$\rho$-meson spectroscopy and diffractive production using the holographic light-front Schr\"odinger equation and the 't Hooft equation

We determine the mass spectroscopy and light-front wave functions (LFWFs) of the $\rho$-meson by solving the holographic Schr\"odinger equation of light-front chiral QCD along with the 't Hooft equation of (1+1)-dimensional QCD in the large $N_c$ limit. Subsequently, we utilize the obtained LFWFs in conjunction with the color glass condensate dipole cross-section to calculate the cross sections for the diffractive $\rho$-meson electroproduction. Our spectroscopic results align well with the experimental data. Predictions for the diffractive cross sections demonstrate good consistency with the available experimental data at different energies from H1 and ZEUS collaborations. Additionally, we show that the resulting LFWFs for the $\rho$-meson can effectively describe various properties, including its decay constant, distribution amplitudes, electromagnetic form factors, charge radius, magnetic and quadrupole moments. Comparative analyses are conducted with experimental measurements and the available theoretical predictions.