<html>
<head>
<meta http-equiv="content-type" content="text/html; charset=ISO-8859-1">
</head>
<body bgcolor="#FFFFFF" text="#000000">
Theory Center Seminar<br>
Monday, Dec. 2, 2013<br>
1:00 p.m. (coffee at 12:45 p.m.)<br>
CEBAF Center, Room L102 <br>
<br>
<b>Solution of the NLO BFKL Equation from Perturbative
Eigenfunctions</b> <br>
<br>
Giovanni Chirilli<br>
The Ohio State University <br>
<br>
The solution of the LO BFKL evolution describes a scattering
amplitude that grows proportionally<br>
to a positive power of the center-of-mass energy of the hadronic
scattering processes: at this order<br>
the kernel of the evolution equation respects the conformal symmetry
of the SL(2,C) Mobius group<br>
and the eigenfunctions are power-like functions of transverse
distance in coordinate space (or, in<br>
momentum space, powers of transverse momenta), while the eigenvalue
of the kernel is related to<br>
the Pomeron intercept. At the NLO there appears also a contribution
to the evolution kernel due<br>
to the running of the QCD coupling constant and the conformal
property of the LO BFKL is lost.<br>
Consequently, the LO BFKL kernels conformal eigenfunctions are not
eigenfunctions of the NLO<br>
BFKL kernel: at this order the power-law growth of the amplitudes
with energy also seems to<br>
be lost because of the non-Regge terms appearing due to the running
coupling effects. Despite a<br>
number of efforts, an exact analytical solution of the NLO BFKL
equation was still lacking. This<br>
is in stark contrast to the DGLAP evolution equation, which is a
renormalization group equation<br>
in the virtuality Q2: the eigenfunctions of that evolution equation
are simple powers of Bjorken-x<br>
variable for the kernel calculated to any order in the coupling
constant. The general form of the<br>
solution for DGLAP equation is well-known with the higher-order
corrections in the powers of the<br>
coupling constant entering into the anomalous dimension of the
operator at hand.<br>
<br>
We derive the solution of the NLO BFKL equation by constructing its
eigenfunctions perturbatively, <br>
using an expansion around the LO BFKL (conformal) eigenfunctions. As
a result we, not only have<br>
a perturbative expansion of the intercept (eigenvalues of the
kernel), but also a perturbative<br>
expansion of the eigenfunctions thus, restoring the power-law growth
of the amplitudes with energy.
</body>
</html>