2007/09/30 by Shoichi Sasaki, Takeshi Yamazaki · 1 citation
Physics and Astronomy · #Particle physics theoretical and experimental studies #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #hep-lat #hep-ph
paper · pdf · doi:10.1103/physrevd.78.014510
published as Phys.Rev.D78:014510,2008 · 46 pages, 44 figures, v2: one section (including four new figures and several new tables) added for comparison with other studies, conclusions remain unchanged, v3: accepted version, v4: published version in PRD
openalex publication_date 2008/07/25 · arxiv created 2009/04/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We present a quenched lattice calculation of the weak nucleon form factors: vector [FV(q2)], induced tensor [FT(q2)], axial vector [FA(q2)] and induced pseudoscalar [FP(q2)] form factors. Our simulations are performed on three different lattice sizes L3\ifmmode×\else\texttimes\fiT=243\ifmmode×\else\texttimes\fi32, 163\ifmmode×\else\texttimes\fi32, and 123\ifmmode×\else\texttimes\fi32 with a lattice cutoff of a^\ensuremath-1\ensuremath≈1.3 GeV and light quark masses down to about 1/4 the strange quark mass (m_\ensuremathπ\ensuremath≈390 MeV) using a combination of the DBW2 gauge action and domain wall fermions. The physical volume of our largest lattice is about (3.6 fm)3, where the finite volume effects on form factors become negligible and the lower momentum transfers (q2\ensuremath≈0.1 GeV2) are accessible. The q2 dependences of form factors in the low q2 region are examined. It is found that the vector, induced tensor, and axial-vector form factors are well described by the dipole form, while the induced pseudoscalar form factor is consistent with pion-pole dominance. We obtain the ratio of axial to vector coupling gA/gV=FA(0)/FV(0)=1.219(38) and the pseudoscalar coupling gP=m_\ensuremathμFP(0.88m_\ensuremathμ2)=8.15(54), where the errors are statistical errors only. These values agree with experimental values from neutron \ensuremathβ decay and muon capture on the proton. However, the root mean-squared radii of the vector, induced tensor, and axial vector underestimate the known experimental values by about 20%. We also calculate the pseudoscalar nucleon matrix element in order to verify the axial Ward-Takahashi identity in terms of the nucleon matrix elements, which may be called as the generalized Goldberger-Treiman relation.