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Evidence for the maximally entangled low $x$ proton in Deep Inelastic Scattering from H1 data
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abstract
We investigate the proposal by Kharzeev and Levin of a maximally entangled proton wave function in Deep Inelastic Scattering at low $x$ and the proposed relation between parton number and final state hadron multiplicity. Contrary to the original formulation we determine partonic entropy from the sum of gluon and quark distribution functions at low $x$, which we obtain from an unintegrated gluon distribution subject to next-to-leading order Balitsky-Fadin-Kuraev-Lipatov evolution. We find for this framework very good agreement with H1 data. We furthermore provide a comparison based on NNPDF parton distribution functions at both next-to-next-to-leading order and next-to-next-to-leading with small $x$ resummation, where the latter provides an acceptable description of data.
Forward citations
Cited by 13 Pith papers
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Emergent Local Phase-Space Scaling in Small-x Gluon Evolution
In the fixed-coupling SO(3)-BK model, Q_s-adaptive coarse graining of the gluon Husimi distribution produces collapse of conditional momentum distributions onto k/Q_s and unit-slope growth of conditional entropy with ...
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Deep inelastic scattering as a probe of entanglement: the complete QCD dipole cascade
The Shannon entropy of dipole multiplicities from the full Levin–Lublinsky equation in DIS reproduces the H1 hadron entropy, growing linearly with ln(1/x) and described by S = ln(2/3⟨n⟩) + 0.85.
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Emergent Local Phase-Space Scaling in Small-x Gluon Evolution
After Q_s-adaptive coarse graining, conditional gluon Husimi momentum distributions from fixed-coupling SO(3)-BK evolution collapse as functions of k/Q_s(Y,b), with conditional entropy growing at unit slope versus ⟨ln Q_s²⟩.
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Reciprocal symmetry and KNO scaling violation in proton-proton collisions
A reciprocal symmetry z↔1/z is identified in KNO scaling violations in pp collisions at 7-13 TeV, imposing P'(<n>)=-P(<n>)/<n> and enabling entanglement entropy extraction from the central multiplicity region.
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Higher-order local constraints from reciprocal symmetry and entanglement entropy of charged-particle multiplicity distributions in $pp$ collisions
The reciprocal symmetry of the KNO-violating term yields the new constraint δ₃=0 at n=⟨n⟩ (untestable at present precision), fails globally at 13 TeV, and the derived entropy S=ln⟨n⟩+I₀−½∫e^{-z}f_s²dz matches ATLAS da...
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Higher-order local constraints from reciprocal symmetry and entanglement entropy of charged-particle multiplicity distributions in $pp$ collisions
Reciprocal symmetry f_s(z)=f_s(1/z) implies local constraints on multiplicity distributions at n=<n> that hold to leading order in ATLAS data, plus a model-independent entanglement entropy expression S=ln<n>+1-½∫e^{-z...
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Reciprocal symmetry and KNO scaling violation in proton-proton collisions
A z ↔ 1/z reciprocal symmetry is found in KNO scaling violations in pp collisions, imposing the constraint P'(⟨n⟩) = −P(⟨n⟩)/⟨n⟩ that enables entanglement entropy extraction from the well-measured multiplicity region.
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Entropy and mean multiplicity from dipole models in the high energy limit
The generalized dipole model fits entropy and mean multiplicity data from proton-proton collisions significantly better than the standard 1D Mueller dipole model.
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An approximate formula for the entropy of the negative binomial distribution
An approximate formula for the entropy of the negative binomial distribution is given, accurate to within 20% for extreme parameter values.
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An approximate formula for the entropy of the negative binomial distribution
An approximate formula for the entropy of the negative binomial distribution is provided, with up to ~20% deviation from exact values for extreme parameters.
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An approximate formula for the entropy of the negative binomial distribution
An approximate formula for the Shannon entropy of the negative binomial distribution is given that remains valid within about 20% for extreme values of the distribution parameters.
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Entanglement entropy, Monte Carlo event generators, and soft gluons DIScovery
Including soft gluons in Monte Carlo generators for DIS aligns parton distributions with inclusive PDFs and makes entropy grow with decreasing x, indicating initial-state origin of the bulk entropy.
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Small $x$ behavior in QCD from maximal entanglement and conformal invariance
Bethe Ansatz finite-size corrections to Lipatov's spin chain yield c=1, which fixes the small-x gluon scaling to x^{-1/3}.
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