We present results for the isoscalar electromagnetic form factors of the nucleon computed on the Coordinated Lattice Simulations (CLS) ensembles with N_f = 2 + 1 flavors of 𝒪(a)-improved Wilson fermions and an 𝒪(a)-improved conserved vector current. In order to estimate the excited-state contamination, we employ several source-sink separations and apply the summation method. For the computation of the quark-disconnected diagrams, a stochastic estimation based on the one-end trick is performed, in combination with a frequency-splitting technique and the hopping parameter expansion. By these means, we obtain a clear signal for the form factors including the quark-disconnected contributions, which have a statistically significant effect on our results.

We present results for the hadronic running of the electromagnetic coupling and the weak mixing angle from simulations of lattice QCD with $N_f=2+1$ flavours of $O(a)$-improved Wilson fermions. Using two different discretisations of the vector current, we compute the quark-connected and -disconnected contributions to the hadronic vacuum polarisation (HVP) functions $\bar{\Pi}^{\gamma\gamma}$ and $\bar{\Pi}^{Z\gamma}$ for spacelike squared momenta $Q^2\leq 7$ $\mathrm{GeV}^2$. Our results are extrapolated to the physical point using ensembles at four lattice spacings, with pion masses ranging from 130 to 420 MeV. We observe a tension of up to 3.5 standard deviations between our lattice results for $\Delta\alpha_{\rm had}^{(5)}(-Q^2)$ and estimates based on the $\textit{R}$-ratio for space-like momenta in the range $Q^2=3-7\,\rm GeV^2$. To obtain an estimate for $\Delta\alpha_\mathrm{had}^{(5)}(M_Z^2)$, we employ the Euclidean split technique. The implications for comparison with global electroweak fits are assessed.

We investigate the impact of the latest Mainz/CLS collaboration’s result for the hadronic vacuum polarization (HVP) on the electroweak (EW) precision science. The subject is closely related to the muon g-2 via the HVP. Both precision tests come under scrutiny with respect to physics Beyond the Standard Model. Our HVP calculation is used for the running electromagnetic coupling at low energy and linked at various matching energies to the higher energy running evaluated by phenomenological approaches. We predict the electromagnetic coupling at the Z-pole (alpha(Mz^2)), providing a lattice-driven input to EW-global fits. Our preliminary alpha(Mz^2) is stable for a wide range of matching energies and comes with various systematics taken into account and consistent with phenomenological estimates.

The electromagnetic coupling $\alpha$ and the electroweak mixing angle $\theta_{\mathrm{W}}$ are parameters of the Standard Model (SM) that enter precision SM tests and play a fundamental r\^ole in beyond SM physics searches. Their values are energy dependent, and non-perturbative hadronic contributions are the main source of uncertainty to the theoretical knowledge of the running with energy. We present a lattice study of the leading hadronic contribution to the running of $\alpha$ and $\sin^2\theta_{\mathrm{W}}$. The former is related to the hadronic vacuum polarization (HVP) function of electromagnetic currents, and the latter to the HVP mixing of the electromagnetic current with the vector part of the weak neutral currents. We use the time-momentum representation (TMR) method to compute the HVP on the lattice, estimating both connected and disconnected contributions on $N_{\mathrm{f}}=2+1$ non-perturbatively $O(a)$-improved Wilson fermions ensembles from the Coordinated Lattice Simulations (CLS) initiative. The use of different lattice spacings and quark masses allows us to reliably extrapolate the results to the physical point.

The persistent discrepancy of about 3.5 standard deviations between the experimental measurement and the Standard Model prediction for the muon anomalous magnetic moment, aµ, is one of the most promising hints for the possible existence of new physics. Here we report on our lattice QCD calculation of the hadronic vacuum polarisation contribution $ a_\mu ^{{\rm{hvp}}} $, based on gauge ensembles with Nf = 2 + 1 flavours of O(a) improved Wilson quarks. We address the conceptual and numerical challenges that one encounters along the way to a sub-percent determination of the hadronic vacuum polarisation contribution. The current status of lattice calculations of $ a_\mu ^{{\rm{hvp}}} $ is presented by performing a detailed comparison with the results from other groups.

We report on our calculation of the strange contribution to the vector and axial vector form factors. The strange charge radii, magnetic moment, and axial charge are extracted by model independent $z$-expansion fits to the $Q^2$-dependence of the respective form factors. Furthermore, the isoscalar contribution to the axial and tensor charge is investigated by combining the calculation of connected and disconnected diagrams. The required renormalization is performed with the Rome-Southampton method. We make use of the CLS $N_f=2+1$ $\mathcal{O}(a)$-improved Wilson fermion ensembles. Results are reported for pion masses in the range $m_\pi=200-360\,\text{MeV}$ and lattice spacings $a=0.05-0.086\,\text{fm}$.

