First-Principles Determination of the Proton-Proton Fusion Matrix Element from Lattice QCD

TL;DR

This paper presents a lattice QCD calculation of the proton-proton fusion matrix element, addressing the challenges of finite-volume effects and rescattering, and providing insights into weak nuclear reactions from first principles.

Contribution

The study introduces a novel lattice QCD approach to compute the pp fusion matrix element, incorporating finite-volume corrections and rescattering effects, advancing ab initio nuclear reaction calculations.

Findings

Rescattering effects significantly alter the two-body contribution.

The matrix element deviation indicates a small two-body current contribution.

The low-energy constant L_{1,A} is compatible with phenomenological values despite uncertainties.

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 pp fusion matrix element at m_pi~432 MeV. We implement Lellouch-Luscher (LL) finite-volume (FV) corrections within a 2+J->2 framework, accounting for two-nucleon (2N) rescattering, to relate FV matrix elements to infinite-volume counterparts. Excited-state contamination is suppressed using bi-local nucleon-nucleon interpolating operators and a variational analysis with three lowest momenta. This enables determination of 2N energy spectrum and scattering parameters via Luscher's FV formalism. Before including rescattering effects in the LL factor, we obtain <d|J|pp>/g_A = 0.984(10), where g_A is the axial charge. The deviation from unity indicates a small nonvanishing 2-body current contribution. Our analysis shows that rescattering effects in LL factors substantially modify the 2-body contribution, while large uncertainties in 2N scattering parameters propagate strongly into FV corrections. Thus, precise determination of the 2-body low-energy constant L_{1,A} remains highly challenging with current lattice inputs. Despite the large uncertainty, L_{1,A}=6.0(7.1) fm^3 is compatible, at the level of naturalness, with phenomenological extractions. This work demonstrates feasibility and intrinsic challenges of ab initio lattice QCD calculations of weak 2N reactions, and establishes a foundation for future studies at or near the physical pion mass.