= Solution
In <gluon-fusion Higgs production>, two <gluons> couple to a closed <top quark> loop, and the <Higgs boson> couples to that massive <quark> through its <Yukawa interaction>. The right panel of the diagram in <3/c> shows one explicit colour-flow component: internal $t_r\to t_b$ at one <gluon> insertion, then $t_b\to t_r$ at the other; the colour-neutral <Higgs boson> insertion preserves the internal <color charge>. Include both loop orderings. The <color charge> factor is
$$
\operatorname{tr}(T^aT^b)=\frac12\delta^{ab},
$$
so the two incoming <gluons> are projected onto a <colour singlet>. The <Yukawa coupling> is $y_t=\sqrt2m_t/v$, and the $h\bar tt$ vertex has strength $m_t/v$. No direct tree-level $hgg$ <mass> coupling is needed. Integrating out a sufficiently heavy <top quark> generates an effective interaction proportional to $(h/v)G^a_{\mu\nu}G^{a\mu\nu}$, which is allowed by <gauge invariance> even though the <gluon> is massless.
There is also no kinematic obstacle: two massless particles with nonparallel <momenta> can have nonzero total <invariant mass>. In particular, head-on <gluons> have $\hat s=4E_1E_2$, providing the <energy> needed for the <Higgs boson> at the <LHC>.
Back to article page
