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Description
Recent studies have shown that hadronic multiplicity in deep inelastic scattering can be associated with entanglement entropy. However, this definition is intrinsically longitudinal and does not capture the full phase-space structure of the proton, in particular the transverse position and momentum degrees of freedom of partons. In this work, we investigate the proton Wehrl entropy constructed from the gluon Husimi distribution, which provides a positive-definite phase-space description. We employ a gluon light-front spectator model based on soft-wall AdS/QCD-inspired wave functions, with free parameters constrained by global NNPDF fits, allowing us to compute both parton distribution functions and Wigner distributions. The Husimi distribution is obtained via Gaussian smearing of the Wigner distribution with width given by the saturation scale in the GBW model. We show that the entanglement entropy naturally emerges from the normalization of the Husimi distribution when computing the Wehrl entropy, while additional contributions arise from transverse phase-space degrees of freedom. Numerical results for the proton entanglement entropy are compared with CMS data, and the behaviour of the Wehrl entropy is presented for different values of the virtuality.
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