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<p>We explore the recently derived equation that resums DGLAP corrections to the JIMWLK Hamiltonian in the simplified setting of the SU(2) gauge theory. We solve the equation numerically for the scattering matrix of a dressed gluon for a particular initial condition, that corresponds to a dipole initial state. We evolve the <i>S</i>-matrix of a single dressed gluon from the scale <i>Q</i><sub><i>P</i></sub>, which is the inverse color correlation length in the projectile to <i>Q</i> ≫ <i>Q</i><sub><i>P</i></sub> which corresponds to the hard resolution scale provided by the target. As expected, <i>S</i> ceases to be unitary if evolved to significant ln <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <msup> <mi>Q</mi> <mn>2</mn> </msup> <mo>/</mo> <msubsup> <mi>Q</mi> <mi>P</mi> <mn>2</mn> </msubsup> </math></EquationSource> <EquationSource Format="TEX">\( {Q}^2/{Q}_P^2 \)</EquationSource> </InlineEquation>. Our numerical results indicate an interesting universal (independent of the coupling constant) pattern for this deviation from unitarity.</p>

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Exploring the DGLAP resummation in the JIMWLK Hamiltonian

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  • 发表日期：

    2025年7月18日

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  • Néstor Armesto,
  • Alex Kovner,
  • Víctor López-Pardo

摘要

We explore the recently derived equation that resums DGLAP corrections to the JIMWLK Hamiltonian in the simplified setting of the SU(2) gauge theory. We solve the equation numerically for the scattering matrix of a dressed gluon for a particular initial condition, that corresponds to a dipole initial state. We evolve the S-matrix of a single dressed gluon from the scale QP, which is the inverse color correlation length in the projectile to Q ≫ QP which corresponds to the hard resolution scale provided by the target. As expected, S ceases to be unitary if evolved to significant ln Q 2 / Q P 2 \( {Q}^2/{Q}_P^2 \) . Our numerical results indicate an interesting universal (independent of the coupling constant) pattern for this deviation from unitarity.