Phenomenology of a double dilaton soft-wall model: Alpha strong from Ricci flow and pion Form Factors at intermediate-energy region

TL;DR

This work develops a holographic QCD framework in which the running strong coupling $\alpha_s$ arises from Ricci Flow-driven metric evolution together with a double-dilaton soft-wall background, yielding an infrared fixed point and a smooth connection to perturbative QCD above a few GeV. Through a data-driven parameterization and large-$N_c$ corrections, the authors achieve a credible high-energy matching to four-loop pQCD and produce realistic vector/scalar/tensor meson spectra and decay constants. They then apply the running coupling to neutral and charged pion form factors in the intermediate energy region, fitting low-energy coefficients against experimental data to extend the validity of the distributions-amplitude formalism. Overall, the paper provides a coherent bridge between nonperturbative holographic dynamics and perturbative QCD, with concrete predictions for hadron spectra and pion structure that can guide future refinements and extensions to other dilaton backgrounds.

Abstract

Through a holographic model of QCD, we present a phenomenological approach to study the running of the strong coupling constant α_s in both non-perturbative and perturbative regimes. The renormalization of the metric tensor, driven by the Ricci Flow, and the breaking of conformal and chiral symmetries -- thanks to introducing a double dilaton model and large-$N_c$ corrections -- allow us to relate the existence of an infrared fixed point in the coupling constant with a smooth matching to pQCD well above 2 GeV. This is done through a model with two fit parameters and one matching point. The proposed dilaton model yields linear Regge trajectories and decay constants for scalar, vector, and tensor meson families similar to their experimental counterparts. We finally study neutral and charged pion form factors to show an application of the running coupling constant obtained.

Figures (6)

• Figure 1: Model from Eq.(\ref{['eqn:parametrization']}) (dotted blue), matching to perturbative QCD running coupling using DDSW model Eq.(\ref{['eqn:largeN']}) for $n=2$ (dashed purple), resummed (red) Eq.(\ref{['eqn:Resum']}). Their $\chi^2/DOF$ values are $1.45$, $0.99$ and $0.93$, respectively. We also compare with the holographic light-front model Brodsky (dotted black). The dashed vertical lines indicate the matching point with perturbative QCD for $n=2$ and the resummed version (so for $Q>2.39$ and $Q>3.79$, respectively, we have perturbative QCD running coupling in the same color).
• Figure 2: Vector meson Regge trajectories $(M_n^2,n)$ for the DDSW model (red points), the SW model (blue stars), and comparison with experimental data (purple boxes) Workman, Navas.
• Figure 3: Scalar meson Regge trajectories $(M_n^2,n)$ for the DDSW model (red points), the SW model (blue stars), and comparison with experimental data (purple boxes) Navas.
• Figure 4: Proposal for tensor meson Regge trajectory $(M_n^2,n)$ for the DDSW model (red points), the SW model (blue stars), and comparison with experimental data (purple boxes)Navas.
• Figure 5: Neutral pion electromagnetic form factor. Prediction from Eq.(\ref{['eqn:neutralFFExpansion']}) in dashed blue and result from matching procedure described in the text at low energies in solid blue. Fit to data using the same parametrization in solid blue. Experimental data are in green dots (Belle Belle), black triangles (BaBar BaBar), red stars (CLEO CLEO) and purple triangles (CELLO CELLO).