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

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 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 mq 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 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 scenario of no fine-tuning in the light quark mass mq.

Nuclear currents in chiral effective field theory

“…the 3 S 1 and 1 S 0 scattering lengths at unphysical (but not too large) quark masses are available, see Refs. [173] and references therein for a discussion of the current status of research along this line.…”

θ -dependence of light nuclei and nucleosynthesis

“…There have been many studies relating the sensitivity of carbon production to fundamental physics in relation to the anthropic principle [23,24,26,[86][87][88][89][90][91][92]. The production of 12 C in stars requires a triple fine tuning: (i) the decay lifetime of 8 Be, is relatively long, and is of order 10 −16 s, which is four orders of magnitude longer than the scattering time for two α particles, (ii) there must exist an excited state of carbon which lies just above the energy of 8 Be + α and (iii) the energy level of 16 O which sits at 7.1197 MeV must be nonresonant and below the energy of 12 C + α, at 7.1616 MeV, so that most of the produced carbon is not destroyed by further stellar processing.…”

“…Quark mass variation of nuclear properties and reactions are considered, e.g., in Refs. [13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Furthermore, if the variation of quark masses is due to an overall variation in the Yukawa couplings, it will feed into variations of a host of fundamental observables including the gauge couplings, and affect Big Bang Nucleosynthesis (BBN) [27][28][29][30][31], the lifetime of long-lived nuclei [32], and atomic clocks [33].…”

Subleading contributions to the nuclear scalar isoscalar current

“…the 3 S 1 and 1 S 0 scattering lengths at unphysical (but not too large) quark masses are available, see Refs. [63] and references therein for a discussion of the current status of research along this line. Last but not least, we found, similarly to the one-pion exchange contributions, no 1/m-corrections and no energydependent short-range terms at the order we are working.…”

“…Interestingly, the scalar matrix elements were found in these studies to be strongly affected by nuclear effects (in contrast to the axial-vector and tensor charges), which indicates that scalar exchange currents may play an important role. Last but not least, as will be shown below, the scalar isoscalar currents are directly related to the quark mass dependence of the nuclear forces, a subject that gained a lot of attention in the EFT community in connection with ongoing lattice QCD efforts in the multibaryon sector [47][48][49][50][51][52][53][54][55], a conjectured infrared renormalization group limit cycle in QCD [56,57], searches for possible temporal variation of the light quark masses [58,59] and anthropic considerations related to the famous Hoyle state in 12 C [60][61][62][63].…”