arXiv:2003.00112 · International Journal of Modern Physics E

Gluon shadowing and nuclear entanglement entropy

P. Castorina, Alfredo Iorio, Daniele Lanteri, Petr Lukeš

Published Feb 1, 2021• 9 citations

Abstract

Relying on previous results, that link entanglement entropy and parton distribution functions in deep inelastic scattering, and focusing on the small Bjorken scaling region we present here indications that gluon shadowing might indeed be explained as due to a depletion of the entanglement entropy, between observed and unobserved degrees of freedom, per nucleon within a nucleus, with respect to the free nucleon. We apply to gluon shadowing the general Page approach to the calculation of the entanglement entropy in bipartite systems, giving physical motivations of the results.

DOI: 10.1142/s0218301321500105

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arXiv:2003.00112 · International Journal of Modern Physics E

Gluon shadowing and nuclear entanglement entropy

P. Castorina, Alfredo Iorio, Daniele Lanteri, Petr Lukeš

Published Feb 1, 2021• 9 citations

arXiv HTML PDF

Abstract

DOI: 10.1142/s0218301321500105

Related papers

Entanglement entropy of the proton in coordinate space

Adrian Dumitru, Alex Kovner, Vladimir V. Skokov

We calculate the entanglement entropy of a model proton wave function in coordinate space by integrating out degrees of freedom outside a small circular region $\overline{A}$ of radius $L$ , where $L$ is much smaller than the size of the proton. The wave function provides a nonperturbative distribution of three valence quarks. In addition, we include the perturbative emission of a single gluon and calculate the entanglement entropy of gluons in $\overline{A}$ . For both quarks and gluons, we obtain the same simple result: ${S}_{E}=\ensuremath{-}\ensuremath{\int}\frac{dx}{\mathrm{\ensuremath{\Delta}}x}{N}_{{L}^{2}}(x)\mathrm{log}[{N}_{{a}^{2}}(x)]$, where $a$ is the UV cutoff in coordinate space and $\mathrm{\ensuremath{\Delta}}x$ is the longitudinal resolution scale. Here ${N}_{S}(x)$ is the number of partons (of the appropriate species) with longitudinal momentum fraction $x$ inside an area $S$ . It is related to the standard parton distribution function by ${N}_{S}(x)=\frac{S}{{A}_{p}}\mathrm{\ensuremath{\Delta}}xF(x)$, where ${A}_{p}$ denotes the transverse area of the proton.We calculate the entanglement entropy of a model proton wave function in coordinate space by integrating out degrees of freedom outside a small circular region $\overline{A}$ of radius $L$, where $L$ is much smaller than the size of the proton. The wave function provides a nonperturbative distribution of three valence quarks. In addition, we include the perturbative emission of a single gluon and calculate the entanglement entropy of gluons in $\overline{A}$. For both quarks and gluons, we obtain the same simple result: ${S}_{E}=\ensuremath{-}\ensuremath{\int}\frac{dx}{\mathrm{\ensuremath{\Delta}}x}{N}_{{L}^{2}}(x)\mathrm{log}[{N}_{{a}^{2}}(x)]$, where $a$ is the UV cutoff in coordinate space and $\mathrm{\ensuremath{\Delta}}x$ is the longitudinal resolution scale. Here ${N}_{S}(x)$ is the number of partons (of the appropriate species) with longitudinal momentum fraction $x$ inside an area $S$. It is related to the standard parton distribution function by ${N}_{S}(x)=\frac{S}{{A}_{p}}\mathrm{\ensuremath{\Delta}}xF(x)$, where ${A}_{p}$ denotes the transverse area of the proton.

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arXiv:2605.11171May 11, 20260 citations

We calculate the entanglement entropy of a model proton wave function in coordinate space by integrating out degrees of freedom outside a small circular region

\overline{A}

of radius

L

, where

L

is much smaller than the size of the proton. The wave function provides a nonperturbative distribution of three valence quarks. In addition, we include the perturbative emission of a single gluon and calculate the entanglement entropy of gluons in

\overline{A}

. For both quarks and gluons, we obtain the same simple result: ${S}_{E}=\ensuremath{-}\ensuremath{\int}\frac{dx}{\mathrm{\ensuremath{\Delta}}x}{N}_{{L}^{2}}(x)\mathrm{log}[{N}_{{a}^{2}}(x)]$, where

a

is the UV cutoff in coordinate space and $\mathrm{\ensuremath{\Delta}}x$ is the longitudinal resolution scale. Here

{N}_{S}(x)

is the number of partons (of the appropriate species) with longitudinal momentum fraction

x

inside an area

S

. It is related to the standard parton distribution function by ${N}_{S}(x)=\frac{S}{{A}_{p}}\mathrm{\ensuremath{\Delta}}xF(x)$, where

{A}_{p}

denotes the transverse area of the proton.

m

is the proton mass and

x

is the Bjorken

x

. The central charge

c

of Lipatov's spin chain is determined here to be

c=1

; using the proposed relation between the entanglement entropy and parton distributions, this corresponds to the gluon structure function growing at small

x

as $xG(x)\ensuremath{\sim}1/{x}^{1/3}$.

We study entanglement entropy in Deep Inelastic Scattering (DIS) using the dipole formulation of the high-energy limit of QCD. We argue that a reduced density matrix arises in low

x

DIS due to a trace over unobserved color degrees of freedom and we obtain entanglement entropy in terms of dipole multiplicities, directly from the von Neumann entropy. Dipole multiplicities are obtained from a solution to low

x

evolution equations, which we solve numerically. Unlike previous studies, we take into account both transverse-size and azimuthal-angle dependence in the dipole evolution kernel. We study both the exact solution of the equation as well as its double leading-logarithmic approximation (DLLA). We find that for the same initial dipole size, the DLLA solution generates a larger entropy. Finally, we calculate the dipole multiplicities and entanglement entropy and compare our results to the Shannon entropy of hadron multiplicities, as measured by the H1 collaboration.