The static multipole moments of Δ₁₂₃₆(3/2,3/2) from superconvergence inNγ → Δπ scattering

Abstract

Saturating superconvergence sum rules inNγ→Δπ scattering byN andΔ, we are able to relate the (isoscalar) dipole magnetic moment$\tilde \mu _\Delta$ and the quadrupole electric moment$\tilde Q_\Delta$ of the isobarΔ to the electric charge$\tilde Z_\Delta$ and the dipole magnetic momentμ _N of the nucleonN. The numerical results are:$\tilde \mu _\Delta \equiv \mu _{\Delta ^ + } + \mu _{\Delta ^0 } = 3.26$ (in unitse/2M)=2.48 (in unitse/2m), and$\tilde Q_\Delta \equiv Q_{\Delta ^ + } + Q_{\Delta ^0 } = 0.050$ (in unitse/M ²)=0.029 (in unitse/m ²), whereM(m) is the mass ofΔ(N). Neglecting the pion mass and takingM=m,μ _n /μ _p =−2/3, we get theSU ₆ result μ_Δ+=μ _p .