Spin-spin entanglement in diffractive heavy-quark production

We calculate the spin density matrix of a heavy-quark-antiquark pair ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>b</a:mi> <a:mover accent="true"> <a:mi>b</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> </a:math> , <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>c</e:mi> <e:mover accent="true"> <e:mi>c</e:mi> <e:mo stretchy="false">¯</e:mo> </e:mover> </e:math> or <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>s</i:mi> <i:mover accent="true"> <i:mi>s</i:mi> <i:mo stretchy="false">¯</i:mo> </i:mover> </i:math> ) 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-Clauser-Horne-Shimony-Holt 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.