The Off-diagonal Goldberger-Treiman Relation and Its Discrepancy

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We study the off-diagonal Goldberger-Treiman relation (ODGTR) and its discrepancy (ODGTD) in the N, Delta, pi sector through O(p²) using heavy baryon chiral perturbation theory. To this order, the ODGTD and axial vector N to Delta 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 Delta.