Nucleon isovector charges and twist-2 matrix elements with Nf=2+1 dynamical Wilson quarks

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 ${M}_{\ensuremath{\pi}}\ensuremath{\approx}200\text{ }\text{ }\mathrm{MeV}$. Several source-sink separations (typically $\ensuremath{\sim}1.0$ to $\ensuremath{\sim}1.5\text{ }\text{ }\mathrm{fm}$) allow us to assess excited-state contamination. Results on individual ensembles are obtained from simultaneous two-state fits across all observables and all available sou…

The hadronic contribution to the running of the electromagnetic coupling and the electroweak mixing angle

37th International Symposium on Lattice Field Theory, Wuhan, China, 16 Jun 2019 - 22 Jun 2019; PoS(LATTICE 2019)010 (2019).

Nucleon average quark momentum fraction with Nf = 2+1 Wilson fermions

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.

Nucleon isovector charges and twist-2 matrix elements with Nf=2+1 dynamical Wilson quarks

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 Nf=2+1 Wilson fermions, covering four values of the lattice spacing and pion masses down to Mπ≈200 MeV. Several source-sink separations (typically ∼1.0 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 R…

Strange Electromagnetic Form Factors of the Nucleon with Nf=2+1 O(a) -Improved Wilson Fermions

We present results for the strange contribution to the electromagnetic form factors of the nucleon computed on the coordinated lattice simulation ensembles with N_{f}=2+1 flavors of O(a)-improved Wilson fermions and an O(a)-improved vector current. Several source-sink separations are investigated in order to estimate the excited-state contamination. We calculate the form factors on six ensembles with lattice spacings in the range of a=0.049-0.086  fm and pion masses in the range of m_{π}=200-360  MeV, which allows for a controlled chiral and continuum extrapolation. In the computation of the quark-disconnected contributions, we employ hierarchical probing as a variance-reduction technique.

The η′ meson at the physical point with Nf = 2 Wilson twisted mass fermions

We present results for the η′ meson and the topological susceptibility in Nf = 2 flavour lattice QCD. The results are obtained using Wilson twisted mass fermions at maximal twist with pion masses ranging from 340 MeV down to the physical point. A comparison to literature values is performed giving a handle on discretisation effects.

The leading hadronic contribution to the running of the Weinberg angle using covariant coordinate-space methods

We present a preliminary study of the leading hadronic contribution to the running of the Weinberg angle $\theta_{\mathrm{W}}$. The running is extracted from the correlation function of the electromagnetic current with the vector part of the weak neutral current using both the standard time-momentum representation method and the Lorentz-covariant coordinate-space method recently introduced by Meyer. Both connected and disconnected contributions have been computed on $N_{\mathrm{f}}=2+1$ non-perturbatively $O(a)$-improved Wilson fermions configurations from the CLS initiative. Similar covariant coordinate-space methods can be used to compute the leading hadronic contribution to the anomalous…

Lattice calculation of the hadronic leading order contribution to the muon g − 2

The European physical journal / Web of Conferences Web of Conferences : proceedings proceedings 234, 01016 - (2020). doi:10.1051/epjconf/202023401016

Model-independent determination of the nucleon charge radius from lattice QCD

Lattice QCD calculations of nucleon form factors are restricted to discrete values of the Euclidean four-momentum transfer. Therefore, the extraction of radii typically relies on parametrizing and fitting the lattice QCD data to obtain its slope close to zero momentum transfer. We investigate a new method, which allows to compute the nucleon radius directly from existing lattice QCD data, without assuming a functional form for the momentum dependence of the underlying form factor. The method is illustrated for the case of the isovector mean square charge radius of the nucleon $\langle r^2_\mathrm{isov} \rangle$ and the quark-connected contributions to $\langle r^2_p\rangle$ and $\langle r^2…

Topological susceptibility and η′ meson mass from Nf=2 lattice QCD at the physical point

