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Register a new userAxial Nucleon and Nucleon to Delta form fractors and the Goldberger-Treiman Relations from Lattice QCD
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We evaluate the nucleon axial form factor, $G_A(q^2)$, and induced pseudoscalar form factor, $G_p(q^2)$, as well as the pion-nucleon form factor, $G_{pi N N}(q^2)$, in lattice QCD. We also evaluate the corresponding nucleon to $Delta$ transition form factors, $C_5^A(q^2)$ and $C_6^A(q^2)$, and the pion-nucleon-$Delta$ form factor $G_{pi NDelta}(q^2)$. The nucleon form factors are evaluated in the quenched theory and with two degenerate flavors of dynamical Wilson fermions. The nucleon to $Delta$ 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 Goldberger-Treiman relations. The ratios $G_{pi NDelta}(q^2)/G_{pi NN}(q^2)$ and $2C_5^A(q^2)/G_A(q^2)$ 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 $1.61(2)$.
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We present results on the nucleon axial vector form factors $G_A(q^2)$ and $G_p(q^2)$ in the quenched theory and using two degenerate flavors of dynamical Wilson fermions for momentum transfer squared from about 0.1 to about 2 GeV^2 and for pion masses in the range of 380 to 600 MeV. We also present results on the corresponding N to Delta axial vector transition form factors $C_5^A(q^2)$ and $C_6^A(q^2)$ using, in addition to Wilson fermions, domain wall valence quarks and dynamical staggered sea quarks provided by the MILC collaboration.
We present results on the nucleon axial form factors within lattice QCD using two flavors of degenerate twisted mass fermions. Volume effects are examined using simulations at two volumes of spatial length $L=2.1$ fm and $L=2.8$ fm. Cut-off effects are investigated using three different values of the lattice spacings, namely $a=0.089$ fm, $a=0.070$ fm and $a=0.056$ fm. The nucleon axial charge is obtained in the continuum limit and chirally extrapolated to the physical pion mass enabling comparison with experiment.
We present preliminary results on the axial form factor $G_A(Q^2)$ and the induced pseudoscalar form factor $G_P(Q^2)$ of the nucleon. A systematic analysis of the excited-state contributions to form factors is performed on the CLS ensemble `N6 with $m_pi = 340 text{MeV}$ and lattice spacing $a sim 0.05 text{fm}$. The relevant three-point functions were computed with source-sink separations ranging from $t_s sim 0.6 text{fm}$ to $t_s sim 1.4 text{fm}$. We observe that the form factors suffer from non-trivial excited-state contributions at the source-sink separations available to us. It is noted that naive plateau fits underestimate the excited-state contributions and that the method of summed operator insertions correctly accounts for these effects.
We report a calculation of the nucleon axial form factors $G_A^q(Q^2)$ and $G_P^q(Q^2)$ for all three light quark flavors $qin{u,d,s}$ in the range $0leq Q^2lesssim 1.2text{ GeV}^2$ using lattice QCD. This work was done using a single ensemble with pion mass 317 MeV and made use of the hierarchical probing technique to efficiently evaluate the required disconnected loops. We perform nonperturbative renormalization of the axial current, including a nonperturbative treatment of the mixing between light and strange currents due to the singlet-nonsinglet difference caused by the axial anomaly. The form factor shapes are fit using the model-independent $z$ expansion. From $G_A^q(Q^2)$, we determine the quark contributions to the nucleon spin and axial radii. By extrapolating the isovector $G_P^{u-d}(Q^2)$, we obtain the induced pseudoscalar coupling relevant for ordinary muon capture and the pion-nucleon coupling constant. We find that the disconnected contributions to $G_P$ form factors are large, and give an interpretation based on the dominant influence of the pseudoscalar poles in these form factors.
We present a new analysis method that allows one to understand and model excited state contributions in observables that are dominated by a pion pole. We apply this method to extract axial and (induced) pseudoscalar nucleon isovector form factors, which satisfy the constraints due to the partial conservation of the axial current up to expected discretization effects. Effective field theory predicts that the leading contribution to the (induced) pseudoscalar form factor originates from an exchange of a virtual pion, and thus exhibits pion pole dominance. Using our new method, we can recover this behavior directly from lattice data. The numerical analysis is based on a large set of ensembles generated by the CLS effort, including physical pion masses, large volumes (with up to $96^3 times 192$ sites and $L m_pi = 6.4$), and lattice spacings down to $0.039 , text{fm}$, which allows us to take all the relevant limits. We find that some observables are much more sensitive to the choice of parametrization of the form factors than others. On the one hand, the $z$-expansion leads to significantly smaller values for the axial dipole mass than the dipole ansatz ($M_A^{text{$z$-exp}}=1.02(10) , text{GeV}$ versus $M_A^{text{dipole}} = 1.31(8) , text{GeV}$). On the other hand, we find that the result for the induced pseudoscalar coupling at the muon capture point is almost independent of the choice of parametrization ($g_P^{star text{$z$-exp}} = 8.68(45)$ and $g_P^{star text{dipole}} = 8.30(24)$), and is in good agreement with both, chiral perturbation theory predictions and experimental measurement via ordinary muon capture. We also determine the axial coupling constant $g_A$.
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