GeV consists of four quarks $ns\bar{n}\bar{s}$, the mass of the isoscalar $ud\bar{s}\bar{s}$($\vartheta^+$-meson) state with $J^P=1^+$ is expected to be lower than that of the $f_1$ meson. Within a flux-tube quark model, a possible resonant state of $ud\bar{s}\bar{s}(J^{P}=1^{+})$ is suggested to appear at $\sim$ 1.4 GeV with the width ${\cal{O}}(20\sim 50)$ MeV. We propose that the $\vartheta^+$-meson is the good candidate for the tetraquark search, which would be observed in the $K^+K^+\pi^-$ decay channel.Comment: prepared for Yukawa International Seminars "New Frontiers in QCD" (YKIS2006), Nov. 20-Dec. 8, 2006, Kyoto, Japan, to appear in Prog. Theor. Phys. Supp

I=2 π\pi-π\pi scattering length with dynamical overlap fermion

We report on a lattice QCD calculation of the I=2 $\pi\pi$ scattering length using the overlap fermion formulation for both sea and valence quarks. We investigate the consistency of the lattice data with the prediction of the next-to-next-to-leading order chiral perturbation theory after correcting finite volume effects. The calculation is performed on gauge ensembles of two-flavor QCD generated by the JLQCD collaboration on a $16^3\times 32$ lattice at a lattice spacing $\sim$ 0.12 fm.Comment: 25 pages, 7 figure

Microscopic identification of dissipative modes in relativistic field theories

We present an argument to support the existence of dissipative modes in relativistic field theories. In an O(N) $\varphi^4$ theory in spatial dimension $d\le 3$, a relaxation constant $\Gamma$ of a two-point function in an infrared region is shown to be finite within the two-particle irreducible (2PI) framework at the next-leading order (NLO) of 1/N expansion. This immediately implies that a slow dissipative mode with a dispersion p_0\sim i\Gamma \p^2 is microscopically identified in the two-point function. Contrary, NLO calculation in the one-particle irreducible (1PI) framework fails to yield a finite relaxation constant. Comparing the results in 1PI and 2PI frameworks, one concludes that dissipation emerges from multiple scattering of a particle with a heat bath, which is appropriately treated in the 2PI-NLO calculation through the resummation of secular terms to improve long-time behavior of the two-point function. Assuming that this slow dissipative mode survives at the critical point, one can identify the dynamic critical exponent $z$ for the two-point function as $z=2-\eta$. We also discuss possible improvement of the result.Comment: 16 pages, 11 figure