Model of pion excitation

We study the vector and axial-vector excitation of a pion to an arbitrary single-particle state. The main inputs to our calculation are a hard-pion representation for the relevant off-shell matrix elements, and use of partial conservation of axial-vector current, the Bjorken-Johnson-Low theorem, and current algebra as constraints. We find that for a model incorporating a finite number of poles, the pion cannot be excited to arbitrarily high-spin states. In a particular model we find a cutoff of J=4, and also obtain predictions involving branching ratios for the decay of f(1268) and g(1680) mesons into A₁(1070)π and ππ composites. The results of our model are checked by comparing with sum rules based on local commutation relations.