We discuss the prospects for improving the precision on the hadronic corrections to the anomalous magnetic moment of the muon, and the plans of the Muon g-2 Theory Initiative to update the Standard Model prediction.

The largest uncertainties in the Standard Model calculation of the anomalous magnetic moment of the muon (g − 2)μ come from hadronic contributions. In particular, it can be expected that in a few years the subleading hadronic light-by-light (HLbL) contribution will dominate the theory uncertainty. We present a dispersive description of the HLbL tensor, which is based on unitarity, analyticity, crossing symmetry, and gauge invariance. Such a model-independent Approach opens up an avenue towards a data-driven determination of the HLbL contribution to the (g − 2)μ.

Based on dispersion theory, we present a formalism for a model-independent evaluation of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon. In particular, we comment on the definition of the pion pole in this framework and provide a master formula that relates the effect from ππ intermediate states to the partial waves for the process γ * γ * → ππ. All contributions are expressed in terms of on-shell form factors and scattering amplitudes, and as such amenable to an experimental determination.

The recently proposed hard-pion chiral perturbation theory predicts that the leading chiral logarithms factorize with respect to the energy dependence in the chiral limit. This claim has been successfully tested in the pion form factors up to two loops in chiral perturbation theory. In the present paper we explain this factorization property at two loops and even show that it is valid to all orders for a subclass of diagrams. We also demonstrate that factorization is violated starting at three loops.

We present a high-statistics calculation of nucleon electromagnetic form factors in $N_f=2+1$ lattice QCD using domain wall quarks on fine lattices, to attain a new level of precision in systematic and statistical errors. Our calculations use $32^3 \times 64$ lattices with lattice spacing a=0.084 fm for pion masses of 297, 355, and 403 MeV, and we perform an overdetermined analysis using on the order of 3600 to 7000 measurements to calculate nucleon electric and magnetic form factors up to $Q^2 \approx$ 1.05 GeV$^2$. Results are shown to be consistent with those obtained using valence domain wall quarks with improved staggered sea quarks, and using coarse domain wall lattices. We determine the isovector Dirac radius $r_1^v$, Pauli radius $r_2^v$ and anomalous magnetic moment $\kappa_v$. We also determine connected contributions to the corresponding isoscalar observables. We extrapolate these observables to the physical pion mass using two different formulations of two-flavor chiral effective field theory at one loop: the heavy baryon Small Scale Expansion (SSE) and covariant baryon chiral perturbation theory. The isovector results and the connected contributions to the isoscalar results are compared with experiment, and the need for calculations at smaller pion masses is discussed.

M. F. Lin ∗a†, J. D. Bratt a, M. Engelhardt b, Ph. Hägler c, T. R. Hemmert d, H. B. Meyer a, J. W. Negele a, A. V. Pochinsky a, M. Procura a, W. Schroers e, S. Syritsyn a aCenter for Theoretical Physics, Massachusetts Institute o f T chnology, Cambridge, MA 02139, USA b Physics Department, New Mexico State University, Las Cruce s, NM 88003-8001, USA c Institut für Theoretische Physik T39, Physik-Department d er TU München, James-Franck-Straße, D-85747 Garching, Germany d Theoretische Physik, Universität Regensburg, D-93040 Reg ensburg, Germany e Institute of Physics, Academia Sinica, Taipei 115, Taiwan

We present the recent high-statistics calculations of the nucleon electromagnetic form factors with fully dynamical domain wall fermions on the 32^3x64 lattices generated by the RBC and UKQCD collaborations, with pion masses at roughly 297 MeV, 355 MeV and 403 MeV. We study the phenomenological fits to the momentum transfer dependence of the form factors and investigate chiral extrapolations for the Dirac radius, Pauli radius and the anomalous magnetic moment using two variants of chiral effective field theories, the small scale expansion (SSE) and covariant baryon chiral perturbation theory.

We present high statistics results for the structure of the nucleon from a mixed-action calculation using 2+1 flavors of asqtad sea and domain wall valence fermions. We perform extrapolations of our data based on different chiral effective field theory schemes and compare our results with available information from phenomenology. We discuss vector and axial form factors of the nucleon, moments of generalized parton distributions, including moments of forward parton distributions, and implications for the decomposition of the nucleon spin.

We present initial calculations of nucleon matrix elements of twist-two operators with 2+1 flavors of domain wall fermions at a lattice spacing a = 0.084 fm for pion masses down to 300 MeV. We also compare the results with the domain wall calculations on a coarser lattice.

We calculate the light hadron spectrum in full QCD using two plus one flavor asqtad sea quarks and domain wall valence quarks. Meson and baryon masses are calculated on a lattice of spatial size $L\ensuremath{\approx}2.5\text{ }\text{ }\mathrm{fm}$, and a lattice spacing of $a\ensuremath{\approx}0.124\text{ }\text{ }\mathrm{fm}$, for pion masses as light as ${m}_{\ensuremath{\pi}}\ensuremath{\approx}300\text{ }\text{ }\mathrm{MeV}$, and compared with the results by the MILC Collaboration with asqtad valence quarks at the same lattice spacing. Two- and three-flavor chiral extrapolations of the baryon masses are performed using both continuum and mixed action heavy baryon chiral perturbation theory. Both the three-flavor and two-flavor functional forms describe our lattice results, although the low-energy constants from the next-to-leading order $SU(3)$ fits are inconsistent with their phenomenological values. Next-to-next-to-leading order $SU(2)$ continuum formulae provide a good fit to the data and yield an extrapolated nucleon mass consistent with experiment, but the convergence pattern indicates that even our lightest pion mass may be at the upper end of the chiral regime. Surprisingly, our nucleon masses are essentially linear in ${m}_{\ensuremath{\pi}}$ over our full range of pion masses, and we show this feature is common to all recent dynamical calculations of the nucleon mass. The origin of this linearity is not presently understood, and lighter pion masses and increased control of systematic errors will be needed to resolve this puzzling behavior.

