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Register a new userThe Axial Form Factor of the Nucleon
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E.J. Beise
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The parity violation programs at MIT-Bates, Jefferson Lab and Mainz are presently focused on developing a better understanding of the sea-quark contributions to the vector matrix elements of nucleon structure. The success of these programs will allow precise semi-leptonic tests of the Standard Model such as that planned by the QWeak collaboration. In order to determine the vector matrix elements, a good understanding of the nucleons axial vector form factor as seen by an electron, G^e_A, is also required. While the vector electroweak form factors provide information about the nucleons charge and magnetism, the axial form factor is related to the nucleons spin. Its Q2=0 value at leading order, g_A, is well known from nucleon and nuclear beta decay, and its precise determination is of interest for tests of CKM unitarity. Most information about its Q2 dependence comes from quasielastic neutrino scattering and from pion electroproduction, and a recent reanalysis of the neutrino data have brought these two types of measurements into excellent agreement. However, these experiments are not sensitive to additional higher order corrections, such as nucleon anapole contributions, that are present in parity-violating electron scattering. In this talk I will attempt to review what is presently known about the axial form factor and its various pieces including the higher order contributions, discuss the the various experimental sectors, and give an update on its determination through PV electron scattering.
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Motivated by the emerging possibilities to study threshold pion electroproduction at large momentum transfers at Jefferson Laboratory following the 12 GeV upgrade, we provide a short theory summary and an estimate of the nucleon axial form factor for large virtualities in the $Q^2 = 1-10~text{GeV}^2$ range using next-to-leading order light-cone sum rules.
It is well established that the nucleon form factors can be related to Generalized Parton Distributions (GPDs) through sum-rules. On the other hand, GPDs can be expressed in terms of Parton Distribution Functions (PDFs) according to Diehls model. In this work, we use this model to calculate polarized GPDs for quarks ($widetilde{H}_q$) using the available polarized PDFs obtained from the experimental data, and then study the axial form factor of nucleon. We determine parameters of the model using standard $chi^2$ analysis of experimental data. It is shown that some parameters should be readjusted, as compared to some previously reported values, to obtain better consistency between the theoretical predictions and experimental data. Moreover, we study in details the uncertainty of nucleon axial form factor due to various sources.
The nucleon axial form factor is a dominant contribution to errors in neutrino oscillation studies. Lattice QCD calculations can help control theory errors by providing first-principles information on nucleon form factors. In these proceedings, we present preliminary results on a blinded calculation of $g_A$ and the axial form factor using HISQ staggered baryons with 2+1+1 flavors of sea quarks. Calculations are done using physical light quark masses and are absolutely normalized. We discuss fitting form factor data with the model-independent $z$ expansion parametrization.
We present results on the isoscalar form factors including the disconnected contributions, as well as on the strange and charm quark form factors. Using previous results on the isovector form factors, we determine the flavor decomposition of the nucleon axial form factors. These are computed using an ensemble of $N_f=2+1+1$ twisted mass fermions simulated with physical values of quark masses. We investigate the SU(3) flavor symmetry and show that there is up to 10% breaking for the axial and up to 50% for the induced pseudoscalar form factors. By fitting the $Q^2$-dependence, we determined the corresponding root mean square radii. The pseudoscalar coupling of the $eta$ meson and the nucleon is found to be $g_{eta NN}=3.7(1.0)(0.7)$, and the Goldberger-Treiman discrepancy for the octet combination about 50%.
Precise proton and neutron form factor measurements at Jefferson Lab, using spin observables, have recently made a significant contribution to the unraveling of the internal structure of the nucleon. Accurate experimental measurements of the nucleon form factors are a test-bed for understanding how the nucleons static properties and dynamical behavior emerge from QCD, the theory of the strong interactions between quarks. There has been enormous theoretical progress, since the publication of the Jefferson Lab proton form factor ratio data, aiming at reevaluating the picture of the nucleon. We will review the experimental and theoretical developments in this field and discuss the outlook for the future.
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