Pseudoscalar meson radial excitations

Goldstone modes are the only pseudoscalar mesons to possess a nonzero leptonic decay constant in the chiral limit when chiral symmetry is dynamically broken. The decay constants of their radial excitations vanish. These features and aspects of their impact on the meson spectrum are illustrated using a manifestly covariant and symmetry-preserving model of the kernels in the gap and Bethe-Salpeter equations.

Figure 1

Dimensionless low-order Chebyshev moments of the scalar function that characterizes the dominant amplitude in Eq. (13) for the ground $\left({\pi }_0\right)$ and first excited $\left({\pi }_1\right)$ states.

Figure 2

Evolution of the mesons’ masses with renormalized current-quark mass, $m_q=m(\zeta =1\mathrm{GeV})$.

Figure 3

Evolution of the mesons’ leptonic decay constants with renormalised current-quark mass, $m_q=m(\zeta =1\mathrm{GeV})$.