Light baryon spectra and Regge trajectories from anomalous holographic hard wall models

Abstract

In this work we propose anomalous versions of the holographic hard wall (HW) model to describe the spectra of light baryons of spin 1/2 and 3/2, and obtain their Regge trajectories. The anomalous contributions to the dimensions of the baryonic operators of logarithm form come from a semiclassical analysis of the AdS/CFT correspondence and were used recently for glueballs and light unflavoured mesons. Inspired by these results, we first propose an anomalous dimension of the form $\Delta_{\rm anom.}=a\ln L +b$, where $a$ and $b$ are phenomenological constants to be adjusted numerically to better fit the experimental data of the PDG, and $L$ is the angular momentum of each baryonic state. Second, we discuss the case where the anomalous dimension also depends on the spin $S$ as $\Delta_{\rm anom.}=a\ln (L+S+1/2) +b$, and fix the parameters $a$ and $b$ targeting PDG data. These two models, called AHW$_1$ and AHW$_2$, give better results for light baryon masses $(M)$ in comparison with the original HW model and show approximately linear Regge trajectories $(M^2\times L)$. We also consider a third anomalous HW model in which the dimension of the baryonic operator increases as $\Delta_{\rm Lin.}=a L^c +b$, where $a$, $b$, and $c$ are constants adjusted to fit the light baryonic masses of PDG. Apart from compatible masses with PDG data, this case produces Regge trajectories that are asymptotically linear.