On running coupling in the JIMWLK evolution and its Langevin formulation
摘要
Various conventional running coupling prescriptions reproducing β0-dependent terms of NLO JIMWLK are reviewed and found to be theoretically inconsistent: the JIMWLK evolution Hamiltonian with running coupling violates the requirement of positive semidefiniteness. This requirement appears to be tightly related to the possibility of having a Langevin formulation for the evolution.
We also review the scheme that attributes a part of β0-dependent terms to the DGLAP evolution of the projectile. The remaining β0-dependent contributions sum up into so-called “daughter dipole” prescription, which leads to a manifestly positive semidefinite Hamiltonian.