Minimal length effect on meson form factors in light front AdS$_{5}$/QCD

TL;DR

This paper explores how a minimal length scale, introduced via the Generalized Uncertainty Principle, affects meson form factors in light-front holographic QCD, leading to improved agreement with experimental data and insights into quantum gravity effects on strong interactions.

Contribution

It introduces a GUP-corrected light-front wave function incorporating all Fock states, providing a novel framework to study quantum gravitational effects in hadronic physics.

Findings

GUP enhances meson form factors, aligning better with experimental data.

Fock state overlaps are amplified by minimal length effects.

Numerical results up to Q^2 = 4 GeV^2 match observed pion form factors.

Abstract

In this article, we investigate the impact of a minimal length scale, introduced via the Generalized Uncertainty Principle (GUP), on meson form factors within light-front holographic QCD (\(\mathrm{AdS}_5 / \mathrm{QCD}\)). By incorporating GUP through deformed operators in the QCD Lagrangian, we derive a GUP-corrected light-front wave function (LFWF) that includes contributions from all Fock states, weighted by probabilities \(a_n^2\). The resulting form factors account for transitions between Fock states via coefficients \(\mathcal{C}_{nm}\), revealing a net positive \(\beta\)-like correction driven by dominant positive coefficients (e.g., \(\mathcal{C}_{04}\), \(\mathcal{C}_{12}\)). This enhancement improves agreement with experimental pion form factor data. Our model is formulated to include all Fock states via the general summation over \( n \), but numerical evaluations truncate to \( n=0, 1, 2 \), sufficient for describing experimental data up to \( Q^2 \leq 4 \, \text{GeV}^2 \). Our findings suggest that minimal length effects amplify Fock state overlaps, offering insights into the interplay between quantum gravitational corrections and strong interaction dynamics. This generalized framework advances LFH QCD by capturing multi-parton contributions and paves the way for studying GUP effects in other hadronic systems.