Entanglement entropy and entropy production in the color glass condensate framework

Abstract

We compute the entanglement entropy of soft gluons in the wave function of a fast moving hadron and discuss its basic properties. We also derive the expression for entropy production in a high energy hadronic collision within the Color Glass formalism. We show that long range rapidity correlations give negative contribution to the production entropy. We calculate the (naturally defined) temperature of the produced system of particles, and show that it is proportional to the average transverse momentum of the produced particles.

Classical and quantum entropy of parton distributions

“…This is essentially due to the transverse dynamics of QCD, and is also a consequence of geometric scaling which holds perfectly for the model at hand (that is, xW (x, q ⊥ ) depends only on the ratio q 2 ⊥ /Q 2 s (Y )). The parametric dependence S W ∝ C F Q 2 s /α s agrees with the previous results in [6][7][8] using other definitions of entropy. For a large nucleus with atomic number A,…”

“…Since quantum field theory is not commonly formulated in terms of state vectors |ψ and a density matrix, it appears difficult to define and evaluate the von Neumann (entanglement) entropy S vN in a model-independent way. (Such a construction is nevertheless possible within certain frameworks [8,9,12], and we shall discuss one such model in a later section.) We thus turn to the Wehrl entropy.…”

“…In recent years, several authors have introduced the notion of entropy of small-x gluons in the hadron wavefunction and discussed its connection to the multiplicity in the final state [6][7][8][9][10][11] (see also [12]). A hadron in its ground state is a pure quantum state for which the standard quantum (von Neumann) entropy vanishes.…”

“…As experiment can only probe a small part of the hadron wavefunction above a certain value of x while the rest being integrated, an entanglement entropy may be defined and calculated. However, previous discussions along this line relied on particular formalisms at small-x (the Color Glass Condensate formalism [8] and the dipole formalism [9]) which cannot be straightforwardly generalized to the quark sector or to the large-x region. It would be interesting to have a more accessible, model-independent definition of entropy in terms of the quark and gluon field operators so that it can be analyzed by various perturbative and nonperturbative means.…”

Chiral symmetry breaking, entanglement, and the nucleon spin decomposition

“…One way is to partition the nucleon state vector into a bipartite system, trace over one of the subspaces, and obtain an entanglement entropy. This partitioning has been done in momentum space in the context of high-energy scattering [5], and in position space in the context of deep-inelastic scattering [6]. These partitionings rely on being in a regime of large momentum transfer where non-perturbative aspects of QCD are subsumed into parton distribution functions.…”