Abstract
We explore the link between the chiral symmetry of QCD and the numerical results of the light-front quark model, analyzing both the two-point and three-point functions of the pion. Including the axial-vector coupling as well as the pseudoscalar coupling in the light-front quark model, we discuss the implication of the chiral anomaly in describing the pion decay constant, the pion-photon transition form factor and the electromagnetic form factor of the pion. In constraining the model parameters, we find that the chiral anomaly plays a critical role and the analysis of $F_{\pi\gamma}(Q^2)$ in timelike region is important. Our results indicate that the constituent quark picture is effective for the low and high $Q^2$ ranges implementing the quark mass evolution effect as $Q^2$ grows.
Highlights
Due to just a single hadron involvement, the mesonphoton transition is well known to be the simplest exclusive process in testing the quantum chromodynamics (QCD) and understanding the structure of the meson [1]
While the form factors obtained from the mixing of the different quark mass eigenstates are not much different from each other in the spacelike region, their predictions for the timelike region are very different due to the resonance feature in the timelike region
As the chiral anomaly [2] is the key to understand the π0 → γγ decay rate resolving the issue with the SutherlandVeltman theorem [38], we attempt to include the axialvector coupling in addition to the pseudoscalar coupling in our lightfront quark models (LFQMs) for the pion to explore a well-defined chiral limit still providing a good description of the pion electromagnetic and transition form factors [12,14,17]
Summary
Due to just a single hadron involvement, the mesonphoton transition is well known to be the simplest exclusive process in testing the quantum chromodynamics (QCD) and understanding the structure of the meson [1]. Our direct calculation in timelike region showed the complete agreement with the analytic continuation result from spacelike region and the result from the dispersion relation (DR) between the real and imaginary parts of the form factor This development added more predictability to the lightfront quark models (LFQMs) [12,13,14,15,16,17,18,19,20,21,22] which have been successful in describing hadron phenomenology based on the constant constituent quark and antiquark masses. It appears important to analyze the contribution from the axial-vector coupling together with the contribution from the pseudoscalar coupling to explore the correlation between the nontrivial QCD vacuum effect and the constituent quark mass as well as the parameter of the trial wave function in the LFQM built on the variational principle.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
