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 pâŠ, and it deviates from the perturbative calculation at small pâŠ 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 pâŠ region which has important implications to the phenomenology of the hadron-nucleus and deep inelastic scattering at high energies.
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We wish to thank Shaoyang Jia, Wenyang Qian, Shuo Tang, Anji Yu for valuable discussions. M. Li acknowledges the communication with A. Dumitru and discussions with M. Sievert, G. Beuf and T. Lappi. M. Li would also like to thank the hospitality of the QCD Theory Group of University of Jyväskylä during the progress of this work. G. Chen acknowledges discussion with R. J. Fries on this project. X. Zhao is supported by Key Research Program of Frontier Sciences, CAS, Grant No. ZDBS-LY-7020. This work was supported in part by the U.S. Department of Energy (DOE) under Grants No. DE-FG02-87ER40371, No. DE-SC0018223 (SciDAC-4/NUCLEI), No. DE-SC0015376 (DOE Topical Collaboration in Nuclear Theory for Double-Beta Decay and Fundamental Symmetries). This research used resources of the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility operated under Contract No. DE-AC02-05CH11231. This work has been supported in part by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No ERC-2015-CoG-681707). The content of this article does not reflect the official opinion of the European Union and responsibility for the information and views expressed therein lies entirely with the authors.
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