In order to advance lattice calculations of moments of unpolarized, helicity, and transversity distributions, electromagnetic form factors, and generalized form factors of the nucleon to a new level of precision, this work investigates several key aspects of precision lattice calculations. We calculate the number of configurations required for constant statistical errors as a function of pion mass, describe the coherent sink method to help achieve these statistics, examine the statistical correlations between separate measurements, study correlations in the behavior of form factors at different momentum transfer, examine volume dependence, and compare mixed action results with those using comparable dynamical domain wall configurations. We also show selected form factor results and comment on the QCD evolution of our calculations of the flavor non-singlet nucleon angular momentum.

An updated and extended analysis of the quark-mass dependence of the nucleon's axial-vector coupling constant ${g}_{A}$ is presented in comparison with state-of-the-art lattice QCD results. Special emphasis is placed on the role of the $\ensuremath{\Delta}(1232)$ isobar. It is pointed out that standard chiral perturbation theory of the pion-nucleon system at order ${p}^{4}$ fails to provide an interpolation between the lattice data and the physical point. In constrast, a version of chiral effective field theory with explicit inclusion of the $\ensuremath{\Delta}(1232)$ proves to be successful. Detailed error analysis and convergence tests are performed. Integrating out the $\ensuremath{\Delta}(1232)$ as an explicit degree of freedom introduces uncontrolled errors for pion masses ${m}_{\ensuremath{\pi}}\ensuremath{\gtrsim}300\text{ }\text{ }\mathrm{MeV}$.

An updated and extended analysis of the quark-mass dependence of the nucleon's axial-vector coupling constant g(A) is presented in comparison with state-of-the-art lattice QCD results. Special emphasis is placed on the role of the Delta(1232) isobar. It is pointed out that standard chiral perturbation theory of the pion-nucleon system at order p(4) fails to provide an interpolation between the lattice data and the physical point. In constrast, a version of chiral effective field theory with explicit inclusion of the Delta(1232) proves to be successful. Detailed error analysis and convergence tests are performed. Integrating out the Delta(1232) as an explicit degree of freedom introduces uncontrolled errors for pion masses m(pi)greater than or similar to 300 MeV.

Previous extrapolations of lattice QCD results for the nucleon mass to the physically relevant region of small quark masses, using chiral effective field theory, are extended and expanded in several directions. A detailed error analysis is performed. An approach with explicit $\ensuremath{\Delta}(1232)$ degrees of freedom is compared to a calculation with only pion and nucleon degrees of freedom. The role of the $\ensuremath{\Delta}(1232)$ for the low-energy constants of the latter theory is elucidated. The consistency with the chiral perturbation theory analysis of pion-nucleon scattering data is examined. It is demonstrated that this consistency can indeed be achieved if the $\ensuremath{\Delta}(1232)$ dominance of the $P$-wave pion-nucleon low-energy constant ${c}_{3}$ is accounted for. Introduction of the $\ensuremath{\Delta}(1232)$ as an explicit propagating degree of freedom is not crucial in order to describe the quark-mass dependence of the nucleon mass, in contrast to the situation with spin observables of the nucleon. The dependence on finite lattice volume is shown to yield valuable additional constraints. What emerges is a consistent and stable extrapolation scheme for pion masses below 0.6 GeV.

We present an updated analysis of the quark mass dependence of the nucleon mass MN and nucleon axial-vector coupling g(A), comparing different formulations of SU(2) Baryon Chiral Effective Field Theory, with and without explicit Delta(1232) degrees of freedom. We discuss the outcome of the corresponding interpolations between lattice QCD data and the physical values for these two nucleon observables. It turns out that in order to obtain successful interpolating functions at one-loop order, the inclusion of explicit Delta(1232) degrees of freedom is not decisive for the nucleon mass but crucial for g(A). A chiral extrapolation of recent lattice results by the LHP collaboration is also shown.

We analyze the quark mass dependence of the nucleon mass M-N and the axial-vector coupling constant g(A) in the framework of the effective low-energy theory of QCD in the one-nucleon sector and two flavor case, namely SU(2) Baryon Chiral Perturbation Theory (BChPT). The relevant formulae are compared with those obtained using an extension of this effective field theory which explicitly includes Delta (1232) degrees of freedom. A numerical analysis is performed taking as input lattice QCD data. It turns out that in order to obtain at the one-loop level an interpolating function able to connect the physical point with present lattice data at relatively large pion masses, the inclusion of explicit Delta (1232) degrees of freedom is not decisive for the nucleon mass but crucial for g(A).

We report on recent work about the study of quark mass dependence of nucleon magnetic moments and axial-vector coupling constant. We examine the feasibility of chiral effective field theory methods for the extrapolation of lattice QCD data obtained at relative large pion masses down to the physical values.