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Register a new userAxial Vector Form Factors from Lattice QCD that Satisfy the PCAC Relation
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Previous lattice QCD calculations of axial vector and pseudoscalar form factors show significant deviation from the partially conserved axial current (PCAC) relation between them. Since the original correlation functions satisfy PCAC, the observed deviations from the operator identity cast doubt on whether all the systematics in the extraction of form factors from the correlation functions are under control. We identify the problematic systematic as a missed excited state, whose energy as a function of the momentum transfer squared, $Q^2$, is determined from the analysis of the 3-point functions themselves. Its mass is much smaller than those of the excited states previously considered and including it impacts the extraction of all the ground state matrix elements. The form factors extracted using these mass/energy gaps satisfy PCAC and other consistency conditions, and validate the pion-pole dominance hypothesis. We also show that the extraction of the axial charge $g_A$ is very sensitive to the value of the mass gaps of the excited states used and current lattice data do not provide an unambiguous determination of these, unlike the $Q^2 eq 0$ case. To highlight the differences and improvement between the conventional versus the new analysis strategy, we present a comparison of results obtained on a physical pion mass ensemble at $aapprox 0.0871,mathrm{fm}$. With the new strategy, we find $g_A = 1.30(6)$. A very significant improvement over previous lattice results is found for the axial charge radius $r_A = 0.74(6),mathrm{fm}$, extracted using the $z$-expansion to parameterize the $Q^2$ behavior of $G_A(Q^2)$, and $g_P^ast = 8.06(44)$ obtained using the pion pole-dominance ansatz to fit the $Q^2$ behavior of the induced pseudoscalar form factor $widetilde{G}_P(Q^2)$.
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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 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.
We present the first calculation on the $Delta$ axial-vector and pseudoscalar form factors using lattice QCD. Two Goldberger-Treiman relations are derived and examined. A combined chiral fit is performed to the nucleon axial charge, N to $Delta$ axial transition coupling constant and $Delta$ axial charge.
It has been observed in multiple lattice determinations of isovector axial and pseudoscalar nucleon form factors, that, despite the fact that the partial conservation of the axialvector current is fulfilled on the level of correlation functions, the corresponding relation for form factors (sometimes called the generalized Goldberger-Treiman relation in the literature) is broken rather badly. In this work we trace this difference back to excited state contributions and propose a new projection method that resolves this problem. We demonstrate the efficacy of this method by computing the axial and pseudoscalar form factors as well as related quantities on ensembles with two flavors of improved Wilson fermions using pion masses down to 150 MeV. To this end, we perform the $z$-expansion with analytically enforced asymptotic behaviour and extrapolate to the physical point.
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