In this paper we explore the computation of topological susceptibility and ${\ensuremath{\eta}}^{\ensuremath{'}}$ meson mass in ${N}_{f}=2$ flavor QCD using lattice techniques with a physical value of the pion mass as well as larger pion mass values. We observe that the physical point can be reached without a significant increase in the statistical noise. The mass of the ${\ensuremath{\eta}}^{\ensuremath{'}}$ meson can be obtained from both fermionic two point functions and topological charge density correlation functions, giving compatible results. With the pion mass dependence of the ${\ensuremath{\eta}}^{\ensuremath{'}}$ mass being flat we arrive at ${M}_{{\ensuremath{\eta}}^{\ensuremath…

The nucleon sigma terms with $N_f = 2 + 1$ O($a$)-improved Wilson fermions

We present a lattice-QCD based analysis of the nucleon sigma terms using gauge ensembles with $N_f = 2 + 1$ flavors of ${\cal O}(a)$-improved Wilson fermions, with a complete error budget concerning excited-state contaminations, chiral extrapolation as well as finite-size and lattice spacing effects. We compute the sigma terms determined directly from the matrix elements of the scalar currents. For the pion nucleon sigma term, we obtain $\sigma_{\pi N} = (43.6\pm3.8)$ MeV, where the error includes all systematics. The tension with extractions based on dispersion theory persists at the 3-$\sigma$ level. For the strange sigma term, we obtain a non-zero value, $\sigma_s=(27.1\pm9.8)$ MeV.

Hadronic light-by-light contribution to $(g-2)_\mu $ from lattice QCD: a complete calculation

The European physical journal / C 81(7), 651 (2021). doi:10.1140/epjc/s10052-021-09455-4

Flavor-singlet meson decay constants from Nf=2+1+1 twisted mass lattice QCD

We present an improved analysis of our lattice data for the $\ensuremath{\eta}--{\ensuremath{\eta}}^{\ensuremath{'}}$ system, including a correction of the relevant correlation functions for residual topological finite size effects and employing consistent chiral and continuum fits. From this analysis we update our physical results for the masses ${M}_{\ensuremath{\eta}}=557(11{)}_{\text{stat}}(03{)}_{\ensuremath{\chi}\mathrm{PT}}\text{ }\text{ }\mathrm{MeV}$ and ${M}_{\ensuremath{\eta}}^{\ensuremath{'}}=911(64{)}_{\text{stat}}(03{)}_{\ensuremath{\chi}\mathrm{PT}}\text{ }\text{ }\mathrm{MeV}$, as well as the mixing angle in the quark flavor basis $\ensuremath{\phi}=38.8(2.2{)}_{\text{stat}}…

Isovector electromagnetic form factors of the nucleon from lattice QCD and the proton radius puzzle

Physical review / D 103(9), 094522 (2021). doi:10.1103/PhysRevD.103.094522

Leading hadronic contribution to (g−2)μ from lattice QCD with Nf=2+1 flavors of O(a) improved Wilson quarks

The comparison of the theoretical and experimental determinations of the anomalous magnetic moment of the muon (g−2)μ constitutes one of the strongest tests of the Standard Model at low energies. We compute the leading hadronic contribution to (g−2)μ 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 program 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 auxilia…

Nucleon electromagnetic and axial form factors with N$_f$=2 twisted mass fermions at the physical point

We present results for the nucleon electromagnetic and axial form factors using an N$_f$=2 twisted mass fermion ensemble with pion mass of about 131 MeV. We use multiple sink-source separations to identify excited state contamination. Dipole masses for the momentum dependence of the form factors are extracted and compared to experiment, as is the nucleon magnetic moment and charge and magnetic radii.

