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

Area of Science:

• Nuclear Physics
• Quantum Chromodynamics
• Hadron Spectroscopy

Background:

• Lattice QCD calculations of axial vector and pseudoscalar form factors have shown significant deviations from the partially conserved axial current (PCAC) relation.
• These deviations raise concerns about the control of systematic errors in form factor extraction from correlation functions.

Purpose of the Study:

• To identify and address the systematic error causing deviations from the PCAC relation in lattice QCD calculations.
• To improve the extraction of ground state matrix elements and form factors by including a previously overlooked excited state.

Main Methods:

• Analysis of three-point functions to determine the energy of a missed excited state as a function of momentum transfer squared (Q²).
• Incorporation of this excited state's energy into the extraction of ground state form factors.
• Parametrization of the Q² behavior of G_A(Q²) using the z expansion and G̃_P(Q²) using the pion-pole dominance ansatz.

Main Results:

• Inclusion of the identified excited state resolves deviations from the PCAC relation and other consistency conditions.
• The extracted form factors validate the pion-pole dominance hypothesis.
• New values for the axial charge (g_A = 1.30(6)), axial charge radius (r_A = 0.74(6) fm), and g*_P (8.06(44)) were obtained, consistent with phenomenological values.

Conclusions:

• A new analysis strategy incorporating a crucial excited state significantly improves the reliability of lattice QCD calculations for hadron form factors.
• The study highlights the sensitivity of axial charge extraction to excited state contributions and provides unambiguous results at Q² ≠ 0.
• The findings support the pion-pole dominance hypothesis and offer precise values for key hadronic observables.