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

Rafael A. Costa-Silva, Henrique Boschi-Filho

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 $Δ_{\rm anom.}=a\ln L +b$, 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 $Δ_{\rm anom.}=a\ln (L+S+1/2) +b$, 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 $Δ_{\rm Lin.}=a L^c +b$, 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.

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 , where and are phenomenological constants to be adjusted numerically to better fit the experimental data of the PDG, and is the angular momentum of each baryonic state. Second, we discuss the case where the anomalous dimension also depends on the spin as , and fix the parameters and targeting PDG data. These two models, called AHW and AHW, give better results for light baryon masses in comparison with the original HW model and show approximately linear Regge trajectories . We also consider a third anomalous HW model in which the dimension of the baryonic operator increases as , where , , and 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.
Paper Structure (11 sections, 62 equations, 4 figures, 8 tables)

This paper contains 11 sections, 62 equations, 4 figures, 8 tables.

Table of Contents

  1. Introduction
  2. PDG data and Statistical definitions
  3. Brief review of fermions in AdS space
  4. Fermions with spin $1/2$
  5. Fermions with spin $3/2$
  6. A Hard wall model and Anomalous versions
  7. Hard Wall Model
  8. Anomalous Hard Wall Models
  9. Numerical Results for the HW and AHW models
  10. Linear Anomalous Hard Wall
  11. Discussion and Conclusions

Figures (4)

  • Figure 1: Regge trajectories ($M^2\times L$) obtained from the HW model from equations (\ref{['M_+;1/2HW']})-(\ref{['M_-;3/2HW']}), respectively with colors blue (dot-dashed), black(dot-dashed), red (dashed), and grey (dashed), for delta resonances (upper panel) and nucleon resonances (lower panel), with masses $M$ expressed in GeV. As explained in the text, the delta resonances only present states with spin 1/2 with negative parity and spin 3/2 with positive parity, which in the HW are degenerate. Note that the trajectories corresponding to Eqs. \ref{['M_-;1/2HW']} (black/dot-dashed) and \ref{['M_+;3/2HW']} (red/dashed) coincide in both panels. We also present the corresponding experimental values (dots) obtained from the PDG. Each point of a given color corresponds to the trajectory of the same color.
  • Figure 2: Regge trajectories ($M^2\times L$) obtained from the AHW1 model, with anomalous dimension, Eq. (\ref{['deltaanom1']}), from equations (\ref{['M_+;1/2AHW']})-(\ref{['M_-;3/2AHW']}), respectively with colors blue (dot-dashed), black(dot-dashed), red (dashed), and grey (dashed), for delta resonances (upper panel) and nucleon resonances (lower panel), with masses $M$ expressed in GeV. As explained in the text, the delta resonances only present states with spin 1/2 with negative parity and spin 3/2 with positive parity, which in the AHW1 are degenerate. Note that the trajectories corresponding to Eqs. \ref{['M_-;1/2AHW']} (black/dot-dashed) and \ref{['M_+;3/2AHW']} (red/dashed) coincide in both panels. We also present the corresponding experimental values (dots) obtained from the PDG. Each point of a given color corresponds to the trajectory of the same color.
  • Figure 3: Regge trajectories ($M^2\times L$) obtained from the AHW2 model, with anomalous dimension, Eq. (\ref{['deltaanom2']}), from equations (\ref{['M_+;1/2AHW']})-(\ref{['M_-;3/2AHW']}), respectively with colors blue (dot-dashed), black(dot-dashed), red (dashed), and grey (dashed), for delta resonances (upper panel) and nucleon resonances (lower panel), with masses $M$ expressed in GeV. As explained in the text, the delta resonances only present states with spin 1/2 with negative parity and spin 3/2 with positive parity. In both panels, we also present the corresponding experimental values (dots) obtained from the PDG. Each point of a given color corresponds to the trajectory of the same color.
  • Figure 4: Regge trajectories ($L\times M^2$) for baryons, with masses $M$ expressed in GeV, from the anomalous linear hard wall model, obtained from equations (\ref{['M_+;1/2ALHW']})-(\ref{['M_-;3/2ALHW']}), respectively with colors blue (dot-dashed), black (dashed), red (dot-dashed), and grey (dashed). Note that the trajectories corresponding to Eqs. \ref{['M_-;1/2ALHW']} (black) and \ref{['M_+;3/2ALHW']} (red) coincide. Upper panel: Delta resonances; Lower panel: Nucleon resonances. In both cases, we also present the points corresponding to the experimental values obtained from the PDG. Each point of a given color corresponds to the trajectory of the same color.