Radial excitations of heavy-light mesons from QCD sum rules

TL;DR

This paper extends QCD sum rules to estimate decay constants of radially excited heavy-light mesons, using experimental data and heavy-quark limit estimates, revealing smaller decay constants compared to ground states.

Contribution

It introduces a modified sum rule approach to predict decay constants of first radial excitations of heavy-light mesons, incorporating resonance masses as inputs.

Findings

Decay constants of radial excitations are systematically smaller than ground states.

Experimental data for charmed mesons used, bottom meson masses estimated from heavy-quark limit.

Results applicable to heavy-to-light form factors and nonleptonic B-meson decay calculations.

Abstract

QCD sum rules are commonly used to predict the characteristics of ground-state hadrons. We demonstrate that two-point sum rules for the decay constants of charmed ($D^{(*)},D_s^{(*)}$) and bottom ($B^{(*)},B_s^{(*)}$) mesons can also be modified to estimate the decay constants of the first radial excitations, $D^{(*)'},D_s^{(*)'}$ and $B^{(*)'},B_s^{(*)'}$, respectively, provided the masses of these resonances are used as an input. For the radially excited charmed mesons we use available experimental data, whereas the masses of analogous bottom mesons are estimated from the heavy-quark limit. The decay constants predicted for the radial excitations of heavy-light pseudoscalar and vector mesons are systematically smaller than those of the ground states and we comment on the possible origin of this difference. Our results can be used in the sum rule calculations of heavy-to-light form factors and in the factorization approximations for nonleptonic $B$-meson decays where the decay constants of charmed mesons enter as input parameters.