We present calculations of radiative transitions between vector and pseudoscalar quarkonia in the light-front Hamiltonian approach. The valence sector light-front wavefunctions of heavy quarkonia are obtained from the Basis Light-Front Quantization (BLFQ) approach in a holographic basis. We study the transition form factor with both the traditional "good current" J + and the transverse current J ⊥ (in particular, J R = J x + iJ y ). This allows us to investigate the role of rotational symmetry by considering vector mesons with different magnetic projections (m j = 0, ±1). We use the m j = 0 state of the vector meson to obtain the transition form factor, since this procedure employs the dominant spin components of the light-front wavefunctions and is more robust in practical calculations. While the m j = ±1 states are also examined, transition form factors depend on subdominant components of the light-front wavefunctions and are less robust. Transitions between states below the open-flavor thresholds are computed, including those for excited states. Comparisons are made with the experimental measurements as well as with Lattice QCD and quark model results. In addition, we apply the transverse current to calculate the decay constant of vector mesons where we obtain consistent results using either m j = 0 or m j = 1 light-front wavefunctions. This consistency provides evidence for features of rotational symmetry within the model.

We investigate the scattering of a quark on a heavy nucleus at high energies using the time-dependent basis light-front quantization (tBLFQ) formalism, which is the first application of the tBLFQ formalism in QCD. We present the real-time evolution of the quark wave function in a strong classical color field of the relativistic nucleus, described as the Color Glass Condensate. The quark and the nucleus color field are simulated in the QCD SU(3) color space. We calculate the total and the differential cross sections, and the quark distribution in coordinate and color spaces using the tBLFQ approach. We recover the eikonal cross sections in the eikonal limit. We find that the differential cross section from the tBLFQ simulation is in agreement with a perturbative calculation at large p ⊥ , and it deviates from the perturbative calculation at small p ⊥ due to higher-order contributions. In particular, we relax the eikonal limit by letting the quark carry realistic finite longitudinal momenta. We study the sub-eikonal effect on the quark through the transverse coordinate distribution of the quark with different longitudinal momentum, and we find the sub-eikonal effect to be sizable. Our results can significantly reduce the theoretical uncertainties in small p ⊥ region which has important implications to the phenomenology of the hadron-nucleus and deep inelastic scattering at high energies.