Exploring the DGLAP resummation in the JIMWLK Hamiltonian

A bstract 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 Q P , which is the inverse color correlation length in the projectile to Q ≫ Q P which corresponds to the hard resolution scale provided by the target. As expected, S ceases to be unitary if evolved to significant ln $$ {Q}^2/{Q}_P^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>Q</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>/</mml:mo> <mml:msubsup> <mml:mi>Q</mml:mi> <mml:mi>P</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> . Our numerical results indicate an interesting universal (independent of the coupling constant) pattern for this deviation from unitarity.