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We present a first-principles lattice QCD þ QED calculation at physical pion mass of the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. The total contribution of up, down, strange, and charm quarks including QED and strong isospin breaking effects is a

In a large-momentum nucleon state, the matrix element of a gauge-invariant Euclidean Wilson line operator accessible from lattice QCD can be related to the standard light-cone parton distribution function through the large-momentum effective theory (LaMET) expansion. This relation is given by a factorization formula with a non-trivial matching coefficient. Using the operator product expansion we derive the large-momentum factorization of the quasi-parton distribution function in LaMET, and show that the more recently discussed pseudo-parton distribution approach also obeys an equivalent factorization formula. Explicit results for the coefficients are obtained and compared at one-loop. We also prove that the matching coefficients in the MS scheme depend on the large partonic momentum rather than the nucleon momentum.

We present lattice results for the isovector unpolarized parton distribution with nonperturbative RI/MOM-scheme renormalization on the lattice. In the framework of large-momentum effective field theory (LaMET), the full Bjorken-x dependence of a momentum-dependent quasi-distribution is calculated on the lattice and matched to the ordinary lightcone parton distribution at one-loop order, with power corrections included. The important step of RI/MOM renormalization that connects the lattice and continuum matrix elements is detailed in this paper. A few consequences of the results are also addressed here.

We present the first lattice-QCD calculation of the pion distribution amplitude using the largemomentum effective field theory (LaMET) approach, which allows us to extract light cone parton observables from a Euclidean lattice. The mass corrections needed to extract the pion distribution amplitude from this approach are calculated to all orders in m 2 π =P 2 z . We also implement the Wilson-line renormalization which is crucial to remove the power divergences in this approach, and find that it reduces the oscillation at the end points of the distribution amplitude. Our exploratory result at 310-MeV pion mass favors a single-hump form broader than the asymptotic form of the pion distribution amplitude.

We report the first result for the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment with all errors systematically controlled. Several ensembles using 2+1 flavors of physical mass Möbius domain-wall fermions, generated by the RBC/UKQCD collaborations, are employed to take the continuum and infinite volume limits of finite volume lattice QED+QCD. We find a HLbL µ = 7.20(3.98)stat(1.65)sys × 10 −10 . Our value is consistent with previous model results and leaves little room for this notoriously difficult hadronic contribution to explain the difference between the Standard Model and the BNL experiment.

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The quark-connected part of the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment is computed using lattice QCD with chiral fermions. We report several significant algorithmic improvements and demonstrate their effectiveness through specific calculations which show a reduction in statistical errors by more than an order of magnitude. The most realistic of these calculations is performed with a near-physical, 171 MeV pion mass on a (4.6 fm) 3 spatial volume using the 32 3 × 64 Iwasaki+DSDR gauge ensemble of the RBC/UKQCD Collaboration.