We present a lattice calculation of the leading hadronic contribution to the anomalous magnetic moment of the muon. This work is based on a subset of the CLS ensembles with $N_f = 2+1$ dynamical quarks and a quenched charm quark. Noise reduction techniques are used to improve significantly the statistical precision of the dominant light quark contribution. The main source of systematic error comes from finite size effects which are estimated using the formalism described in Ref. [7] and based on our knowledge of the timelike pion form factor. The strange and charm quark contributions are under control and an estimate of the quark-disconnected contribution is included. Isospin breaking effects will be studied in a future publication but are included in the systematic error using an estimate based on published lattice results. Our final result, $a_\mu^{\rm hvp} = (720.0\pm 12.4 \pm 6.8)\times 10^{-10}$, has a precision of about 2%.

We carry out lattice simulations of two-color QCD and spectroscopy at finite density with two flavors of rooted-staggered quarks and a diquark source term. As in a previous four-flavor study [J. B. Kogut, D. Toublan, and D. K. Sinclair, The PseudoGoldstone spectrum of two color QCD at finite density, Phys. Rev. D 68, 054507 (2003).], for small values of the inverse gauge coupling we observe a Goldstone spectrum which reflects the symmetry-breaking pattern of a Gaussian symplectic chiral random-matrix ensemble (GSE) with Dyson index beta(D) = 4, which corresponds to any-color QCD with adjoint quarks in the continuum instead of QC(2)D with fundamental quarks. We show that this unphysical behavior occurs only inside of the bulk phase of SU(2) gauge theory, where the density of Z(2) monopoles is high. Using an improved gauge action and a somewhat larger inverse coupling to suppress these monopoles, we demonstrate that the continuum Goldstone spectrum of two-color QCD, corresponding to a Gaussian orthogonal ensemble (GOE) with Dyson index beta(D) = 1, is recovered also with rooted-staggered quarks once simulations are performed away from the bulk phase. We further demonstrate how this change of random-matrix ensemble is reflected in the distribution of eigenvalues of the Dirac operator. By computing the unfolded level spacings inside and outside of the bulk phase, we demonstrate that, starting with the low-lying eigenmodes which determine the infrared physics, the distribution of eigenmodes continuously changes from the GSE to the GOE one as monopoles are suppressed.

The comparison of the theoretical and experimental determinations of the anomalous magnetic moment of the muon $(g-2)_\mu$ constitutes one of the strongest tests of the Standard Model at low energies. In this article, we compute the leading hadronic contribution to $(g-2)_\mu$ using lattice QCD simulations employing Wilson quarks. Gauge field ensembles at four different lattice spacings and several values of the pion mass down to its physical value are used. We apply the O($a$) improvement programme with two discretizations of the vector current to better constrain the approach to the continuum limit. The electromagnetic current correlators are computed in the time-momentum representation. In addition, we perform auxiliary calculations of the pion form factor at timelike momenta in order to better constrain the tail of the isovector correlator and to correct its dominant finite-size effect. For the numerically dominant light-quark contribution, we have rescaled the lepton mass by the pion decay constant computed on each lattice ensemble. We perform a combined chiral and continuum extrapolation to the physical point, and our final result is $ a_\mu^{\rm hvp}=(720.0\pm12.4_{\rm stat}\,\pm9.9_{\rm syst})\cdot10^{-10}$. It contains the contributions of quark-disconnected diagrams, and the systematic error has been enlarged to account for the missing isospin-breaking effects.

We present results from a lattice QCD study of nucleon matrix elements at vanishing momentum transfer for local and twist-2 isovector operator insertions. Computations are performed on gauge ensembles with nonperturbatively improved N-f =2 + 1 Wilson fermions, covering four values of the lattice spacing and pion masses down to M-pi approximate to 200 MeV. Several source-sink separations (typically similar to 1.0 to similar to 1.5 fm) allow us to assess excited-state contamination. Results on individual ensembles are obtained from simultaneous two-state fits across all observables and all available source-sink separations with the energy gap as a common fit parameter. Renormalization has been performed nonperturbatively using the Rome-Southampton method for all but the finest lattice spacing for which an extrapolation has been used. Physical results are quoted in the (MS) over bar scheme at a scale of mu = 2 GeV and are obtained from a combined chiral, continuum, and finite-size extrapolation. For the nucleon isovector axial, scalar, and tensor charges we find physical values of g(A)(u-d) = 1.242(25)(stat)((+00)(-31))sys, g(S)(u-d) = 1.13(11)(stat)((+07)(-06))sys and g(T)(u-d) = 0.965 (38)(stat)((+13)(-41))sys, respectively, where individual systematic errors in each direction from the chiral, continuum, and finite-size extrapolation have been added in quadrature. Our final results for the isovector average quark momentum fraction and the isovector helicity and transversity moments are given by < x >(u-d) = 0.180(25)(stat)((+14)(-06))sys, < x >(Delta u-Delta d) = 0.221(25)(stat)((+10)(-00))sys and < x >delta u-delta d = 0.212(32)(stat)((+20)(-10))sys, respectively.

