The 2nd order corrections to the hard pomeron and the running coupling

It is shown that solutions to the 2nd order BFKL eigenvalue equation exist for arbitrary large real values of the complex angular momentum j. This cor responds to a cut in the complex j plane along the whole real axis, and it makes the use of the complex angular momentum variable for the calculation of the high-energy behavior somewhat questionable. The eigenfunctions conta in non-perturbative pieces which behave as exp(-1/alpha(s)b) and have no co unterpart in the leading-log BFKL equation. The high-energy behavior of the 2nd order BFKL Green function as found by other authors, is reproduced by excluding these non-perturbative pieces of the eigenfunctions. (C) 1998 Els evier Science B.V. All rights reserved.