Determination of the Δ ( 1232 ) axial and pseudoscalar form factors from lattice QCD

• Published in: Physical review. D, Particles, fields, gravitation, and cosmology Particles, fields, gravitation, and cosmology, 2013-06, Vol.87 (11), Article 114513
• Main Authors: Alexandrou, Constantia, Gregory, Eric B., Korzec, Tomasz, Koutsou, Giannis, Negele, John W., Sato, Toru, Tsapalis, Antonios
• Format: Article
• Language: English
• Subjects: Constants; Domain walls; Dominance; Form factors; Invariants; Joining; Lattices; Mathematical analysis; Quantum chromodynamics
• ISSN: 1550-7998; 1550-2368
• DOI: 10.1103/PhysRevD.87.114513

We present a lattice QCD calculation of the Delta (1232) matrix elements of the axial-vector and pseudoscalar currents. The decomposition of these matrix elements into the appropriate Lorentz invariant form factors is carried out, and the techniques to calculate the form factors are developed and tested using quenched configurations. Results are obtained for 2 + 1 domain wall fermions and within a hybrid scheme with domain wall valence and staggered sea quarks. Two Goldberger-Treiman-type relations connecting the axial to the pseudoscalar effective couplings are derived. These and further relations based on the pion-pole dominance hypothesis are examined using the lattice QCD results, finding support for their validity. Using lattice QCD results on the axial charges of the nucleon and the Delta , as well as the nucleon-to- Delta transition coupling constant, we perform a combined chiral fit to all three quantities and study their pion mass dependence as the chiral limit is approached.