126 f(-p₁) + f(-p₂) → W⁺(ν(p₃) + e⁺(p₄)) + W^-(e^-(p₅) + ν(p₆)), (gg only, (H + gg → WW) squared)

126.1 H → W⁺W^- production, (m_t = finite), processes 123-127

These processes represent the production of a Higgs boson that decays to W⁺W^-, with subsequent decay into leptons. For process 123, the exact form of the triangle loop coupling a Higgs boson to two gluons is included, with both top and bottom quarks circulating in the loop. This is to be contrasted with process 113 in which only the top quark contribution is included in the effective coupling approach.

Process 124 includes only the effect of the interference of the Higgs and gg → W⁺W^- amplitudes, as described in ref. [1]. The calculation is available at LO only. LO corresponds to O(α_s²) in this case. The calculation of loops containing the third quark generation includes the effect of the top quark mass (but m_b = 0), while the first two generations are considered massless. For numerical stability, a small cut on the transverse momentum of the W bosons is applied: p_T(W) > 0.05 GeV for loops containing massless (first or second generation) quarks, p_T(W) > 2 GeV for (t,b) loops. This typically removes less than 0.1% of the cross section. The values of these cutoffs can be changed by editing src/HWW/gg_WW_int.f and recompiling.

Process 125 includes all gg-initiated diagrams that have a Higgs boson in the s-channel, namely the square of the s-channel Higgs boson production and the interference with the diagrams that do not contain a Higgs boson, (i.e. gg → W⁺W^-→ ν_ee⁺e^-ν_e), i.e. |M_H|² + 2|M_H^*M_WW|.

The result for the square of the box diagrams alone, i.e. the process gg → W⁺W^-→ ν_ee⁺e^-ν_e, may be obtained by running process nproc=61 with part=virt and ggonly=.true.

Process 126 calculates the full result for this process from gg-initiated diagrams. This includes diagrams that have a Higgs boson in the s-channel, the continuum W⁺W^- diagrams described above and their interference, i.e. |M_H + M_WW|².

Process 127 calculates the full result for this process for gg-initiated box diagrams alone, gg → W⁺W^-, i.e. |M_WW|².

126.2 Plotter

nplotter_VV.f is the default plotting routine.

126.3 Example input and output file(s)

input126.ini process126.out

References