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Chiral symmetry breaking from five dimensional spaces

Leandro Da Rold, Alex Pomarol

TL;DR

This work presents a five dimensional AdS-like model that realizes chiral symmetry breaking in QCD via a bulk scalar and chiral gauge fields. By computing current correlators, meson spectra, and the chiral Lagrangian parameters L_i, the authors show quantitative agreement with experimental data within ~30% for reasonable parameter choices and derive robust relations such as M_ρ^2 ≈ 3 g_{ρππ}^2 F_π^2 and F_ρ ≈ √3 F_π, as well as a vector meson dominated pion form factor. The framework naturally yields vector meson dominance and tree-level zero for BR(a1 → π γ), with predictions remaining stable under infrared metric variations; it also provides a tractable path to explore electroweak symmetry breaking and the S parameter via an operator of dimension d. An appendix generalizes the results to chiral breaking induced by operators of dimension d, highlighting the S parameter’s sensitivity to d, while maintaining the overall phenomenological success of the holographic approach.

Abstract

Based on the AdS/CFT correspondence we study the breaking of the chiral symmetry in QCD using a simple five dimensional model. The model gives definite predictions for the spectrum of vector mesons, their decay constants and interactions as a function of one parameter related to the quark condensate. We calculate the coefficients $L_i$ of the low-energy QCD chiral lagrangian, as well as other physical quantities for the pions. All the predictions are shown to be in good agreement with the experimental data. We also show that they are robust under modifications of the 5D metric in the IR, and that some of them arise as a consequence of the higher-dimensional gauge symmetry. For example, at the tree-level, we find $M_ρ\simeq \sqrt{3} g_{ρππ} F_π$, $F_ρ\simeq \sqrt{3} F_π$ and BR($a_1\to πγ)=0$.

Chiral symmetry breaking from five dimensional spaces

TL;DR

This work presents a five dimensional AdS-like model that realizes chiral symmetry breaking in QCD via a bulk scalar and chiral gauge fields. By computing current correlators, meson spectra, and the chiral Lagrangian parameters L_i, the authors show quantitative agreement with experimental data within ~30% for reasonable parameter choices and derive robust relations such as M_ρ^2 ≈ 3 g_{ρππ}^2 F_π^2 and F_ρ ≈ √3 F_π, as well as a vector meson dominated pion form factor. The framework naturally yields vector meson dominance and tree-level zero for BR(a1 → π γ), with predictions remaining stable under infrared metric variations; it also provides a tractable path to explore electroweak symmetry breaking and the S parameter via an operator of dimension d. An appendix generalizes the results to chiral breaking induced by operators of dimension d, highlighting the S parameter’s sensitivity to d, while maintaining the overall phenomenological success of the holographic approach.

Abstract

Based on the AdS/CFT correspondence we study the breaking of the chiral symmetry in QCD using a simple five dimensional model. The model gives definite predictions for the spectrum of vector mesons, their decay constants and interactions as a function of one parameter related to the quark condensate. We calculate the coefficients of the low-energy QCD chiral lagrangian, as well as other physical quantities for the pions. All the predictions are shown to be in good agreement with the experimental data. We also show that they are robust under modifications of the 5D metric in the IR, and that some of them arise as a consequence of the higher-dimensional gauge symmetry. For example, at the tree-level, we find , and BR(.

Paper Structure

This paper contains 9 sections, 70 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. A 5D model for chiral symmetry breaking
  3. Vector, axial-vector and PGB sectors
  4. The current-current correlators $\Pi_{V,A}$
  5. Vector meson interactions
  6. The electromagnetic form factor of the pion
  7. The effective lagrangian for the $\rho$ meson
  8. The chiral lagrangian for the PGB
  9. Conclusions

Figures (5)

  • Figure 1: Mass of the first axial-vector resonance as a function of $\xi$. The solid line is the exact result, while the dashed line corresponds to the approximate value coming from Eq. (\ref{['massa1']}). The shadow band shows the experimental value $M_{a_1}=1230\pm 40$ MeV.
  • Figure 2: Wave-function of the $n=1,2$ vector resonance, the $n=1$ axial-vector resonance and the PGB.
  • Figure 3: Coupling of the $n=1,2,3$ vector resonance to two PGB. We also show the approximate value for $n=1$ given by $g_{1\pi\pi}^{app}=M_{V_1}/(\sqrt{3}\,F_{\pi})$ -see Eq. (\ref{['KSRF2']}).
  • Figure 4: Electromagnetic pion form factor as a function of the transfer momentum $p$ for $\xi=4$. The solid line is the exact result, while the dashed line is obtained by considering only the rho meson (VMD).
  • Figure 5: Predictions of the model for some physical quantities as a function of $\xi$ divided by their experimental value. We have taken $M_q=0$.