Particle distribution in intense fields in a light-front Hamiltonian approach

Guangyao Chen, Xingbo Zhao, Yang Li, Kirill Tuchin, and James P. Vary

Phys. Rev. D 95, 096012 – Published 30 May 2017

Abstract

We study the real-time evolution of an electron influenced by intense electromagnetic fields using the time-dependent basis light-front quantization (tBLFQ) framework. We focus on demonstrating the nonperturbative feature of the tBLFQ approach through a realistic application of the strong coupling QED problem, in which the electromagnetic fields are generated by an ultrarelativistic nucleus. We calculate transitions of an electron influenced by such electromagnetic fields and we show agreement with light-front perturbation theory when the atomic number of the nucleus is small. We compare tBLFQ simulations with perturbative calculations for nuclei with different atomic numbers, and obtain the significant higher-order contributions for heavy nuclei. The simulated real-time evolution of the momentum distribution of an electron evolving inside the strong electromagnetic fields exhibits significant nonperturbative corrections compared to light-front perturbation theory calculations. The formalism used in this investigation can be extended to QCD problems in heavy ion collisions and electron ion collisions.

Received 24 February 2017

DOI:https://doi.org/10.1103/PhysRevD.95.096012

Physics Subject Headings (PhySH)

Particle interactions

Particles & Fields

Authors & Affiliations

Guangyao Chen^1,*, Xingbo Zhao^2,†, Yang Li^1,‡, Kirill Tuchin^1,§, and James P. Vary^1,∥

¹Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA
²Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China

^*gchen@iastate.edu
^†xbzhao@impcas.ac.cn
^‡leeyoung@iastate.edu
^§tuchin@iastate.edu
^∥jvary@iastate.edu

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Issue

Vol. 95, Iss. 9 — 1 May 2017

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Images

Figure 1
A typical $x^{-}$ distribution of the $-$ component of the potential, $A^{-}$ , produced by a heavy ion moving along the positive (left) and the negative (right) $z$ axis in rapidity $y = \pm 5.3$ at $x^{+} = 0$ , for the modes with transverse momentum $k_{⊥} = 1 GeV$ . The potential as a function of $x^{-}$ can be obtained through a Fourier transformation of Eq. (14). The width of such a distribution increases as the transverse momentum decreases.
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Figure 2
Comparison of transition amplitude $⟨ ϕ_{f} | W_{1} | ϕ_{0} ⟩$ in momentum basis and BLFQ basis as a function of $p_{f}^{x}$ in units of the HO length scale $b$ . Initial state $ϕ_{0}$ has longitudinal momentum $p_{0}^{+} = 3 π / 10 GeV$ , and helicity $λ_{0} = 1 / 2$ ; in transverse direction, it is a Gaussian wave packet centered at $p_{0}^{⊥} = (b / 2, 0)$ with width $σ_{0} = b / 2$ . Final state $ϕ_{f}$ has longitudinal momentum $p_{f}^{+} = 7 π / 10 GeV$ , $λ_{f} = 1 / 2$ and $p_{f}^{y} = 0$ . HO parameter $b = 1000 m_{e}$ . Left: Comparison with the momentum basis transition amplitude using the BLFQ basis calculation at different $N_{\max}$ . Right: Comparison with the momentum basis transition amplitude using the BLFQ basis calculation averaged over two $N_{\max}$ .
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Figure 3
Transition rate as a function of exposure time $T$ for an electron between a specific initial and a specific final state induced by the potential which is generated by nuclei with atomic number $Z = 1$ , 28, 56, 79, the coupling between electron and background field $α \equiv Z α_{em}$ with $α_{em} = 1 / 137$ . The nucleus is moving along the positive $z$ axis with $y = 5.3$ . The initial and final states are kinetic energy eigenstates with energies $P_{β, i}^{-} = 0.455 GeV$ and $P_{β, f}^{-} = 0.955 GeV$ . The calculation is performed using $N_{\max} = 32$ , $K = 32$ , $L = 10 {GeV}^{- 1}$ and $b = 1000 m_{e}$ ; see the text for details.
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Figure 4
Snapshots in time $x^{+}$ of the transverse momentum distribution of an electron inside the e.m. field generated by a gold nucleus moving along the positive $z$ axis with rapidity $y = 5.3$ . The initial state of the electron is the BLFQ basis state with $k = \frac{17}{2}$ , $n = 0$ , $m = 0$ and $λ = \frac{1}{2}$ at $x^{+} = 0$ . Note that the chosen initial state is not an eigenstate of the pure BLFQ Hamiltonian. The calculation is performed using $N_{\max} = 32$ , $K = 32$ , $L = 10 {GeV}^{- 1}$ and $b = 1000 m_{e}$ .
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Figure 5
Snapshot of transverse momentum distribution on a semilog scale for the same process in Fig. 4 at $x^{+} = 50 {GeV}^{- 1}$ .
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Figure 6
Snapshots of the longitudinal momentum distribution for the same process in Fig. 4. Horizontal bars indicate the momentum bin width for the discretized plane waves in the longitudinal direction.
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