Luchang Jin

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.

Final technical report for DOE-HEP award "Theoretical high energy physics and lattice methods" (DE-SC0026314)

In this work, we perform a lattice QCD calculation of the branching ratios and the form factors of radiative leptonic decays P → ℓ ν ℓ γ ( P = π , K ) using N f = 2 + 1 domain wall fermion ensembles generated by the RBC and UKQCD Collaborations at the physical pion mass. We adopt the infinite-volume reconstruction (IVR) method, which extends lattice data to infinite volume and effectively controls the finite-volume effects. This study represents a first step toward a complete calculation of radiative corrections to leptonic decays using the IVR method, including both real photon emissions and virtual photon loops. For decays involving a final-state electron, collinear radiative corrections, enhanced by the large logarithmic factors such as ln ( m π 2 / m e 2 ) and ln ( m K 2 / m e 2 ) , can reach the level of O ( 10 % ) and are essential at the current level of theoretical and experimental precision. After including these corrections, our result for π → e ν e γ agrees with the PIBETA measurement; for K → e ν e γ , our results are consistent with the KLOE data and exhibit a 1.7 σ tension with E36; and for K → μ ν μ γ , where radiative corrections are negligible, our results confirm the previously observed discrepancies between lattice results and the ISTRA/OKA measurements at large photon energies, and with the E787 results at large muon-photon angles.

We compute the complex, long-distance two-photon-exchange amplitude which contributes to the rare K L → μ + μ − decay from lattice QCD. We use a 24 3 × 64 physical-pion-mass gauge field ensemble at an inverse lattice spacing of 1.023 GeV and a QED ∞ -based formalism. Our implementation strategies for all five non-SU(3)-flavor-suppressed diagram topologies are given in detail. We achieve a 25% statistical precision on the dispersive part of this long-distance amplitude. This calculation is carried out with 2 + 1 quark flavors and therefore requires the addition of counterterms to compensate for the absence of the Glashow-Iliopoulos-Maiani mechanism. These counterterms are not included in the current calculation and will be the subject of a second paper. Although a direct comparison to experiment cannot yet be made because of those omitted counterterms, the present exploratory calculation allows one to identify principal sources of statistical uncertainty in this calculation. The precision of our results is limited by the reconstruction of the physical contribution of the η intermediate state, for which various strategies are tested and compared.

We use lattice field theory to study the finite-volume energy spectrum of the π π system in S U ( 2 ) chiral effective field theory (ChEFT) at leading order in the chiral expansion. This finite-volume spectrum can be directly related to the (infinite-volume) π π scattering phase shifts by Lüscher’s formula. We compare our results to the finite-volume spectrum obtained from lattice QCD by the RBC-UKQCD Collaboration. Our calculation and the lattice QCD calculation are both performed with the physical pion mass and the same lattice volume (as measured in physical units). However, we find significant differences between the two calculations in the isospin I = 0 channel. In particular, there is a nearly stable σ resonance in our lattice ChEFT calculation, which is absent in the lattice QCD calculation. This likely indicates that ChEFT does not converge well with a naive lattice regularization.

Neutrinoless double-beta ( 0 ν β β ) decays provide an excellent probe for determining whether neutrinos are Dirac or Majorana fermions. The short-range matrix elements associated with the π − → π + e e process contribute at leading order in the 0 ν β β decay channel n n → p p e e through pion exchange between nucleons. However, current lattice calculations show notable discrepancies in predicting these short-range contributions. To address this issue, we perform a lattice QCD calculation of the π − → π + e e matrix elements using domain wall fermion ensembles at the physical pion mass generated by the RBC/UKQCD Collaboration. To mitigate contamination from around-the-world effects, we develop a new method to reconstruct and subtract them directly from lattice data. We then perform nonperturbative renormalization in the regularization-independent symmetric momentum-subtraction scheme (RI/SMOM), using the ( γ μ , γ μ ) and ( q , q ) projectors. Compared with previous studies, this work reduces the uncertainties in the matrix elements and provides an independent cross-check that helps to reconcile the discrepancies among previous lattice calculations.

Final technical report for DOE-HEP early career award "Lattice Calculation of the QED Corrections to Meson Leptonic Decay" (DE-SC0021147)

We develop an extended framework for the hybrid Monte Carlo (HMC) algorithm in lattice gauge theory by embedding the S U ( N ) group into the space of general complex matrices, M N ( C ) . Auxiliary directions will be completely factorized in the path integral, and the embedding does not alter the expectation values of the original theory. We perform the molecular dynamics updates by using the matrix elements of W ∈ M N ( C ) as the dynamical variables without group theoretic constraints. The framework enables us to introduce nonseparable Hamiltonians for the HMC in lattice gauge theory exactly, whose immediate application includes the Riemannian manifold HMC.

We provide the first calculation of the Euclidean long-distance window of the isospin-symmetric light-quark connected contribution to the hadronic vacuum polarization for the muon g − 2 and find a μ LD , iso , conn , ud = 411.4 ( 4.3 ) ( 2.4 ) × 10 − 10 . We also provide the currently most precise calculation of the total isospin-symmetric light-quark connected contribution, a μ iso , conn , ud = 666.2 ( 4.3 ) ( 2.5 ) × 10 − 10 in the BMW20 world, which is more than 4 σ larger compared to the data-driven estimates of Boito [] and 1.7 σ larger compared to the lattice QCD result of BMW20.