First-principles determination of the proton-proton fusion matrix element from lattice QCD

Authors:
Open Access
Publisher website
Google Scholar
Abstract
Proton-proton fusion is the fundamental weak reaction initiating stellar energy production, and a first-principles determination of its matrix element remains a long-standing goal of nuclear theory. We present a lattice QCD calculation of the proton-proton fusion matrix element at a pion mass of m π ≈ 432 MeV . For this process, we implement Lellouch–Lüscher finite-volume corrections within a systematic 2 + J → 2 framework, explicitly accounting for two-nucleon rescattering effects, to relate finite-volume matrix elements to their infinite-volume counterparts. Excited-state contamination is suppressed using bilocal nucleon-nucleon interpolating operators, together with a variational analysis employing operators with the three lowest momenta. This strategy enables the determination of the two-nucleon energy spectrum and scattering parameters via Lüscher’s finite-volume formalism. Prior to including rescattering effects in the Lellouch–Lüscher factor, we obtain a reference value ⟨ d | J | p p ⟩ / g A = 0.984 ( 10 ) , where g A is the nucleon axial charge. The deviation from unity indicates a small but nonvanishing contribution from two-body currents. Our analysis shows that rescattering effects entering the Lellouch–Lüscher factors can substantially modify the two-body contribution, while large uncertainties in the two-nucleon scattering parameters propagate strongly into the finite-volume corrections. As a result, a precise determination of the two-body low-energy constant L 1 , A remains highly challenging with current lattice inputs. Despite the large uncertainty, the resulting value L 1 , A = 6.0 ( 7.1 ) fm 3 is compatible, at the level of naturalness and order of magnitude, with existing phenomenological extractions from experimental data. This work demonstrates both the feasibility and the intrinsic challenges of lattice QCD calculations of weak two-nucleon reactions, and establishes a foundation for future studies at or near the physical pion mass.
Funding Information
  • National Natural Science Foundation of China (12125501)
  • National Natural Science Foundation of China (12550007)
  • National Natural Science Foundation of China (12293060)
  • National Natural Science Foundation of China (12293063)
  • U.S. Department of Energy (DE-SC0010339)
  • U.S. Department of Energy (DE-SC0026314)
  • Office of Science (DE-SC0021147)

This publication has 57 references indexed in Scilit: