Nuclei from QCD : Strategy, Challenges and Status

• The strategy aims to calculate nuclear properties and processes from the light-quark masses, the strong-interaction scale, and electroweak couplings.Source: INTRODUCTION · p. 1

QCD TO NUCLEI: STRATEGY

• The program matches lattice QCD and effective theories across overlapping atomic-number ranges to create an indirect but rigorous QCD-to-nuclei connection.Each theory has controlled expansion parameters and respects QCD symmetries.Source: QCD TO NUCLEI: STRATEGY · p. 2
• Lattice QCD for A ≤4 would define nucleon interactions through four-body operators, with calculations possibly extending to A ∼8.Source: QCD TO NUCLEI: STRATEGY · p. 2
• GFMC and NCSM can match chiral-potential parameters to lattice QCD and calculate nuclear properties up to A ∼20 −30.Their computational cost grows approximately as (A!)2, limiting sufficiently large nuclei.Source: QCD TO NUCLEI: STRATEGY · p. 2
• Coupled-cluster calculations extend the strategy toward A<∼100 by matching truncated cluster expansions to NCSM or GFMC results.The method is unlikely to remain practical for very large atomic numbers.Source: QCD TO NUCLEI: STRATEGY · p. 2
• Density functional theory is proposed for very large nuclei and nuclear matter, but it remains the program’s least rigorously developed component.Latticized chiral theory is also being explored for infinite nuclear matter.Source: QCD TO NUCLEI: STRATEGY · p. 3

QCD TO NUCLEI: ONE OF THE CHALLENGES

• The triple-α process depends on closely positioned 8Be and 12C states and a sub-threshold 16O state that supports carbon production.Source: QCD TO NUCLEI: ONE OF THE CHALLENGES · p. 3
• A ∼0.5% change in the NN interaction strength was sufficient to produce a universe without significant amounts of 12C or 16O [15] [16].Source: QCD TO NUCLEI: ONE OF THE CHALLENGES · p. 3
• The relevant fine-tuning concerns relative rather than absolute energy-level locations, so varying only the 12C** level may not measure system robustness.Source: QCD TO NUCLEI: ONE OF THE CHALLENGES · p. 3
• Dependence of these fine-tunings on m_q, ΛQCD, and αe remains difficult to study because computational power and theoretical infrastructure are insufficient.Only crude estimates of nuclear dependence on these fundamental constants are currently possible [18] [19].Source: QCD TO NUCLEI: ONE OF THE CHALLENGES · pp. 3–4
• The allowed ∼100 keV variation in a 12C level relative to hundreds-of-MeV strong-interaction scales implies fine-tuning among the f_i at approximately 10^-4.Source: QCD TO NUCLEI: ONE OF THE CHALLENGES · p. 4

Nucleon-Nucleon Interactions

• One-pion exchange describes the long-range NN interaction, while two-pion exchange accounts for the intermediate-range attraction [20].The short-range component is represented with an EFT-consistent functional form rather than assumed meson exchange.Source: Nucleon-Nucleon Interactions · p. 4
• The deuteron binding energy is ∼2.2 MeV and the 1S0 scattering length is ∼−24 fm, reflecting the interaction’s fine-tuned behavior.Source: Nucleon-Nucleon Interactions · p. 4
• NN EFT expands around a non-trivial, unstable infrared fixed point, so dimension-6 four-nucleon operators are not suppressed relative to dimension-4 pion-nucleon interactions [24] [25] [27] [28].In the 1S0 channel, long-distance pionic effects can be treated perturbatively [24] [25] [29].Source: Nucleon-Nucleon Interactions · p. 4

• Recent work has advanced calculations of nuclear properties from QCD using the proposed strategy.Source: QCD TO NUCLEI: STATUS · p. 5

