Abstract
A necessary ingredient for extending the BFKL equation to next-to-next-to-leading logarithmic (NNLL) accuracy is the one-loop central emission vertex (CEV) for two gluons which are not strongly ordered in rapidity. Here we consider the one-loop six-gluon amplitude in \( \mathcal{N} \) = 4 super Yang-Mills (SYM) theory in a central next-to-multi-Regge kinematic (NMRK) limit, we show that its dispersive part factorises in terms of the two-gluon CEV, and we use it to extract the one-loop two-gluon CEV for any helicity configuration within this theory. This is a component of the two-gluon CEV in QCD. Although computed in the NMRK limit, both the colour structure and the kinematic dependence of the two-gluon CEV capture much of the complexity of the six-gluon amplitudes in general kinematics. In fact, the transcendental functions of the latter can be conveniently written in terms of impact factors, trajectories, single-emission CEVs and a remainder, which is a function of the conformally invariant cross ratios which characterise the six-gluon amplitudes in planar \( \mathcal{N} \) = 4 SYM. Finally, as expected, in the MRK limit the two-gluon CEV neatly factorises in terms of two single-emission CEVs.
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ArXiv ePrint: 2204.12459
On leave from INFN, Laboratori Nazionali di Frascati, Italy. (Vittorio Del Duca)
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Byrne, E.P., Del Duca, V., Dixon, L.J. et al. One-loop central-emission vertex for two gluons in \( \mathcal{N} \) = 4 super Yang-Mills theory. J. High Energ. Phys. 2022, 271 (2022). https://doi.org/10.1007/JHEP08(2022)271
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DOI: https://doi.org/10.1007/JHEP08(2022)271