Abstract
We present results for the production of a pair of on-shell Z bosons via gluon fusion. This process occurs both through the production and decay of the Higgs boson, and through continuum production where the Z boson couples to a loop of massless quarks or to a massive quark. We calculate the interference of the two processes and its contribution to the cross section up to and including order O(alpha_s^3). The two-loop contributions to the amplitude are all known analytically, except for the continuum production through loops of top quarks of mass m. The latter contribution is important for the invariant mass of the two Z bosons, (as measured by the mass of their leptonic decay products, m_4l), in a regime where m_4l > 2m because of the contributions of longitudinal bosons. We examine all the contributions to the virtual amplitude involving top quarks, as expansions about the heavy top quark limit. Comparison with the analytic results, where known, allows us to assess the validity of the heavy quark expansion, and it extensions. We give results for the NLO corrections to this interference, including both real and virtual radiation.
Highlights
Out by Kauer and Passarino [1], despite the narrow width of the Higgs boson, the Higgsmediated diagram gives a significant contribution for m4l > mH
We present results for the production of a pair of on-shell Z bosons via gluongluon fusion
The massive quark box contributions are computed by factoring out the exact LO amplitude according to eq (3.27), with the Pade approximant corresponding to n = m = 3 in the definition given in eq (2.28)
Summary
We give a detailed discussion of single Higgs boson production at LO and NLO QCD and its subsequent decay to a pair of on-shell Z bosons. As mentioned earlier the LO and NLO amplitudes for single Higgs boson production have been known for a long time; either approximate results in terms of Taylor expansions in the inverse of the top quark mass s/m2 [8, 12, 24,25,26,27,28] or results keeping the exact top mass dependence [12, 29]. The explicit scale dependence of the renormalised strong coupling constant αS(nf )(μ) is dropped in the following to simplify our notation.
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