Measurement of the triple gluon vertex from double quark tagged 4-jet events

The 4-jet events collected by the DELPHI experiment at LEP1 in 1992, 1993 and 1994 are analysed to determine the contribution of the triple-gluon vertex. Two of the four jets are tagged as jets from $b$- or $c$-quarks using lifetime and lepton transverse momentum information. The 4-jet contributions from double-gluon bremsstrahlung, the triple-gluon vertex, and secondary quark-antiquark pair production then yield significantly different two-dimensional distributions in the generalized Nachtmann Reiter angle %$\Theta^{*}_{NR}$ versus the opening angle of the two secondary jets. These distributions are used to fit $C_A/C_F$, the ratio of the coupling strength of the triple-gluon vertex to that of gluon bremsstrahlung, and $N_C/N_A$, the ratio of the number of quark colours to the number of gluons, giving \begin{center} $C_A/C_F=2.51 \pm 0.28$ ~and~ $N_C/N_A=0.38 \pm 0.10$ \end{center} in agreement with the values expected from QCD: \begin{center} $C_A/C_F = 9/4 = 2.25$ ~and~ $N_C/N_A = 3/8 = 0.375$. \end{center}