Proof of the multi-Regge form of QCD amplitudes with gluon exchanges in the NLA

Abstract

The multi-Regge form of QCD amplitudes with gluon exchanges is proved in the next-to-leading approximation. The proof is based on the bootstrap relations, which are required for the compatibility of this form with the s-channel unitarity. We show that the fulfillment of all these relations ensures the Reggeized form of energy dependent radiative corrections order by order in perturbation theory. Then we prove that all these relations are fulfilled if several bootstrap conditions on the Reggeon vertices and trajectory hold true. Now all these conditions are checked and proved to be satisfied.

The infrared structure of gauge theory amplitudes and their high-energy limit

“…The factorized form of eq. (1.4), which has been shown to hold at NLL accuracy [6] for the real part of the amplitude, is consistent with eq. (1.2), and thus with the assumptions that the only singularities in the complex angular momentum plane should be isolated poles.…”

“…(1.4). All these commutators however appear as phases, so that they will contribute only to the imaginary part of the amplitude: we see, on the other hand, that infrared poles for the real part of the amplitude Reggeize at NLL accuracy for arbitrary color exchanges in the t channel, extending the results of [6]. At NNLL accuracy, we predict that the simple form of Regge factorization, which is based on the assumption that only Regge poles arise in the angular momentum complex plane, must break down also for the…”

Improved TMD factorization for forward dijet production in dilute-dense hadronic collisions

“…One must then resort to different methods, such as those of ref. [59]. Any progress towards an all-order proof of either HEF or TMD factorization for forward dijet production in dilute-dense collisions will naturally carry JHEP09(2015)106 over to our improved TMD factorization formula (6.27) that combines both regimes.…”

Discontinuities of multi-Regge amplitudes

“…The most known application of the s i j -channel discontinuities is the proof of the multi-Regge form of QCD amplitudes [4]. Compatibility of the s-channel unitarity with the multi-Regge form leads to the bootstrap relations connecting discontinuities of the amplitudes with their real parts and the gluon trajectories:…”