We obtain relations between partial-wave amplitudes for $\pi N\to \pi N$ and $\pi N\to \pi \Delta$ directly from large $N_c$ QCD. While linear relations among certain amplitudes holding at leading order (LO) in $1/N_c$ were derived in the context of chiral soliton models two decades ago, the present work employs a fully model-independent framework based on consistency with the large $N_c$ expansion. At LO in $1/N_c$ we reproduce the soliton model results; however, this method allows for systematic corrections. At next-to-leading order (NLO), most relations require additional unknown functions beyond those appearing at LO and thus have little additional predictive power. However, three NLO relations for the $\pi N\to \pi \Delta$ reaction are independent of unknown functions and make predictions accurate at this order. The amplitudes relevant to two of these relations were previously extracted from experiment. These relations describe experiment dramatically better than their LO counterparts.

• Received 15 March 2004

DOI:https://doi.org/10.1103/PhysRevD.70.056004