Electromagnetic couplings of radially excited light vector mesons from QCD sum rules

The couplings of unflavored vector mesons to the $e^+e^-$ annihilation are an important source of information on the nature and structure of these resonances which play a prominent role in the hadron phenomenology. The couplings of many radially excited heavy vector mesons are measured, while the corresponding couplings for light vector mesons are not known. We propose a phenomenological method allowing to estimate these unknown couplings. The method is suggested by our observation that the electromagnetic coupling of the $n$-th radial excitation of $S$-wave heavy vector meson decouples from the $e^+e^-$ annihilation with nearly exponential rate with $n$. It becomes natural to assume that the same effect takes place in the light vector mesons and this would allow to estimate the unknown couplings. We tested this assumption with the help of a generalized version of borelized QCD spectral sum rules saturated by a linear radial trajectory of meson states taken from the phenomenology. This leads to a consistent setup which is able to predict the decoupling rate. The calculated rate turned out to be almost the same as in the heavy vector mesons. Our result may be interpreted as an effective account for non-trivial electromagnetic formfactor in meson decays to $e^+e^-$, thus looking beyond the large-$N_c$ limit. On the one hand, we argue that the given decoupling does not necessary contradict to the previous large-$N_c$ results for the Regge like meson spectra.