Ultrarelativistic quark-nucleus scattering in a light-front Hamiltonian approach

Abstract

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.

Scattering in strong electromagnetic fields: Transverse size effects in time-dependent basis light-front quantization

“…Overall, the tBLFQ results are slightly smaller than the perturbative results. This discrepancy may be attributed to the fact that the CM motion of the initial state in our tBLFQ calculation is a Gaussian wave packet in the transverse plane (21), rather than a momentum eigenstate as in the perturbative calculation. Another main difference in Fig.…”

“…An extension of this framework which is suitable for investigating e.g. QFT scattering processes in time-dependent background fields is time-dependent basis light-front quantization (tBLFQ) [20,21]. The idea of tBLFQ can also be used in nuclear physics [22].…”

Initial State Summary of Hard Probes 2020

“…Further progress reported included extensions beyond the eikonal approximation: 1) in the calculation of quark-nucleus scattering in a light-front Hamiltonian approach [55], and 2) by including large gluons in the target, which also aims at developing a unified picture for particle production at small and large [56]. A generalized connection between transverse momentum dependent PDFs (TMDs) and the CGC EFT, using a new approach to TMDs at small employing transverse gauge link operators [57] was presented, as well as the first computation of entanglement and "ignorance" entropies within the CGC EFT, the latter reflecting our inability to perform a complete set of measurements (sensitive to off-diagonal elements of the density matrix) [58].…”

Memory effect in Yang-Mills theory

“…There are also further O( ) effects, like the one coming from careful gauge transformation between A + and A i gauges when also fluctuations are included, studied in Appendix A. Quantitative conclusions are only possible by numerical means. Solving Wong's equations numerically has been extensively studied [25][26][27].…”