Quasiparton distributions in massive QED2: Toward quantum computation

Abstract

We analyze the quasiparton distributions of the lightest <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mi>η</a:mi> <a:mo>′</a:mo> </a:msup> </a:math> meson in massive two-dimensional quantum electrodynamics (QED2) by exact diagonalization. The Hamiltonian and boost operators are mapped onto spin qubits in a spatial lattice with open boundary conditions. The lowest excited state in the exact diagonalization is shown to interpolate continuously between an anomalous <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msup> <c:mi>η</c:mi> <c:mo>′</c:mo> </c:msup> </c:math> state at strong coupling, and a nonanomalous heavy meson at weak coupling, with a cusp at the critical point. The boosted <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msup> <e:mi>η</e:mi> <e:mo>′</e:mo> </e:msup> </e:math> state follows relativistic kinematics but with large deviations in the luminal limit. The spatial quasiparton distribution function and amplitude for the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msup> <g:mi>η</g:mi> <g:mo>′</g:mo> </g:msup> </g:math> state are computed numerically for increasing rapidity both at strong and weak coupling, and compared to the exact light front results. The numerical results from the boosted form of the spatial parton distributions, compare fairly with the inverse Fourier transformation of the luminal parton distributions, derived in the lowest Fock space approximation. Our analysis points out some of the limitations facing the current lattice program for the parton distributions. Published by the American Physical Society 2024

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