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

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