Abstract
Abstract Basing on the Slavnov-Taylor identities, we derive a new prescription to obtain gauge invariant tree-level scattering amplitudes for the process g * g → N g within high energy factorization. Using the helicity method, we check the formalism up to several final state gluons, and we present analytical formulas for the the helicity amplitudes for N = 2. We also compare the method with Lipatov’s effective action approach.
Highlights
BK [6, 7], CCFM [8, 9] or recently proposed new evolution equations accounting for both saturation and processes at large momentum transfers [10, 11]
We check the formalism up to several final state gluons, and we present analytical formulas for the the helicity amplitudes for N = 2
Our construction holds for any number of final state gluons and as an example we give a detailed derivation and discussion for the helicity amplitudes of the process g∗g → gg
Summary
Our considerations of the off-shell amplitudes are embedded in the formalism of high energy factorization. The basic observation is that the cross section for a hadronic process can be decomposed at high energies into transversal momentum dependent parton densities and the hard partonic cross section with off-shell initial state partons. In the considered high energy limit, the incident momenta are parametrized as k1μ ≃ ξ1nμa + k1μT , k2μ ≃ ξ2nμb + k2μT ,. The above might be taken as a prescription to calculate amplitudes for arbitrary processes, but it will in general not lead to gauge-invariant results. To achieve the latter, additional contributions are needed. They are usually obtained by considering a larger, fully on-shell, process from which an amplitude for the off-shell process is extracted.
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