Dyson-Schwinger-equation study of pseudoscalar meson radial excitations
Andreas Krassnigg
Argonne National Laboratory

We solve the QCD gap equation for a quark in rainbow approximation and the Bethe-Salpeter equation for the pion and its first excited state in ladder approximation, employing an Ansatz used successfully in the past to describe; e. g., the properties of vector and flavor nonsinglet pseudoscalar mesons[1]. In addition to the masses of the ground and excited state pions, their leptonic decay constants are also calculated. We investigate the dependence of the excited-state mass on the model parameters, and also explore in detail the dependence of masses and leptonic decay constants as functions of the current quark mass, including a solution in the chiral limit. The exact result that the leptonic decay constant of the first excited state of the pion must vanish in the chiral limit [2] is reproduced by the numerical study. Further, immediate applications of this work include the case for unequal quark masses (excitations of the K meson).

This work was supported by the Austrian Research Foundation FWF, Erwin-Schroedinger-Stipendium no. J2233-N08 and the Department of Energy, Office of Nuclear Physics, contract no. W-31-109-ENG-38.

References 1. P. Maris and C.D. Roberts, Int. J. Mod. Phys. E 12, 297-365 (2003) 2. A. Holl, A. Krassnigg, and C.D. Roberts, nucl-th/0406030