The decay constant of the first excited pion from lattice QCD

Abstract

We review the theory that predicts that the decay constant of the excited light pseudo-scalar mesons are suppressed in the chiral limit relative to the pion decay constant. We compute the decay constant of the first excited pion ($\ddot{I}{€}^{\prime }$) using unquenched QCD at a fixed lattice spacing with sea quarks of mass as low as a third the mass of the strange quark. The final result is very sensitive to the improvement conditions. We obtain $f_{\ddot{I}{€}^{\prime }}/f_{\ddot{I}}€$ = 0.078(93) in the chiral limit.

Updated references. Clarified discussion around equations 2 and 3