B-(*())(B)over-bar(()*()) intermediate states contribution to Gamma(4S, 5S) -> eta(b) + gamma radiative decay

In this work, we investigate the rescattering effects in the radiative decay Gamma(5S) -> eta(b) + gamma , which were suggested to be crucially important for understanding the anomalous largeness of the branching ratios B(Gamma(5S) -> Gamma(1S) + pi pi) and B(Gamma(5S) -> Gamma(1S) + eta). Our calculations show that the rescattering effects may enhance Gamma(Gamma(10860) -> eta(b) +gamma) by four orders, but the tetraquark structure does not. Recently the BABAR and CLEO collaborations have measured the mass of eta(b) and the branching ratios B(Gamma(2S) -> eta(b) +gamma), B(Gamma(3S) -> eta(b) +gamma). We hope that very soon, Gamma(10860) -> eta(b) + gamma) will be measured and it would be an ideal opportunity for testing whether the rescattering or the tetraquark structure is responsible for the anomaly of B(Gamma(5S) -> Gamma(nS) pi(+) pi(-))(n = 1, 2, 3)), i. e., the future measurements on the radiative decays of Gamma(5S) might be a touchstone of the two mechanisms.