Highly excited mesons, linear Regge trajectories, and the pattern of the chiral symmetry realization

Abstract

The chiral symmetry of QCD shows up in the linear Weyl-Wigner mode at short Euclidean distances or at high temperatures. On the other hand, low-lying hadronic states exhibit the nonlinear Nambu-Goldstone mode. An interesting question was raised as to whether the linear realization of the chiral symmetry is asymptotically restored for highly excited states. We address it in a number of ways. On the phenomenological side we argue that to the extent the meson Regge trajectories are observed to be linear and equidistant, the Weyl-Wigner mode is not realized. This picture is supported by quasiclassical arguments implying that the quark spin interactions in high excitations are weak, the trajectories are linear, and there is no chiral symmetry restoration. Then we use the string/gauge duality. In the top-down Sakai-Sugimoto construction the nonlinear realization of the chiral symmetry is built in. In the bottom-up AdS/QCD construction by Erlich et al., and Karch et al. the situation is more ambiguous. However, in this approach linearity and equidistance of the Regge trajectories can be naturally implemented, with the chiral symmetry in the Nambu-Goldstone mode.Asymptotic chiral symmetry restoration might be possible if a nonlinearity (convergence) of the Regge trajectories in an "intermediate window" of n, J, beyond the explored domain, takes place. This would signal the failure of the quasiclassical picture.

Thermodynamics of SU(N) Yang-Mills theories in 2 + 1 dimensions II — The deconfined phase

“…Later, in [91], it was claimed that this model was inconsistent with the OPEs, but the arguments of [91] were called into question in [92], due to subtleties in the regularization of infinite sums like (4.21). More recently, works like [93][94][95] claim that the Regge slopes should be equal whereas the opposite conclusion was reached in [96][97][98]. We have found above that in our model, there are different asymptotic Regge slopes Λ A > Λ V .…”

Mesons in gauge/gravity duals

“…The basic AdS/QCD model does not have the expected Regge behaviour for the towers of radially excited states (M 2 n ∼ n) [261][262][263][264]. To see this, consider the action for the gauge field in AdS describing the rho mesons, If we impose the IR boundary by putting in a hard cut-off then the Schrödinger potential in the IR is that of a square well.…”

Massive holographic QCD in the Veneziano limit

“…The speed of the convergence is best visible 21 The question whether the slopes should be the same in QCD is unsettled [131][132][133][134][135][136][137][138][139], but usually they are assumed to be, which can be obtained for potentials I by changing the IR asymptotics of w(λ) [42].…”