Nucleon radii and form factors at $Q^2=0$ using momentum derivatives
- Nesreen HASAN
- Nesreen HASAN (Bergische Universitaet Wuppertal)
- Stefan MEINEL (Department of Physics, University of Arizona; RIKEN BNL Research Center, Brookhaven National Laboratory)
- Jeremy GREEN (NIC, Deutsches Elektronen-Synchrotron)
- Michael ENGELHARDT (Department of Physics, New Mexico State University)
- Stefan KRIEG (IAS, Juelich Supercomputing Centre; Bergische Universitaet Wuppertal)
- Sergey SYRITSYN (IKEN BNL Research Center, Brookhaven National Laboratory)
- John NEGELE (Center for Theoretical Physics, Massachusetts Institute of Technology)
- Andrew POCHINSKY (Center for Theoretical Physics, Massachusetts Institute of Technology)
The conventional approach for calculating the nucleon radius on a finite-size lattice requires interpolation of form factors in the quantized momentum transfer $Q^2$. This interpolation is model-dependent and is therefore a source of systematic uncertainty. Recently, we have presented a derivative method for computing the isovector Dirac radius and the anomalous magnetic moment of the nucleon directly at zero momentum transfer. This approach is based on the Rome method and relies on calculating the first- and second-order momentum derivatives of nucleon correlation functions with respect to the initial-state momentum. We also extended the use of this method to include the extraction of the nucleon axial radius and the induced pseudoscalar form factor at $Q^2=0$. We found the aforementioned setup of the derivative method to result in large statistical uncertainties when compared with the conventional approach, especially for the Dirac and axial radii.
Here, we present an alternative setup for the derivative method which was originally suggested by B. C. Tiburzi for the pion charge radius. In this setup, mixed momentum derivatives of the correlation functions, that are first-order momentum derivatives with respect to both initial- and final-state momenta, allow for the extraction of the nucleon Dirac radius. We show that this alternative setup successfully reduces the statistical uncertainties, while still producing results compatible with the conventional approach.
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