Isovector Axial Vector Form Factors of the Nucleon from Lattice QCD with Nf=2+1 O(a)-improved Wilson Fermions

We present the analysis of isovector axial vector nucleon form factors on a set of $N_f=2+1$ CLS ensembles with $\mathcal O(a)$-improved Wilson fermions and L\"uscher-Weisz gauge action. The set of ensembles covers a pion mass range of $130-353\,$MeV with lattice spacings between $0.05\,$fm and $0.09\,$fm. In particular, the set includes a $L/a=96$ ensemble at the physical pion mass. For the purpose of the form factor extraction, we employ both the summed operator insertion method (summation method) and explicit two-state fits in order to account for excited-state contributions to the nucleon correlation functions. To describe the $Q^{2}$-behavior of the form factors, we perform $z$-expansi…

Hadronic Contributions to the Anomalous Magnetic Moment of the Muon from Lattice QCD

The Standard Model of Particle Physics describes three of the four known fundamental interactions: the strong interaction between quarks and gluons, the electromagnetic interaction, and the weak interaction. While the Standard Model is extremely successful, we know that it is not a complete description of nature. One way to search for physics beyond the Standard Model lies in the measurement of precision observables. The anomalous magnetic moment of the muon \(a_\mu \equiv \frac{1}{2}(g-2)_\mu \), quantifying the deviation of the gyromagnetic ratio from the exact value of 2 predicted by the Dirac equation, is one such precision observable. It exhibits a persistent discrepancy of 3.5 standar…

Isovector Axial Form Factor of the Nucleon from Lattice QCD

The isovector axial form factor of the nucleon plays a key role in interpreting data from long-baseline neutrino oscillation experiments. We present a lattice QCD calculation of this form factor, introducing a new method to directly extract its z-expansion from lattice correlators. Our final parameterization of the form factor, which extends up to spacelike virtualities of 0.7 GeV^2 with fully quantified uncertainties, agrees with previous lattice calculations but is significantly less steep than neutrino-deuterium scattering data suggests.

A new method for suppressing excited-state contaminations on the nucleon form factors

One of the most challenging tasks in lattice calculations of baryon form factors is the analysis and control of excited-state contaminations. Taking the isovector axial form factors of the nucleon as an example, both a dispersive representation and a calculation in chiral effective field theory show that the excited-state contributions become dominant at fixed source-sink separation when the axial current is spatially distant from the nucleon source location. We address this effect with a new method in which the axial current is localized by a Gaussian wave-packet and apply it on a CLS ensemble with $N_f=2+1$ flavors of O($a$) improved Wilson fermions with a pion mass of $m_\pi=200\,$MeV.

The anomalous magnetic moment of the muon in the Standard Model

We are very grateful to the Fermilab Directorate and the Fermilab Theoretical Physics Department for their financial and logistical support of the first workshop of the Muon g -2 Theory Initiative (held near Fermilab in June 2017) [123], which was crucial for its success, and indeed for the successful start of the Initiative. Financial support for this workshop was also provided by the Fermilab Distinguished Scholars program, the Universities Research Association through a URA Visiting Scholar award, the Riken Brookhaven Research Center, and the Japan Society for the Promotion of Science under Grant No. KAKEHNHI-17H02906. We thank Shoji Hashimoto, Toru Iijima, Takashi Kaneko, and Shohei Nis…

The pion-nucleon sigma term with $N_f = 2 + 1$ O($a$)-improved Wilson fermions

Isovector Axial Vector Form Factors of the Nucleon from Lattice QCD with $N_{f}=2+1$ $\mathcal O(a)$-improved Wilson Fermions

We present the analysis of isovector axial vector nucleon form factors on a set of $N_f=2+1$ CLS ensembles with $\mathcal O(a)$-improved Wilson fermions and Lüscher-Weisz gauge action. The set of ensembles covers a pion mass range of $130-353\,$MeV with lattice spacings between $0.05\,$fm and $0.09\,$fm. In particular, the set includes a $L/a=96$ ensemble at the physical pion mass. For the purpose of the form factor extraction, we employ both the summed operator insertion method (summation method) and explicit two-state fits in order to account for excited-state contributions to the nucleon correlation functions. To describe the $Q^{2}$-behavior of the form factors, we perform $z$-expansion…