TY - JOUR

T1 - Calculation of the derivative of nucleon form factors in lattice QCD at on a volume

AU - Ishikawa, Ken Ichi

AU - Kuramashi, Yoshinobu

AU - Sasaki, Shoichi

AU - Shintani, Eigo

AU - Yamazaki, Takeshi

N1 - Funding Information:
University of Tsukuba University of Tokyo RIKEN Ministry of Education, Culture, Sports, Science and Technology
Funding Information:
We thank members of the PACS collaboration for useful discussions. Numerical calculations in this work were performed on Oakforest-PACS in Joint Center for Advanced High Performance Computing (JCAHPC) and Cygnus in Center for Computational Sciences at University of Tsukuba under Multidisciplinary Cooperative Research Program of Center for Computational Sciences, University of Tsukuba, and Wisteria/BDEC-01 in the Information Technology Center, The University of Tokyo. This research also used computational resources of the HPCI system provided by Information Technology Center of the University of Tokyo and RIKEN CCS through the HPCI System Research Project (Project ID: hp170022, hp180051, hp180072, hp180126, hp190025, hp190081, hp200062, hp200188, hp210088). The calculation employed OpenQCD system . This work was supported in part by Grants-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology (No. 18K03605, No. 19H01892).
Publisher Copyright:
© 2021 Published by the American Physical Society

PY - 2021/10/1

Y1 - 2021/10/1

N2 - We present a direct calculation for the first derivative of the isovector nucleon form factors with respect to the momentum transfer using the lower moments of the nucleon 3-point function in the coordinate space. Our numerical simulations are performed using the nonperturbatively -improved Wilson quark action and Iwasaki gauge action near the physical point, corresponding to the pion mass , on a lattice at a single lattice spacing of . In the momentum derivative approach, we can directly evaluate the mean square radii for the electric, magnetic, and axial-vector form factors, and also the magnetic moment without the extrapolation to the zero momentum point. These results are compared with the ones determined by the standard method, where the extrapolations of the corresponding form factors are carried out by fitting models. We find that the new results from the momentum derivative method are obtained with a larger statistical error than the standard method, but with a smaller systematic error associated with the data analysis. Within the total error range of the statistical and systematic errors combined, the two results are in good agreement. On the other hand, two variations of the momentum derivative of the induced pseudoscalar form factor at the zero momentum point show some discrepancy. It seems to be caused by a finite volume effect, since a similar trend is not observed on a large volume, but seen on a small volume in our pilot calculations at a heavier pion mass of . Furthermore, we discuss an equivalence between the momentum derivative method and the similar approach with the point splitting vector current.

AB - We present a direct calculation for the first derivative of the isovector nucleon form factors with respect to the momentum transfer using the lower moments of the nucleon 3-point function in the coordinate space. Our numerical simulations are performed using the nonperturbatively -improved Wilson quark action and Iwasaki gauge action near the physical point, corresponding to the pion mass , on a lattice at a single lattice spacing of . In the momentum derivative approach, we can directly evaluate the mean square radii for the electric, magnetic, and axial-vector form factors, and also the magnetic moment without the extrapolation to the zero momentum point. These results are compared with the ones determined by the standard method, where the extrapolations of the corresponding form factors are carried out by fitting models. We find that the new results from the momentum derivative method are obtained with a larger statistical error than the standard method, but with a smaller systematic error associated with the data analysis. Within the total error range of the statistical and systematic errors combined, the two results are in good agreement. On the other hand, two variations of the momentum derivative of the induced pseudoscalar form factor at the zero momentum point show some discrepancy. It seems to be caused by a finite volume effect, since a similar trend is not observed on a large volume, but seen on a small volume in our pilot calculations at a heavier pion mass of . Furthermore, we discuss an equivalence between the momentum derivative method and the similar approach with the point splitting vector current.

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U2 - 10.1103/PhysRevD.104.074514

DO - 10.1103/PhysRevD.104.074514

M3 - Article

AN - SCOPUS:85117396605

VL - 104

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 7

M1 - 074015

ER -