Two-loop QCD helicity amplitudes for $ q\overline q $ → W ±γ and $ q\overline q $ → Z 0γ

Abstract

The self-couplings of the electroweak gauge bosons are probed at hadron colliders through the production of a massive gauge boson and a photon. To extend the theoretical description of this type of final states towards next-to-next-to-leading order (NNLO) in QCD, we derive the two-loop QCD corrections to the helicity amplitudes describing the production of a massive gauge boson in association with a real photon. Our results are obtained by applying projectors to the general parton-level tensor structure. The leptonic decay of the vector boson is included, thus allowing for a fully exclusive description of the final state. The infrared poles of the amplitudes are described by an infrared factorization formula. We provide an analytic expression for the finite remainder of the amplitude in terms of one-and two-dimensional harmonic polylogarithms. The amplitudes are expressed in the physical kinematics relevant to gauge-boson-plus-photon production at hadron colliders. As a by-product, we also derive the two-loop QCD amplitudes for vector-boson-plus-jet production at hadron colliders.

Two-loop master integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering

“…NLO corrections to the production of a vector boson with a jet were considered in [29][30][31][32]. The two-loop QCD helicity amplitudes for the production of a Z or a W with a photon have also been calculated [33]. For small p T (p T m W , m Z ) the convergence of the fixed-order calculation is spoiled by the large logarithmic terms α n S log m (m 2 W /p 2 T ) that have to be resummed [34][35][36][37][38][39][40][41][42][43][44].…”

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

“…As a new ingredient, each vector boson pair production process at NNLO requires the two-loop corrections to the basic scattering amplitude for quark-antiquark annihilation: qq → V 1 V 2 . These have been known for a while already for γγ [19,20] and V γ [21,22] production, enabling the calculations of these processes [23,24] to NNLO accuracy.…”

The two-loop master integrals for $ q\overline{q} $ → VV

“…NNLO QCD corrections were calculated up to now for γγ [11] and Zγ [12] production. Key ingredient to the NNLO calculations are the two-loop matrix elements for qq → V 1 V 2 , which are known for γγ [13,14] and V γ [15,16] production, and for qq → W W in the high energy approximation [17]. The full calculation of two-loop matrix elements for the production of two massive vector bosons is still an outstanding task, and requires the derivation of a new…”