Line shapes of the Z b ( 10610 ) and Z b ( 10650 ) in the elastic and inelastic channels revisited

The most recent experimental data for all measured production and decay channels of the bottomoniumlike states Zb(10610) and Zb(10650) are analyzed simultaneously using solutions of the Lippmann-Schwinger equations which respect constraints from unitarity and analyticity. The interaction potential in the open-bottom channels B(*)¯B∗+c.c. contains short-range interactions as well as a one-pion exchange. It is found that the long-range interaction does not affect the line shapes as long as only S waves are considered. Meanwhile, the line shapes can be visibly modified once D waves, mediated by the strong tensor forces from the pion exchange potentials, are included. However, in the fit they get balanced largely by a momentum dependent contact term that appears to be needed also to render the results for the line shapes independent of the cutoff. The resulting line shapes are found to be insensitive to various higher-order interactions included to verify stability of the results. Both Zb states are found to be described by the poles located on the unphysical Riemann sheets in the vicinity of the corresponding thresholds. In particular, the Zb(10610) state is associated with a virtual state residing just below the B¯B∗/¯BB∗ threshold while the Zb(10650) state most likely is a shallow state located just above the B∗¯B∗ threshold