NNLO QCD corrections to pp → γ * γ * in the large N F limit

Abstract

Abstract:We compute the NNLO QCD corrections for the hadroproduction of a pair of off-shell photons in the limit of a large number of quark flavors. We perform a reduction of the two-loop amplitude to master integrals and calculate the latter analytically as a Laurent series in the dimensional regulator using modern integration methods. Real radiation corrections are evaluated numerically with a direct subtraction of infrared limits which we cast in a simple factorized form. The results presented here constitute a gauge invariant part of the full NNLO corrections but are not necessarily dominant. We view this calculation as a step towards a complete computation. Our partial corrections to the total cross-section are about 1%-3% and vary with the virtuality of the two off-shell photons.

The two-loop helicity amplitudes for gg → V 1 V 2 → 4 leptons

“…The former were used for the first NNLO fully-inclusive calculations of ZZ [3] and W + W − [4] production at the LHC, while the latter allowed the computation of the two-loop corrections to qq → V 1 V 2 [39,40]. A subset of these master integrals was also computed independently in [5,41]. While the inclusion of massive top-loop mediated subprocesses would be of interest for some phenomenological applications [20,42], the computation of the two-loop amplitudes requires knowledge of challenging new master integrals, which should be addressed in the future.…”

“…The main production channel for pairs of vector bosons at hadron colliders is quark-antiquark annihilation and great progress has been achieved in the last years with the computation of the next-to-nextto-leading order (NNLO) QCD corrections to qq → γγ [1], qq → Zγ [2], qq → ZZ [3] and qq → W + W − [4] production at the LHC. Furthermore, the fermionic NNLO corrections to qq → γ * γ * were derived in [5].…”

The two-loop helicity amplitudes for q q ¯ ′ → V 1 V 2 → 4 $$ q\overline{q}^{\prime}\to {V}_1{V}_2\to 4 $$ leptons

“…The integrals for the most general case of non-equal masses were derived in [29][30][31], which allowed to construct the full two-loop helicity amplitude for qq → V 1 V 2 in [32]. A subset of these integrals was derived independently in [33,34] and used in the derivation of the fermionic NNLO corrections to γ * γ * production [34]. In this paper, we perform an independent rederivation of these integrals and optimise our solutions for numerical performance.…”

W+W−Production at Hadron Colliders in Next to Next to Leading Order QCD

“…To check and further improve the numerical stability of exceptional phase space points the quadruple precision implementation of the integrand reduction method [43] in CUTTOOLS [44] is employed in combination with ONELOOP [45]. Following the recent computation of the relevant two-loop master integrals [46][47][48][49][50], the last missing contribution-the genuine two-loop correction to the W þ W − amplitude-has been computed by some of us and will be reported elsewhere [51], thereby improving upon earlier results in the high-energy limit [52]. For the numerical evaluation of the multiple polylogarithms in the two-loop expressions, we employ the implementation [53] in the GINAC [54] library.…”