Erratum: Axial nucleon and nucleon toΔform factors and the Goldberger-Treiman relations from lattice QCD [Phys. Rev. D76, 094511 (2007)]

Abstract

We evaluate the nucleon axial form factor, GA(q 2 ), and induced pseudoscalar form factor, Gp(q 2 ), as well as the pion-nucleon form factor, GπNN (q 2 ), in lattice QCD. We also evaluate the corresponding nucleon to ∆ transition form factors, C A 5 (q 2 ) and C A 6 (q 2 ), and the pion-nucleon-∆ form factor GπN∆(q 2 ). The nucleon form factors are evaluated in the quenched theory and with two degenerate flavors of dynamical Wilson fermions. The nucleon to ∆ form factors, besides Wilson fermions, are evaluated using domain wall valence fermions with staggered sea quark configurations for pion masses as low as about 350 MeV. Using these form factors, together with an evaluation of the renormalized quark mass, we investigate the validity of the diagonal and non-diagonal GoldbergerTreiman relations. The ratios GπN∆(q 2 )/GπNN (q 2 ) and 2CA 5 (q 2 )/GA(q 2 ) are constant as a function of the momentum transfer squared and show almost no dependence on the quark mass. We confirm equality of these two ratios consistent with the Goldberger-Treiman relations extracting a mean value of 1.61(2).

Renormalization versus strong form factors for one-boson-exchange potentials

“…This point was explicitly illustrated by using the Skyrme soliton model form factors [30]. In fact, this conclusion is coherent with the early hard core regularizations [3,4,5], recent lattice calculations [36] (where an extremely hard Λ πN N ∼ 1.7GeV and a rather flat behaviour are found) and, as we will show, with the renormalization approach we advocate.…”

“…These include meson theory [22,23,24,25,26,27], Regge models [28], chiral soliton models [29,30,31,32], QCD sum rules [33] the Goldberger-Treimann discrepancy [34] or lattice QCD [35,36] and quark models [37]. Most calculations yield rather small values Λ πN N ∼ 800MeV generating the soft form factor puzzle for the OBE potential for several years since the cut-off could not be lowered below Λ πN N = 1.3GeV without destroying the quality of the fits and the description of the deuteron [10].…”

Nucleon toΔtransition form factors withNF=2+1domain wall fermions

“…However, the discrepancy in the momentum dependence of the dominant dipole form factor remained with lattice results having smaller values at low q 2 -values and a weaker dependence on q 2 . Using the same set of sequential propogators as in the electromagnetic case the axial and pseudo-scalar N to ∆ form factors were studied [21,30]. The strong coupling constant g πN ∆ and non-diagonal Goldberger-Treiman relation were examined in detail and it was demonstrated that the behaviour is very similar manner to the corresponding relations in the nucleon system.…”

“…MeV [21,[28][29][30]. This calculation showed that the unquenched results on the Coulomb quadrupole form factor at low q 2 decreased towards the experimental results.…”

“…They have been studied in neutrino scattering and muon capture experiments, respectively but experimental data are less precise [16,17]. There have also been several lattice evaluations of the nucleon axial charge g A [9,[18][19][20] and of the momentum dependence of the two form factors [12,21]. Partial conservation of axial symmetry (PCAC) leads to a relation between the nucleon axial charge and the pseudo-scalar π − N coupling constant g πN N , the well-known Goldberger-Treiman relation.…”