Axial Vector Form Factors from Lattice QCD that Satisfy the PCAC Relation

Understand

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.