  The triple-alpha process, whereby evolved stars create carbon and oxygen, is
believed to be fine-tuned to a high degree. Such fine-tuning is suggested by
the unusually strong temperature dependence of the triple-alpha reaction rate
at stellar temperatures. This sensitivity is due to the resonant character of
the triple-alpha process, which proceeds through the so-called "Hoyle state" of
$^{12}$C with spin-parity $0^+$. The question of fine-tuning can be studied
within the {\it ab initio} framework of nuclear lattice effective field theory,
which makes it possible to relate {\it ad hoc} changes in the energy of the
Hoyle state to changes in the fundamental parameters of the nuclear
Hamiltonian, which are the light quark mass $m_q$ and the electromagnetic
fine-structure constant. Here, we update the effective field theory calculation
of the sensitivity of the triple-alpha process to small changes in the
fundamental parameters. In particular, we consider recent high-precision
lattice QCD calculations of the nucleon axial coupling $g_A$, as well as new
and more comprehensive results from stellar simulations of the production of
carbon and oxygen. While the updated stellar simulations allow for much larger
{\it ad hoc} shifts in the Hoyle state energy than previously thought, recent
lattice QCD results for the nucleon S-wave singlet and triplet scattering
lengths now disfavor the scenario of no fine-tuning in the light quark mass
$m_q$.