We present a nucleon structure analysis including local isovector charges as well as twist-2 operator insertions. Computations are performed on CLS ensembles with $N_f=2+1$ Wilson fermions, covering four values of the lattice spacing and pion masses down to $M_\pi \approx 200\,\mathrm{MeV}$. Several source-sink separations (typically $\sim 1.0\,\mathrm{fm}$ to $\sim 1.5\,\mathrm{fm}$) allow us to assess excited-state contaminations. Results on each ensemble are obtained from simultaneous two-state fits including all observables and all available source-sink separations with the mass gap as a free fit parameter. Finally, the chiral, continuum and finite size extrapolation is performed to extract physical results.

We report on an analysis of the average quark momentum fraction of the nucleon and related quantities using Nf = 2 + 1 Wilson fermions. Computations are performed on four CLS ensembles covering three values of the lattice spacing at pion masses down to Mπ ≈ 200 MeV. Several source-sink separations (~ 1:0 fm to ~ 1:4 fm) are used to assess the excited-state contamination. To gain further insight, the generalized pencil-of-functions approach has been implemented to reduce the excited-state contamination in the relevant two-and three-point functions. Preliminary results are shown for the isovector nucleon charges from vector, axial vector and tensor derivative (twist-2) operators.

Magnetic moments of the octet baryons are computed using lattice QCD in background magnetic fields, including the first treatment of the magnetically coupled ∑0- ⋀ system. Although the computations are performed for relatively large values of the up and down quark masses, we gain new insight into the symmetries and relations between magnetic moments by working at a three-flavor mass-symmetric point. While the spinflavor symmetry in the large Nc limit of QCD is shared by the naïve constituent quark model, we find instances where quark model predictions are considerably favored over those emerging in the large Nc limit. We suggest further calculations that would shed light on the curious patterns of baryon magnetic moments.

Lattice QCD calculations with background magnetic fields are used to determine the magnetic moments of the octet baryons. Computations are performed at the physical value of the strange quark mass, and two values of the light quark mass, one corresponding to the three-flavor symmetric point, where the pion mass is 800 MeV, and the other corresponding to a pion mass of 450 MeV. The moments are found to exhibit only mild pion-mass dependence when expressed in terms of appropriately chosen magneton units- the natural baryon magneton. A curious pattern is revealed among the anomalous baryon magnetic moments which is linked to the constituent quark model, however, careful scrutiny exposes additional features. Relations expected to hold in the large-Nc limit of QCD are studied; and, in one case, a clear preference for the quark model over the large-Nc prediction is found. The magnetically coupled Lambda-Sigma system is treated in detail at the three-flavor symmetric point, with the lattice QCD results comparing favorably with predictions based on SU(3)F symmetry. This analysis enables the first extraction of the isovector transition magnetic polarizability. The possibility that large magnetic fields stabilize strange matter is explored, but such a scenario is found to be unlikely.

In this contribution we revisit simulations of two-color QCD with rooted staggered quarks at finite density, where baryon-number spontaneously breaks and a diquark condensate forms. We thereby pay special attention to simulating outside the lattice-artifact bulk phase, in which $Z_2$ monopoles condense, and investigate some of the consequences of this, e.g. on the chiral and the diquark condensate which were known to be well described by chiral effective field theory. Not surprisingly, on finer lattices outside the bulk phase the quark condensate now requires additive renormalization before it can be compared with effective field theory predictions. The subtraction must necessarily depend on the chemical potential, however. The diquark condensate is not affected by this problem and remains in good agreement with these predictions. We also compare staggered with Wilson quarks to demonstrate that the two fermion discretizations yield qualitatively different results well below half-filling already. We close with prelimiary results for the Goldstone spectrum to demonstrate that the continuum pattern is recovered also with staggered quarks outside the bulk phase.