Renormalization group improved small-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>x</mml:mi></mml:math>Green’s function

Abstract

We investigate the basic features of the gluon density predicted by a renormalization group improved small-$x$ equation which incorporates both the gluon splitting function at the leading collinear level and the exact Balitskii-Fadin-Kuraev-Lipatov (BFKL) kernel at the next-to-leading level. We provide resummed results for Green's function and its hard Pomeron exponent ${\ensuremath{\omega}}_{s}({\ensuremath{\alpha}}_{s}),$ and for the splitting function and its critical exponent ${\ensuremath{\omega}}_{c}({\ensuremath{\alpha}}_{s}).$ We find that nonlinear resummation effects considerably extend the validity of the hard Pomeron regime by decreasing diffusion corrections to Green's function exponent and by slowing down the drift towards the nonperturbative Pomeron regime. As in previous analyses, the resummed exponents are reduced to phenomenologically interesting values. Furthermore, significant preasymptotic effects are observed. In particular, the resummed splitting function departs from the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) result in the moderate small-$x$ region, showing a shallow dip followed by the expected power increase in the very small-$x$ region. Finally, we outline the extension of the resummation procedure to include the photon impact factors.