Confronting next-leading BFKL kernels with proton structure function   data
  We propose a phenomenological study of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) approach applied to the data on the proton structure function F_2 measured at HERA in the small-x_{Bjorken} region. In a first part we use a simplified ``effective kernel'' approximation leading to few-parameter fits of F_2. It allows for a comparison between leading-logs (LO) and next-to-leading logs (NLO) BFKL approaches in the saddle-point approximation, using known resummed NLO-BFKL kernels. The NLO fits give a qualitatively satisfactory account of the running coupling constant effect but quantitatively the chi squared remains sizeably higher than the LO fit at fixed coupling. In a second part, a comparison of theory and data through a detailed analysis in Mellin space (x_{Bjorken} -> omega) leads to a more model independent approach to the resummed NLO-BFKL kernels we consider and points out some necessary improvements of the extrapolation at higher orders. 
R.Peschanski, C.Royon, L.Schoeffel