We present a direct calculation for the first derivative of the isovector nucleon form factors with respect to the momentum transfer $q^2$ using the lower moments of the nucleon 3-point function in the coordinate space. Our numerical simulations are performed using the $N_f = 2 + 1$ nonperturbatively $O(a)$-improved Wilson quark action and Iwasaki gauge action near the physical point, corresponding to the pion mass $M_π=138$ MeV, on a (5.5 fm)$^4$ lattice at a single lattice spacing of $a = 0.085$ fm. 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 $q^2$ extrapolation to the zero momentum point. These results are compared with the ones determined by the standard method, where the $q^2$ 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 $M_π= 510$ MeV. Furthermore, we discuss an equivalence between the momentum derivative method and the similar approach with the point splitting vector current.
Nucleon-sigma terms at $m_π=222 ~\rm MeV$ with a variational analysis from lattice QCD
John von Neumann-Institut für Computing NIC, Deutsches Elektronen-Synchrotron DESY（约翰·冯·诺依曼计算研究所，德国电子同步加速器）；Fakultät für Physik, Universität Regensburg（物理学院，雷根斯堡大学）
Two-nucleon systems at $m_π\approx292$ MeV from lattice QCD
Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Nanjing Normal University（南京师范大学）；School of Physics, Peking University（北京大学物理学院）；Center for High Energy Physics, Peking University（北京大学高能物理中心）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）；Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心）
