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Register a new userComment about pion electro-production and the axial form factors
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Authors
P.A.M. Guichon
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The claim by Haberzettl (Phys.Rev.Lett.85 (2000) 3576) that the axial form factor of the nucleon cannot be accessed through threshold pion electroproduction is unfounded.
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We use a continuum quark+diquark approach to the nucleon bound-state problem in relativistic quantum field theory to deliver parameter-free predictions for the nucleon axial and induced pseudoscalar form factors, $G_A$ and $G_P$, and unify them with the pseudoscalar form factor $G_5$ or, equivalently, the pion-nucleon form factor $G_{pi NN}$. We explain how partial conservation of the axial-vector current and the associated Goldberger-Treiman relation are satisfied once all necessary couplings of the external current to the building blocks of the nucleon are constructed consistently; in particular, we fully resolve the seagull couplings to the diquark-quark vertices associated with the axial-vector and pseudoscalar currents. Among the results we describe, the following are worth highlighting. A dipole form factor defined by an axial charge $g_A=G_A(0)=1.25(3)$ and a mass-scale $M_A = 1.23(3) m_N$, where $m_N$ is the nucleon mass, can accurately describe the pointwise behavior of $G_A$. Concerning $G_P$, we obtain the pseudoscalar charge $g_p^ast = 8.80(23)$, and find that the pion pole dominance approach delivers a reliable estimate of the directly computed result. Our computed value of the pion-nucleon coupling constant, $g_{pi NN}/m_N =14.02(33)/{rm GeV}$ is consistent with a Roy--Steiner-equation analysis of pion-nucleon scattering. We also observe a marked suppression of the size of the $d$-quark component relative to that of the $u$-quark in the ratio $g_A^d/g_A^u=-0.16(2)$, which highlights the presence of strong diquark correlations inside the nucleon -- both scalar and axial-vector, with the scalar diquark being dominant.
The axial form factor as well as the axial charge of octet baryons are studied in the perturbative chiral quark model (PCQM) with the quark wave functions predetermined by fitting the theoretical results of the proton charge form factor to experimental data. The theoretical results are found, based on the predetermined quark wave functions, in good agreement with experimental data and lattice values. This may indicate that the electric charge and axial charge distributions of the constituent quarks are the same. The study reveals that the meson cloud plays an important role in the axial charge of octet baryons, contributing 30%-40% to the total values, and strange sea quarks have a considerable contribution to the axial charge of the $Sigma$ and $Xi$.
We present first results on the axial and pseudoscalar $Delta$ form factors. The analysis is carried out in the quenched approximation where statistical errors are small and the lattice set-up can be investigated relatively quickly. We also present an analysis with a hybrid action using staggered sea quarks and domain-wall valence fermions.
We consider how to extract the pion form factors in the epsilon regime. Using the correlators with non-zero momenta and taking appropriate ratios of them, we eliminate the dominant finite volume effect from the zero-momentum pion mode. Our preliminary lattice result for the pion charge radius is consistent with the experiment.
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.
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