On the role of cosmological constant in modeling hadrons

TL;DR

This work investigates how conformal symmetry breaking, encoded by an induced cosmological constant in a holographic AdS5/QCD framework, influences hadron spectra and chiral dynamics. By implementing hard-wall and soft-wall models with an induced 4D cosmological constant parameterized by $ω$, the authors solve for scalar, vector, and axial sectors and extract masses, decay constants, and a Gell-Mann–Oakes–Renner–type relation $m_π^2 f_π^2 = 2 m_q σ + \mathcal{F}(z_m, ω)$. A comprehensive $χ^2$ analysis shows that nonzero $ω$ provides better agreement with experimental data for the $ρ$ and $a_1$ systems, with best-fit values $ω \approx 0.037$ (hard wall) and $ω \approx 0.005$ (soft wall), and the GOR correction decreases inversely with $ω$, improving the accuracy of low-energy QCD predictions. The results suggest that incorporating an induced cosmological constant is a meaningful ingredient in holographic QCD, yielding more accurate hadron phenomenology and offering a deeper link between conformal symmetry breaking and nonperturbative hadron structure.

Abstract

Einsteins gravity with a cosmological constant $Λ$ in four dimensions can be reformulated as a $λφ^4$ theory characterized solely by the dimensionless coupling $λ\propto G_N Λ$ ($G_N$ being Newton's constant). The quantum triviality of this theory drives $λ\to 0$, and a deviation from this behavior could be generated by matter couplings. Here, we study the significance of this conformal symmetry and its breaking in modeling non-perturbative QCD. The hadron spectra and correlation functions are studied holographically in an $AdS_5$ geometry with induced cosmological constants on four-dimensional hypersurface. Our analysis shows that the experimentally measured spectra of the $ρ$ and $a_1$ mesons, including their excitations and decay constants, favour a non-vanishing induced cosmological constant in both hard-wall and soft-wall models. Although this behavior is not as sharp in the soft-wall model as in the hard-wall model, it remains consistent. Furthermore, we show that the correction to the Gell-Mann-Oakes-Renner relation has an inverse dependence on the induced cosmological constant, underscoring its significance in holographic descriptions of low-energy QCD.

Figures (8)

• Figure 1: $\chi^2$ computed with the observables in Table \ref{['Model_Results']} as a function of $\omega$, with minima $\approx 0.037$ with $z_m \approx 2.9 \text{GeV}^{-1}$. The minima is depicted as $(\textcolor{red}{\blacktriangledown})$.
• Figure 2: The figure shows the dependence of $z_m$ on $\omega$ after fixing $\rho$ meson mass in our model.
• Figure 3: Dependence axial-vector meson mass $m_{a1}$ and decay constants $F_{\rho}^{1/2}$, $F_{a1}^{1/2}$ on $\omega$.
• Figure 4: The figure shows how the quark mass $m_q$ and the chiral condensate $\sigma$ as a function of $\omega$.
• Figure 5: Dependence of the Gell-Mann-Oakes-Renner relation on $\omega$ is shown by taking the percent error. At the model best-fit point, we can see the relation is satisfied up to $3.6 \%$ accuracy.