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We investigate an implication of the most recent observation of a second$J^\pi = 2^+$ state in $^{12}$C, which was measured using the$^{12}$C($\gamma$,$\alpha$)$^8$Be$_{\textrm{(g.s.)}}$ reaction. In addition tothe dissociation of $^{12}$C to an $\alpha$-particle and $^8$Be in its groundstate, a small fraction of events (2%) were identified as direct decays anddecays to excited states in $^8$Be. This allowed a limit on the direct3$\alpha$ partial decay width to be determined as $\Gamma_{3\alpha} < 32(4)$keV. Since this 2$^+$ state is predicted by all theoretical models to be acollective excitation of the Hoyle state, the 3$\alpha$ partial width of theHoyle state is calculable from the ratio of 3$\alpha$ decay penetrabilities ofthe Hoyle and 2$^+$ states. This was calculated using the semi-classical WKBapproach and we deduce a stringent upper limit for the direct decay branchingratio of the Hoyle state of ${\Gamma_{3\alpha} \over \Gamma} < 5.7 \times10^{-6}$, over an order of magnitude lower than previously reported. Thisresult places the direct measurement of this rare decay mode beyond currentexperimental capabilities.

A stringent upper limit on the direct 3$\alpha$ decay of the Hoyle State in $^{12}$C