• Fully dynamical lattice QCD now supports reliable strong-interaction calculations at small lattice spacings and large volumes.Domain-Wall and Overlap fermions provide good chiral symmetry, while chiral EFT helps control quark-mass, finite-spacing, and finite-volume effects.Source: Lattice QCD · p. 5
• I = 2 ππ scattering agrees well with chiral perturbation theory at pion masses where the perturbative expansion is reliable.Source: Lattice QCD · p. 5, Figure 1 · p. 5
• Baryon-sector progress is supported by Jefferson Laboratory investment and the Chroma lattice software suite.Source: Lattice QCD · pp. 5–6
• Preliminary lattice calculations address the nucleon's light-quark axial-current matrix element and nucleon-nucleon scattering lengths.The axial-current calculation uses low quark masses and large volumes, while the scattering-length results are from fully dynamical QCD.Source: Lattice QCD · p. 6, Figure 2 · p. 6, Figure 3 · p. 6

Light Nuclei

• GFMC calculations with AV18 and IL2 reproduce observed energy levels in light nuclei, including excited states for A = 6,7,8.Future calculations with chiral potentials would enable matching to lattice QCD.Source: Light Nuclei, Chiral Symmetry and the… · p. 7, Figure 4 · p. 7

Chiral Symmetry

• Chiral power counting determines two-, three-, and four-nucleon interactions through four orders, while operators involving four or more nucleons are parametrically suppressed.The framework also supplies the light-quark-mass dependence of nuclear interactions.Source: Light Nuclei, Chiral Symmetry and the… · pp. 7–8, Figure 5 · p. 7
• The resulting EFT and RG framework supports model-independent nuclear predictions by identifying the most general QCD-consistent interactions.Source: Light Nuclei, Chiral Symmetry and the… · p. 8

Renormalization Group

• RG evolution drives modern NN potentials to a common Vlowk interaction at Λ ∼600 MeV.The evolved interactions are softer than bare potentials, making nuclear many-body calculations significantly more convergent.Source: Light Nuclei, Chiral Symmetry and the… · p. 8, Figure 6 · p. 8

The No-Core Shell Model

• The NCSM was developed to implement effective interaction theory and move beyond the inert-core assumption of the traditional shell model.Source: The No-Core Shell Model · p. 8
• The NCSM treats all nucleons as active particles and diagonalizes a Hamiltonian built in a harmonic-oscillator basis with realistic NN, 3N, and 4N interactions.As the model space grows, eigenenergies and states become less dependent on the oscillator scale; an infinite basis would remove that dependence entirely.Source: The No-Core Shell Model · p. 9
• 10B energy levels converge greatly faster with the chiral potential than with the CD-Bonn potential as the basis size increases.The comparison uses NCSM calculations with the two potentials shown in Figure 7.Source: The No-Core Shell Model · p. 9, Figure 7 · p. 9

The Braaten-Hammer Conjecture

• At a pion mass of about 175 MeV, an additional shallow bound state is predicted to appear in the triton spectrum.The prediction follows from possible large scattering lengths in both the 1S0 and 3S1 −3 D1 channels and could be tested with lattice QCD once finite-volume three-body methods are available.Source: The Braaten-Hammer Conjecture · p. 9, Figure 8 · p. 10
• Tuning the up- and down-quark masses so both relevant scattering lengths become infinite would make the system invariant under discrete infrared scale transformations.In that scenario, the triton is predicted to have infinitely many bound states with adjacent-state energies related by a scaling relation.Source: The Braaten-Hammer Conjecture · p. 10
• Figure 8 plots pnn binding momenta against pion mass, marking triton states, physical deuteron and triton energies, and decay thresholds.Source: Figure 8 · p. 10

SUMMARY AND OUTLOOK

• Lattice QCD calculations in A = 2,3,4 systems can be matched onto few-nucleon chiral interactions for nuclear calculations.The resulting interactions are intended for use with GFMC, the NCSM, or potentially a latticized chiral theory.Source: SUMMARY AND OUTLOOK · p. 10