Relationship between forward-kernel and next-to-leading BK positivity obstructions

Determine whether the positivity failure found for the fixed-order forward BFKL kernel and the positivity failure in next-to-leading Balitsky–Kovchegov evolution are manifestations of the same obstruction expressed in different variables.

Background

The discussion compares the paper’s generator-level obstruction for the forward BFKL kernel with a separate instability reported for next-to-leading Balitsky–Kovchegov evolution, in which the dipole amplitude can become negative at small dipole sizes. Both analyses identify double transverse logarithms as an important source of the problem, while resummation of those logarithms stabilizes the BK evolution in the treatment cited.

The paper does not establish whether the two failures are mathematically or physically equivalent. The unresolved issue is specifically whether they represent one common positivity obstruction after changing variables or evolution descriptions.