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

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 $m_q$.

Galilean invariance restoration on the lattice

We consider the breaking of Galilean invariance due to different lattice cutoff effects in moving frames and a nonlocal smearing parameter which is used in the construction of the nuclear lattice interaction. The dispersion relation and neutron-proton scattering phase shifts are used to investigate the Galilean invariance breaking effects and ways to restore it. For $S$-wave channels, ${}^1S_0$ and ${}^3S_1$, we present the neutron-proton scattering phase shifts in moving frames calculated using both Luschers formula and the spherical wall method, as well as the dispersion relation. For the $P$ and $D$ waves, we present the neutron-proton scattering phase shifts in moving frames calculated using the spherical wall method. We find that the Galilean invariance breaking effects stemming from the lattice artifacts partially cancel those caused by the nonlocal smearing parameter. Due to this cancellation, the Galilean invariance breaking effect is small, and the Galilean invariance can be restored by introducing Galilean invariance restoration operators.

Ab initio calculations of the isotopic dependence of nuclear clustering

Nuclear clustering describes the appearance of structures resembling smaller nuclei such as alpha particles (4He nuclei) within the interior of a larger nucleus. While clustering is important for several well-known examples, much remains to be discovered about the general nature of clustering in nuclei. In this letter we present lattice Monte Carlo calculations based on chiral effective field theory for the ground states of helium, beryllium, carbon, and oxygen isotopes. By computing model-independent measures that probe three- and four-nucleon correlations at short distances, we determine the shape of the alpha clusters and the entanglement of nucleons comprising each alpha cluster with the outside medium. We also introduce a new computational approach called the pinhole algorithm, which solves a long-standing deficiency of auxiliary-field Monte Carlo simulations in computing density correlations relative to the center of mass. We use the pinhole algorithm to determine the proton and neutron density distributions and the geometry of cluster correlations in 12C, 14C, and 16C. The structural similarities among the carbon isotopes suggest that 14C and 16C have excitations analogous to the well-known Hoyle state resonance in 12C.

Effective forces between quantum bound states

Recent ab initio lattice studies have found that the interactions between alpha particles (4He nuclei) are sensitive to seemingly minor details of the nucleon-nucleon force such as interaction locality. In order to uncover the essential physics of this puzzling phenomenon without unnecessary complications, we study a simple model involving two-component fermions in one spatial dimension. We probe the interaction between two bound dimers for several different particle-particle interactions and measure an effective potential between the dimers using external point potentials which act as numerical tweezers. We find that the strength and range of the local part of the particle-particle interactions play a dominant role in shaping the interactions between the dimers and can even determine the overall sign of the effective potential.

Recoil corrections in antikaon-deuteron scattering

The recoil retardation effect in the $K^-d$ scattering length is studied. Using the non-relativistic effective field theory approach, it is demonstrated that a systematic perturbative expansion of the recoil corrections in the parameter $xi=M_K/m_N$ is possible in spite of the fact that $K^-d$ scattering at low energies is inherently non-perturbative due to the large values of the $bar KN$ scattering lengths. The first order correction to the $K^-d$ scattering length due to single insertion of the retardation term in the multiple-scattering series is calculated. The recoil effect turns out to be reasonably small even at the physical value of $M_K/m_Nsimeq 0.5$.