Abstract

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 the 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.

Highlights

  • The experimental determinations of the proton charge radius rpE have a discrepancy greater than 5-sigma between the value determined from spectroscopy of muonic hydrogen [1,2] and the CODATA average [3] of experimental results obtained from hydrogen spectroscopy and electron-proton scattering

  • We presented a derivative method for computing nucleon observables at zero momentum transfer

  • We applied the derivative method to the nucleon isovector magnetic moment and electric charge radius as well as the isovector induced pseudoscalar form factor at Q2 1⁄4 0 and the axial radius

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Summary

INTRODUCTION

The experimental determinations of the proton (electric) charge radius rpE have a discrepancy greater than 5-sigma between the value determined from spectroscopy of muonic hydrogen [1,2] and the CODATA average [3] of experimental results obtained from hydrogen spectroscopy and electron-proton scattering. The conventional approach for determining quantities like the charge radius on the lattice involves the computation of form factors at several different discrete values of the initial and final momenta, p⃗ and p⃗ 0, that are allowed by the periodic boundary conditions, followed by a large extrapolation to zero momentum transfer Q2 1⁄4 0. This introduces a source of systematic uncertainty, analogous to the systematic uncertainty associated with the choices of the fit ansatz and range of Q2 in extracting the proton charge radius from electron-proton scattering data.

DEFINITIONS OF THE FORM FACTORS
COMPUTATION OF MATRIX ELEMENTS USING THE TRADITIONAL METHOD
DERIVATIVE METHOD
Momentum derivatives of quark propagator
Flavor structure of correlators constructed from propagator derivatives
Momentum derivatives of the two-point and three-point functions
Momentum derivatives of the ratio
GEð0Þ dGE dQ2
LATTICE SETUP
Derivatives of the two-point functions
Method
Electromagnetic form factors
Axial form factors
SUMMARY AND OUTLOOK

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