BFKL approach and MHV amplitudes
Alex Prygarin
University of Hamburg
The main objective of the talk is the application of the
Balitsky-Fadin-Kuraev-Lipatov (BFKL) approach to the study of the
maximally helicity violating scattering amplitudes in the Regge limit.
The all-loop ansatz for multi-leg MHV amplitudes proposed by Bern,
Dixon and Smirnov (BDS) is violated at two loops for six-gluon
amplitude due to the presence of the Mandelstam (Regge) cuts, which
are described in Yang-Mills theories by the BFKL equation. The BDS
violating term in the multi-Regge kinematics was calculated by
Bartels, Lipatov and Sabio Vera (BLS) using the solution to the octet
BFKL equation. The BDS ansatz differs from the full MHV amplitude by a
multiplicative function, called the remainder function. The remainder
function for six-point MHV amplitude at two loops was calculated from
null polygonal Wilson Loops by Drummond, Henn, Korchemsky and
Sokatchev, then it was expressed in terms of the Goncharov
polylogarithms by Del Duca, Duhr and Smirnov and finally greatly
simplified by Goncharov, Spradlin, Vergu and Volovich (GSVV). We
analyze the GSVV expression and perform an analytic continuation to
the region where the BDS violating term was found by Bartels, Lipatov
and Sabio Vera. The GSVV expression after the analytic continuation
reproduces the BLS result and is in agreement with general properties
of the scattering amplitudes. Using the GSVV formula we obtain the
next-to-leading impact factor necessary in the BFKL approach. We also
calculate the three loop leading logarithmic contribution to the
remainder function of the six-gluon MHV amplitude. The final part of
the talk is devoted to the interplay of the Regge and collinear limits
in the context of the recent paper of Alday, Gaiotto, Maldacena, Sever
and Vieira on the Operator Product Expansion for polygonal null Wilson
Loops.