# An update on fine-tunings in the triple-alpha process

## TL;DR

This paper updates the theoretical analysis of the triple-alpha process's sensitivity to fundamental constants, combining recent lattice QCD results with stellar simulations to assess the degree of fine-tuning required for carbon and oxygen production in stars.

## Contribution

It integrates recent lattice QCD calculations with stellar models to refine understanding of the fine-tuning in the triple-alpha process.

## Key findings

- Updated stellar simulations permit larger shifts in the Hoyle state energy.
- Recent lattice QCD results challenge the no-fine-tuning scenario for the light quark mass.
- The process remains sensitive to fundamental parameters, indicating some degree of fine-tuning.

## Abstract

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 $m_q$.