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Spin-spin entanglement in diffractive heavy quark production

Michael Fucilla, Yoshitaka Hatta

Abstract

We calculate the spin density matrix of a heavy quark-antiquark pair ($b\bar{b}$, $c\bar{c}$ or $s\bar{s}$) diffractively produced in Deep Inelastic Scattering and Ultraperipheral Collisions. We show that the Pomeron exchange leaves characteristic imprints on the entanglement pattern between the quark and the antiquark. For the longitudinally polarized virtual photon, the pair always exhibits maximal entanglement and maximal violation of the Bell-CHSH inequality. For the transversely polarized photon, the pair is always entangled and Bell-violating, reaching maximal entanglement and maximal violation simultaneously when the transverse momentum approximately equals the quark mass.

Spin-spin entanglement in diffractive heavy quark production

Abstract

We calculate the spin density matrix of a heavy quark-antiquark pair (, or ) diffractively produced in Deep Inelastic Scattering and Ultraperipheral Collisions. We show that the Pomeron exchange leaves characteristic imprints on the entanglement pattern between the quark and the antiquark. For the longitudinally polarized virtual photon, the pair always exhibits maximal entanglement and maximal violation of the Bell-CHSH inequality. For the transversely polarized photon, the pair is always entangled and Bell-violating, reaching maximal entanglement and maximal violation simultaneously when the transverse momentum approximately equals the quark mass.

Paper Structure

This paper contains 1 section, 37 equations, 3 figures.

Table of Contents

  1. Spin density matrix element for the transversely polarized photon

Figures (3)

  • Figure 1: $C^T$-matrix at $z=1/2$ as a function of $k_\perp$ (in units of GeV) for the bottom quark $m=4.18$ GeV. We used the GBW model Golec-Biernat:1998zce with $Q^2=9$ GeV$^2$ and $W=100$ GeV.
  • Figure 2: $\Delta_2$ in the $(z,k_\perp)$ plane at $Q^2=9$ GeV$^2$, $m=4.18$ GeV, and $W=100$ GeV.
  • Figure 3: Top: Venn diagram for generic two-qubit systems. Bottom: Venn diagram of a $q\bar{q}$ pair produced in $\gamma^*_T+{\mathbb P}\to q+\bar{q}$. The 'separable' region is the boundary of the entangled region. If the photon is longitudinally polarized, only the shaded ('pure & maximal') region is present.