Off-diagonal Goldberger-Treiman relation and its discrepancy

We study the off-diagonal Goldberger-Treiman relation (ODGTR) and its discrepancy (ODGTD) in the N, Δ, π sector through O(p2) using heavy baryon chiral perturbation theory. To this order, the ODGTD and axial vector N to Δ transition radius are determined solely by low-energy constants. Loop corrections appear at O(p4). For low-energy constants of natural size, the ODGTD would represent a ∼2% correction to the ODGTR. We discuss the implications of the ODGTR and ODGTD for lattice and quark model calculations of the transition form factors and for parity-violating electroexcitation of the Δ.