High Energy / Nuclear Theory / RIKEN Seminars

[Hybrid RBRC seminar] Quark and gluon entanglement in the light-front wave function of the proton at moderate x

by Adrian Dumitru (Dept. of Natural Sciences, Baruch College (CUNY))




The entanglement of small-x gluons in the light-front wave function of
the proton has recently received much attention. In this talk we shall
focus instead on the regime of moderate x where the proton may be
dominated by an effective, non-perturbative 3-quark Fock state, plus
corrections from the |qqqg> Fock state.

We point out that color degrees of freedom in the |qqq> state are
maximally entangled. On the other hand, for N_c --> infinity the
spatial wave function of the proton factorizes into valence quark wave
functions determined by a mean field (E. Witten, Nucl. Phys. B 160
(1979) p. 57), and there is no entanglement of spatial degrees of
freedom.  A model calculation at Nc=3, using a well known valence quark
light-front wave function by Brodsky and Schlumpf, predicts percent
level entanglement of spatial degrees of freedom.

Using light-cone perturbation theory we also obtain the qqqg wave function
and the associated density matrix. Tracing out the quarks, we derive
the reduced density matrix for the degrees of freedom of the gluon.
This density matrix again predicts maximal entanglement of gluon color
but also indicates stronger entanglement of (some of) the gluon
spatial degrees of freedom than for quarks in the |qqq> state.

Organized by

Vladi Skokov