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Register a new userDynamics of in-medium quarkonia in SU(3) and SU(2) gauge theories
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Decoherence dynamics of quarkonia is studied in the high-temperature deconfined phase of SU($N_c$) gauge theories. In particular, we analyze the symmetry properties of SU($N_c$) stochastic potential model and find a novel event-by-event symmetry for $N_c=2$ case, similar to the $G$-parity of hadronic systems. This novel symmetry constrains the relation between diagonal and off-diagonal components of quarkonium density matrix, leaving the latter to be finite at late times. We also present one-dimensional numerical simulation of the model, which indicates the usefulness of the complex potential simulations for the quarkonium survival probabilities in relativistic heavy-ion collisions, provided that the effect of dissipation can be neglected.
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We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory on Kaehler manifolds of the form M x SU(3)/H, with H = SU(2) x U(1) or H = U(1) x U(1). The induced rank two quiver gauge theories on M are worked out in detail for representations of H which descend from a generic irreducible SU(3)-representation. The reduction of the Donaldson-Uhlenbeck-Yau equations on these spaces induces nonabelian quiver vortex equations on M, which we write down explicitly. When M is a noncommutative deformation of the space C^d, we construct explicit BPS and non-BPS solutions of finite energy for all cases. We compute their topological charges in three different ways and propose a novel interpretation of the configurations as states of D-branes. Our methods and results generalize from SU(3) to any compact Lie group.
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 investigate the quantum entanglement entropy for the four-dimensional Euclidean SU(3) gauge theory. We present the first non-perturbative calculation of the entropic $c$-function ($C(l)$) of SU(3) gauge theory in lattice Monte Carlo simulation using the replica method. For $0 leqslant l leqslant 0.7$~fm, where $l$ is the length of the subspace, the entropic $c$-function is almost constant, indicating conformally invariant dynamics. The value of the constant agrees with that perturbatively obtained from free gluons, with 20 % discrepancy. When $l$ is close to the Hadronic scale, the entropic $c$-function decreases smoothly, and it is consistent with zero within error bars at $l gtrsim 0.9$ fm.
In $SU(N)$ gauge theory, it is argued recently that there exists a mixed anomaly between the CP symmetry and the 1-form $mathbb{Z}_N$ symmetry at $theta=pi$, and the anomaly matching requires CP to be spontaneously broken at $theta=pi$ if the system is in the confining phase. In this paper, we elaborate on this discussion by examining the large volume behavior of the partition functions of the $SU(N)/mathbb{Z}_N$ theory on $T^4$ a la t Hooft. The periodicity of the partition function in $theta$, which is not $2pi$ due to fractional instanton numbers, suggests the presence of a phase transition at $theta=pi$. We propose lattice simulations to study the distribution of the instanton number in $SU(N)/mathbb{Z}_N$ theories. A characteristic shape of the distribution is predicted when the system is in the confining phase. The measurements of the distribution may be useful in understanding the phase structure of the theory.
We investigate SU(3) gauge theories in four dimensions with Nf fundamental fermions, on a lattice using the Wilson fermion. Clarifying the vacuum structure in terms of Polyakov loops in spatial directions and properties of temporal propagators using a new method local analysis, we conjecture that the conformal region exists together with the confining region and the deconfining region in the phase structure parametrized by beta and K, both in the cases of the large Nf QCD within the conformal window (referred as Conformal QCD) with an IR cutoff and small Nf QCD at T/Tc>1 with Tc being the chiral transition temperature (referred as High Temperature QCD). Our numerical simulation on a lattice of the size 16^3 x 64 shows the following evidence of the conjecture. In the conformal region we find the vacuum is the nontrivial Z(3) twisted vacuum modified by non-perturbative effects and temporal propagators of meson behave at large t as a power-law corrected Yukawa-type decaying form. The transition from the conformal region to the deconfining region or the confining region is a sharp transition between different vacua and therefore it suggests a first order transition both in Conformal QCD and in High Temperature QCD. Within our fixed lattice simulation, we find that there is a precise correspondence between Conformal QCD and High Temperature QCD in the temporal propagators under the change of the parameters Nf and T/Tc respectively. In particular, we find the correspondence between Conformal QCD with Nf = 7 and High Temperature QCD with Nf=2 at T ~ 2 Tc being in close relation to a meson unparticle model. From this we estimate the anomalous mass dimension gamma* = 1.2 (1) for Nf=7. We also show that the asymptotic state in the limit T/Tc --> infty is a free quark state in the Z(3) twisted vacuum.
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