Quark and gluon entanglement in the proton based on a light-front Hamiltonian

Given that the wave function of a proton can be derived relativistically and nonperturbatively from a light-front quantized Hamiltonian, investigating the quantum correlation between quarks and gluons offers a novel perspective on the internal structure of partons within a proton. In this work, we address this topic by computing the spin and longitudinal momentum entanglement of each parton inside the proton. The utilized wave functions are generated using basis light-front quantization (BLFQ), incorporating both the valence quarks and one dynamical gluon Fock sectors, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mo stretchy="false">|</a:mo><a:mi>q</a:mi><a:mi>q</a:mi><a:mi>q</a:mi><a:mo stretchy="false">⟩</a:mo></a:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mo stretchy="false">|</e:mo><e:mi>q</e:mi><e:mi>q</e:mi><e:mi>q</e:mi><e:mo stretchy="false">⟩</e:mo></e:mrow><e:mo>+</e:mo><e:mrow><e:mo stretchy="false">|</e:mo><e:mi>q</e:mi><e:mi>q</e:mi><e:mi>q</e:mi><e:mi>g</e:mi><e:mo stretchy="false">⟩</e:mo></e:mrow></e:math>. Our calculations indicate that the dynamical gluon significantly enhances entanglement among the proton’s partons. Additionally, we examine the spin entanglement of quarks and gluons at fixed values of longitudinal momentum fraction, revealing that the presence of a gluon may amplify the informational exchanges between quarks. Finally, these findings suggest the potential for experimental verification of the entanglement between partons by measuring parton helicity distributions in the proton.