gg → Z Z: analytic two-loop results for the low- and high-energy regions

Abstract

We compute next-to-leading order virtual two-loop corrections to the process gg → ZZ in the low-and high-energy limits, considering the contributions with virtual top quarks. Analytic results for all 20 form factors are presented including expansion terms up to 1/m 12 t and m 32 t . We use a Padé approximation procedure to extend the radius of convergence of the high-energy expansion and apply this approach to the finite virtual next-to-leading order corrections.

Top quark contribution to two-loop helicity amplitudes for Z boson pair production in gluon fusion

“…Amplitude LLLL LRLL We have checked that the form factors satisfy required (crossing) symmetry relations from refs. [5,9]. We have also checked that we obtain the same finite remainders by using the four-dimensional tensor structures in eq.…”

“…We compared the results of our calculation with those of refs. [9,10] and found good agreement. For the result presented in ref.…”

“…For on-shell production of Z bosons there is a total of 2 × 2 × 3 × 3 = 36 helicity amplitudes, but only 8 of them are independent [3,9,10]. For presenting our results, we only consider decays of the Z bosons to two massless fermions.…”

“…(2.4) and the d-dimensional tensors used in refs. [4,5,9,10]. 4 Using four-dimensional tensors makes intermediate expressions simpler and requires fewer terms in the -expansion of the master integrals.…”

“…The two-loop amplitude for massless internal quarks is also known [4,5]. However, until very recently, contributions of massive quarks have only been calculated approximately [6][7][8][9]. The goal of this paper is to present a calculation of the gg → ZZ two-loop amplitude keeping the dependence on the top quark mass.…”