Abstract
We consider one-loop five-point QCD amplitudes in next-to-multi-Regge kinematics, and evaluate the one-loop impact factor for the emission of two gluons. This is the last ingredient which is necessary to evaluate the gluon-jet impact factor at NNLO accuracy in αs. It is also the first instance in which loop-level QCD amplitudes are evaluated in next-to-multi-Regge kinematics, which requires to apply a different Reggeisation ansatz to each colour-ordered amplitude.
Highlights
In the Regge limit, in which the squared centre-of-mass energy s is much larger than the momentum transfer t, s |t|, 2 → 2 scattering amplitudes are dominated by gluon exchange in the t channel
In order to verify that Regge factorisation holds at NLL accuracy in next-to-multi-Regge kinematics (NMRK), we consider in section 2.3 the one-loop two-quark three-gluon amplitude in NMRK, and we extract again the one-loop impact factor for the emission of two gluons, finding agreement with the previous computation
We use eq (2.35), with the one-loop Regge trajectory (1.7) and the one-loop quark impact factor (2.36), which in particular subtracts out all the 1/Nc terms, and we obtain the one-loop impact factor for the emission of two gluons Agg(1), which is in agreement with eq (2.24), verifying that Regge factorisation holds at NLL accuracy in NMRK, i.e. that at NLL accuracy only the antisymmetric octet 8a is exchanged in the t channel, and within 8a three Reggeised-gluon exchanges are missing
Summary
When loop corrections to the tree amplitude (1.1) are considered, it is found that at leading logarithmic (LL) accuracy in log(s/|t|), the four-gluon amplitude is given to all orders in αs by [1, 8]. The gluon Reggeisation at LL accuracy constitutes the backbone of the Balitsky-FadinKuraev-Lipatov (BFKL) equation [8, 12,13,14], which at t = 0 describes the s-channel cut forward amplitude, which through the optical theorem is equivalent to the squared amplitude integrated over all the allowed final states. Since in the BFKL equation the real emissions are included, in order to match the LL accuracy of the virtual corrections (1.6), amplitudes with five or more gluons are taken in the multi-Regge kinematics (MRK), which requires that the gluons are strongly ordered in rapidity and have comparable transverse momentum, see appendix B. The building blocks of the BFKL equation are the central-emission vertex at tree level, figure 2(a), and the Regge trajectory at one loop (1.7), figure 2(b). The impact factors (1.2) are not part of the gluon ladder, but sit at its ends, and when they are squared they constitute the jet impact factors and contribute to any jet cross section [15,16,17,18,19,20,21] which is computed through the BFKL equation
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