[Jlab-seminars] Theory Center Seminar

[Mary Fox]

Theory Center Seminar
Monday, Dec. 2, 2013
1:00 p.m. (coffee at 12:45 p.m.)
CEBAF Center, Room L102

*Solution of the NLO BFKL Equation from Perturbative Eigenfunctions*

Giovanni Chirilli
The Ohio State University

The solution of the LO BFKL evolution describes a scattering amplitude 
that grows proportionally
to a positive power of the center-of-mass energy of the hadronic 
scattering processes: at this order
the kernel of the evolution equation respects the conformal symmetry of 
the SL(2,C) Mobius group
and the eigenfunctions are power-like functions of transverse distance 
in coordinate space (or, in
momentum space, powers of transverse momenta), while the eigenvalue of 
the kernel is related to
the Pomeron intercept. At the NLO there appears also a contribution to 
the evolution kernel due
to the running of the QCD coupling constant and the conformal property 
of the LO BFKL is lost.
Consequently, the LO BFKL kernels conformal eigenfunctions are not 
eigenfunctions of the NLO
BFKL kernel: at this order the power-law growth of the amplitudes with 
energy also seems to
be lost because of the non-Regge terms appearing due to the running 
coupling effects. Despite a
number of efforts, an exact analytical solution of the NLO BFKL equation 
was still lacking. This
is in stark contrast to the DGLAP evolution equation, which is a 
renormalization group equation
in the virtuality Q2: the eigenfunctions of that evolution equation are 
simple powers of Bjorken-x
variable for the kernel calculated to any order in the coupling 
constant. The general form of the
solution for DGLAP equation is well-known with the higher-order 
corrections in the powers of the
coupling constant entering into the anomalous dimension of the operator 
at hand.

We derive the solution of the NLO BFKL equation by constructing its 
eigenfunctions perturbatively,
using an expansion around the LO BFKL (conformal) eigenfunctions. As a 
result we, not only have
a perturbative expansion of the intercept (eigenvalues of the kernel), 
but also a perturbative
expansion of the eigenfunctions thus, restoring the power-law growth of 
the amplitudes with energy.
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