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

Abstract

AbstractThe 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 $${}^{12}\mathrm{C}$$12C with spin-parity $$0^+$$0+. The question of fine-tuning can be studied within the ab initio framework of nuclear lattice effective field theory, which makes it possible to relate 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 $$m_q$$mq and the electromagnetic fine-structure constant $$\alpha _\mathrm{em}$$αem. 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 $$g_A$$gA, 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 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 “no fine-tuning scenario” for the light quark mass $$m_q$$mq.