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Register a new userCorrections to the ${bf SU(3)times SU(3)}$ Gell-Mann-Oakes-Renner relation and chiral couplings $L^r_8$ and $H^r_2$
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Next to leading order corrections to the $SU(3) times SU(3)$ Gell-Mann-Oakes-Renner relation (GMOR) are obtained using weighted QCD Finite Energy Sum Rules (FESR) involving the pseudoscalar current correlator. Two types of integration kernels in the FESR are used to suppress the contribution of the kaon radial excitations to the hadronic spectral function, one with local and the other with global constraints. The result for the pseudoscalar current correlator at zero momentum is $psi_5(0) = (2.8 pm 0.3) times 10^{-3} GeV^{4}$, leading to the chiral corrections to GMOR: $delta_K = (55 pm 5)%$. The resulting uncertainties are mostly due to variations in the upper limit of integration in the FESR, within the stability regions, and to a much lesser extent due to the uncertainties in the strong coupling and the strange quark mass. Higher order quark mass corrections, vacuum condensates, and the hadronic resonance sector play a negligible role in this determination. These results confirm an independent determination from chiral perturbation theory giving also very large corrections, i.e. roughly an order of magnitude larger than the corresponding corrections in chiral $SU(2) times SU(2)$. Combining these results with our previous determination of the corrections to GMOR in chiral $SU(2) times SU(2)$, $delta_pi$, we are able to determine two low energy constants of chiral perturbation theory, i.e. $L^r_8 = (1.0 pm 0.3) times 10^{-3}$, and $H^r_2 = - (4.7 pm 0.6) times 10^{-3}$, both at the scale of the $rho$-meson mass.
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The next to leading order chiral corrections to the $SU(2)times SU(2)$ Gell-Mann-Oakes-Renner (GMOR) relation are obtained using the pseudoscalar correlator to five-loop order in perturbative QCD, together with new finite energy sum rules (FESR) incorporating polynomial, Legendre type, integration kernels. The purpose of these kernels is to suppress hadronic contributions in the region where they are least known. This reduces considerably the systematic uncertainties arising from the lack of direct experimental information on the hadronic resonance spectral function. Three different methods are used to compute the FESR contour integral in the complex energy (squared) s-plane, i.e. Fixed Order Perturbation Theory, Contour Improved Perturbation Theory, and a fixed renormalization scale scheme. We obtain for the corrections to the GMOR relation, $delta_pi$, the value $delta_pi = (6.2, pm 1.6)%$. This result is substantially more accurate than previous determinations based on QCD sum rules; it is also more reliable as it is basically free of systematic uncertainties. It implies a light quark condensate $<0|bar{u} u|0> simeq <0|bar{d} d|0> equiv <0|bar{q} q|0>|_{2,mathrm{GeV}} = (- 267 pm 5 MeV)^3$. As a byproduct, the chiral perturbation theory (unphysical) low energy constant $H^r_2$ is predicted to be $H^r_2 ( u_chi = M_rho) = - (5.1 pm 1.8)times 10^{-3}$, or $H^r_2 ( u_chi = M_eta) = - (5.7 pm 2.0)times 10^{-3}$.
Above a pseudocritical temperature of chiral symmetry restoration T_c the energy and the pressure are very far from the quark-gluon-plasma limit (i.e. ideal gas of free quarks and gluons). At the same time very soon above T_c fluctuations of conserved charges behave as if quarks were free particles. Within the T_c - 3T_c interval a chiral spin symmetry emerges in QCD which is not consistent with free quarks and suggests that degrees of freedom are chirally symmetric quarks bound into the color-singlet objects by the chromoelectric field. Here we analyse temporal and spatial correlators in this interval and demonstrate that they indicate simultaneously the chiral spin symmetry as well as absence of the interquark interactions in channels constrained by a current conservation. The latter channels are responsible for both fluctuations of conserved charges and for dileptons. Assuming that a SU(2)_color subgroup of SU(3)_color is deconfined soon above T_c but confinement persits in SU(3)_color/SU(2)_color in the interval T_c - 3T_c we are able to reconcile all empirical facts listed above.
Treating the strange quark mass as a heavy scale compared to the light quark mass, we perform a matching of the nucleon mass in the SU(3) sector to the two-flavor case in covariant baryon chiral perturbation theory. The validity of the $19$ low-energy constants appearing in the octet baryon masses up to next-to-next-to-next-to-leading order~cite{Ren:2014vea} is supported by comparing the effective parameters (the combinations of the $19$ couplings) with the corresponding low-energy constants in the SU(2) sector~cite{Alvarez-Ruso:2013fza}. In addition, it is shown that the dependence of the effective parameters and the pion-nucleon sigma term on the strange quark mass is relatively weak around its physical value, thus providing support to the assumption made in Ref.~cite{Alvarez-Ruso:2013fza}.
We compute nonequilibrium dynamics of plasma instabilities in classical-statistical lattice gauge theory in 3+1 dimensions. The simulations are done for the first time for the SU(3) gauge group relevant for quantum chromodynamics. We find a qualitatively similar behavior as compared to earlier investigations in SU(2) gauge theory. The characteristic growth rates are about 25 % lower for given energy density, such that the isotropization process is slower. Measured in units of the characteristic screening mass, the primary growth rate is independent of the number of colors.
We explore a possibility to generate exotic hadrons dynamically in the scattering of hadrons. The s-wave scattering amplitude of an arbitrary hadron with the Nambu-Goldstone boson is constructed so as to satisfy the unitarity condition and the chiral low energy theorem. We find that the chiral interaction for the exotic channels is in most cases repulsive, and that the strength of the possible attractive interaction is uniquely determined. We show that the attractive interaction in exotic channels is not strong enough to generate a bound state, while the interaction in nonexotic channel generate bound states which are considered to be the origin of some resonances observed in nature.
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