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The low-energy, finite-volume spectrum of the two-nucleon system at a quark mass corresponding to a pion mass of $m_{\pi }\approx 806\mathrm{MeV}$is studied with lattice quantum chromodynamics (LQCD) using variational methods. The interpolating-operator sets used in [Variational study of two-nucleon systems with lattice QCD, .] are extended by including a complete basis of local hexaquark operators, as well as plane-wave dibaryon operators built from products of both positive- and negative-parity nucleon operators. Results are presented for the isosinglet and isotriplet two-nucleon channels. In both channels, noticeably weaker variational bounds on the lowest few energy eigenvalues are obtained from operator sets which contain only hexaquark operators or operators constructed from the product of two negative-parity nucleons, while other operator sets produce low-energy variational bounds which are consistent within statistical uncertainties. The consequences of these studies for the LQCD understanding of the two-nucleon spectrum are investigated. Published by the American Physical Society2025 

We present complete results for the hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment $a_{\mu }$in the short- and intermediate-distance window regions, which account for roughly 10% and 35% of the total HVP contribution to $a_{\mu }$, respectively. In particular, we perform lattice-QCD calculations for the isospin-symmetric connected and disconnected contributions, as well as corrections due to strong-isospin breaking. For the short-distance window observables, we investigate the so-called log-enhancement effects as well as the significant oscillations associated with staggered quarks in this region. For the dominant, isospin-symmetric light-quark-connected contribution, we obtain $a_{\mu }^{ll,\mathrm{SD}}\left(\mathrm{conn}\right)=48.139\left(11{)}_{\mathrm{stat}}\right(91{)}_{\mathrm{syst}}[92{]}_{\text{total}}\times {10}^{-10}$and $a_{\mu }^{ll,\mathrm{W}}\left(\mathrm{conn}\right)=206.90\left(14{)}_{\mathrm{stat}}\right(61{)}_{\mathrm{syst}}[63{]}_{\text{total}}\times {10}^{-10}$. We use Bayesian model averaging to fully estimate the covariance matrix between the individual contributions. Our determinations of the complete window contributions are $a_{\mu }^{\mathrm{SD}}=69.05\left(1{)}_{\mathrm{stat}}\right(21{)}_{\mathrm{syst}}[21{]}_{\text{total}}\times {10}^{-10}$and $a_{\mu }^{\mathrm{W}}=236.45\left(17{)}_{\mathrm{stat}}\right(83{)}_{\mathrm{syst}}[85{]}_{\text{total}}\times {10}^{-10}$. This work is part of our ongoing effort to compute all contributions to HVP with an overall uncertainty at the few-permille level. Published by the American Physical Society2025