It would be very useful to find a way of reducing excited-state effects in lattice QCD calculations of nucleon structure that has a low computational cost. We explore the use of hybrid interpolators, which contain a nontrivial gluonic excitation, in
a variational basis together with the standard interpolator with tuned smearing width. Using the clover discretization of the field strength tensor, a calculation using a fixed linear combination of standard and hybrid interpolators can be done using the same number of quark propagators as a standard calculation, making this a cost-effective option. We find that such an interpolator, optimized by solving a generalized eigenvalue problem, reduces excited-state contributions in two-point correlators. However, the effect in three-point correlators, which are needed for computing nucleon matrix elements, is mixed: for some matrix elements such as the tensor charge, excited-state effects are suppressed, whereas for others such as the axial charge, they are enhanced. The results illustrate that the variational method is not guaranteed to reduce the net contribution from excited states except in its asymptotic regime, and suggest that it may be important to use a large basis of interpolators capable of isolating all of the relevant low-lying states.
We report on lattice QCD calculations of the nucleon isovector axial, scalar, and tensor charges. Our calculations are performed on two 2+1-flavor ensembles generated using a 2-HEX-smeared Wilson-clover action at the physical pion mass and lattice sp
acings $aapprox$ 0.116 and 0.093 fm. We use a wide range of source-sink separations - eight values ranging from roughly 0.4 to 1.4 fm on the coarse ensemble and three values from 0.9 to 1.5 fm on the fine ensemble - which allows us to perform an extensive study of excited-state effects using different analysis and fit strategies. To determine the renormalization factors, we use the nonperturbative Rome-Southampton approach and compare RI-MOM and RI-SMOM intermediate schemes to estimate the systematic uncertainties. Our final results are computed in the MS-bar scheme at scale 2 GeV. The tensor and axial charges have uncertainties of roughly 4%, $g_T=0.972(41)$ and $g_A=1.265(49)$. The resulting scalar charge, $g_S=0.927(303)$, has a much larger uncertainty due to a stronger dependence on the choice of intermediate renormalization scheme and on the lattice spacing.
We describe a procedure for extracting momentum derivatives of nucleon matrix elements on the lattice directly at $Q^2=0$. This is based on the Rome method for computing momentum derivatives of quark propagators. We apply this procedure to extract th
e nucleon isovector magnetic moment and charge radius as well as the isovector induced pseudoscalar form factor at $Q^2=0$ and the axial radius. For comparison, we also determine these quantities with the traditional approach of computing the corresponding form factors, i.e. $G^v_E(Q^2)$ and $G_M^v(Q^2)$ for the case of the vector current and $G_P^v(Q^2)$ and $G_A^v(Q^2)$ for the axial current, at multiple $Q^2$ values followed by $z$-expansion fits. We perform our calculations at the physical pion mass using a 2HEX-smeared Wilson-clover action. To control the effects of excited-state contamination, the calculations were done at three source-sink separations and the summation method was used. The derivative method produces results consistent with those from the traditional approach but with larger statistical uncertainties especially for the isovector charge and axial radii.
We report a calculation of the nucleon axial form factors $G_A^q(Q^2)$ and $G_P^q(Q^2)$ for all three light quark flavors $qin{u,d,s}$ in the range $0leq Q^2lesssim 1.2text{ GeV}^2$ using lattice QCD. This work was done using a single ensemble with p
ion mass 317 MeV and made use of the hierarchical probing technique to efficiently evaluate the required disconnected loops. We perform nonperturbative renormalization of the axial current, including a nonperturbative treatment of the mixing between light and strange currents due to the singlet-nonsinglet difference caused by the axial anomaly. The form factor shapes are fit using the model-independent $z$ expansion. From $G_A^q(Q^2)$, we determine the quark contributions to the nucleon spin and axial radii. By extrapolating the isovector $G_P^{u-d}(Q^2)$, we obtain the induced pseudoscalar coupling relevant for ordinary muon capture and the pion-nucleon coupling constant. We find that the disconnected contributions to $G_P$ form factors are large, and give an interpretation based on the dominant influence of the pseudoscalar poles in these form factors.
We describe a lattice approach for directly computing momentum derivatives of nucleon matrix elements using the Rome method, which we apply to obtain the isovector magnetic moment and Dirac radius. We present preliminary results calculated at the phy
sical pion mass using a 2HEX-smeared Wilson-clover action. For removing the effects of excited-state contamination, the calculations were done at three source-sink separations and the summation method was used.
