feynlag.export.ufo.vvvv.adjoint_vvv

feynlag.export.ufo.vvvv.adjoint_vvv(group)

Colour-stripped VVV coupling of an UNBROKEN non-abelian group.

The cubic twin of adjoint_vvvv(). An unbroken group’s 3-boson vertex is ONE UFO particle repeated three times, with the adjoint index carried by ADJOINT_VVV_COLOR, so the coupling that pairs with it must be colour-stripped.

cubic_couplings works in the weak basis, where its entry for a component triple is -g * f^{abc} — it already contains the colour factor. Feeding those component-specific values to the writer alongside a colour tensor multiplies by colour twice. Divided out, the coupling is -g on every triple, independent of N (verified for SU(2), SU(3) and SU(4) against every non-zero structure constant) — matching MadGraph’s stock sm GC_10 = -G for [g,g,g].

That bug hid for a long time because the only exported triple was (G_1,G_2,G_3), and f^{123} = 1 makes the colour factor unity, so the emitted number was accidentally right.

No ``feynman_rule`` flag, unlike adjoint_vvvv(). The cubic carries one derivative, so the i from d_mu -> i p_mu cancels the Feynman-rule i and cubic_couplings’ output is already the vertex coefficient — real for a real basis, which is why ggg = -g_s has no i while gggg = i g_s^2 does. (Confirmed by differentiating -1/4 F F directly, including the Feynman i: it reproduces cubic_couplings exactly.) The quartic has no derivative, so its i survives and has to be added.

Returns:

the single VVV1 coupling, to be emitted with ADJOINT_VVV_COLOR.