Nucleon axial form factor from lattice QCD.

Results for the isovector axial form factors of the proton from a lattice QCD calculation are presented for both point-split and local currents. They are obtained on a quenched 163 × 24 lattice at β = 6.0 with Wilson fermions for a range of quark masses from strange to charm. For each quark mass, we find that the axial form factor falls off slower than the corresponding proton electric form factor. Results extrapolated to the chiral limit show that the q2 dependence of the axial form factor agrees reasonably well with experiment. The axial coupling constant gA calculated for the local and the point-split currents is about 6% and 12% smaller than the experimental value respectively. PACS numbers: 12.38 Gc, 14.20 Dh, 13.60.-r ∗ Present address: Institute of High Energy Physics, Beijing, China As have electromagnetic form factors, the isovector axial form factor gA(q ) has been commonly used to constrain the construction of models of the nucleon in order to incorporate PCAC and the Goldberger-Treiman relation [1, 2]. Similar to vector meson dominance in electromagnetic form factors, the isovector axial form factor seems to be quite sensitive to whether degrees of freedom in the A1 channel (e.g. ρπ, ωππ or A1 itself) are introduced in the effective theory [3, 4, 5]. In view of the fact that the EM form factors and the magnetic moments of the nucleon in recent lattice QCD calculations are within 10 to 15% of the experimental results [6, 7], it is natural to extend the study to the axial form factor and to determine to what extent the experimental results can be reproduced in lattice QCD, subject to the limitations of the quenched approximation, finite size effects and the extrapolation to the chiral limit. Especially interesting is to check the q dependence of the axial vs. the electric form factors to see if the experimental difference between them is borne out in the lattice calculation; the q dependence of their ratio should be fairly independent of the systematic errors due to the present limitations of the lattice calculation. In this paper, we study the axial form factor in lattice QCD with Wilson fermions and compare it to the electric form factor calculated previously and to experiment. We examine its systematics as a function of the quark mass from strange to twice that of the charm mass, and compare the axial coupling constant gA to previous quenched calculations with different volumes [8, 9, 10, 11]. Fixing gA to the non-relativistic value of 5/3, we determine the finite lattice renormalization for heavy quarks. Assuming axial dominance, we extract the A1NN form factor. Lattice gauge calculations have been carried out to study the electromagnetic form factors of the pion[12] and the nucleon[6, 7]. The same sequential source technique (SST) using the zero-momentum point nucleon interpolating field as the secondary source is applied here to study the axial form factors [7]. In choosing the final hadron as the secondary source, one can sew the quark propagators together at the point where the current couples in the three-point function. This has the advantage of being able to study different currents at various momentum transfers. The lattice twoand three-point functions that we calculate are the following: G PP (t, ~ p) = ∑ ~x e 〈0|T (χ(x)χ̄(0)|0〉, (1) G PAP (tf , ~ p, t, ~q) = ∑ ~xf ,~x e p·~xf+i~ 〈0|T (χ(xf )Aμ(x)χ̄ (0))|0〉, (2) where χ is the proton interpolating field and Aμ(x) is either the point-split axial vector current A μ = i2κ[ψ̄(x) 1 2 γμγ5Uμ(x)ψ(x+ μ̂)+ψ̄(x+ μ̂) 1 2 γμγ5U † μ(x)ψ(x)], (3) or the local current A μ = i2κψ̄(x)γμγ5ψ(x). (4)