Production cross section of rotating string

We calculate production cross sections of a single rotating string from a collision of two light states in bosonic string theory. We find that the cross sections are written in terms of the modified Bessel function of the first kind with the degree given by the angular momentum in the high energy regime. We also obtain a similar formula from the partial wave expansion of four point amplitudes. Asymptotic behavior of the cross sections is consistent with a well known form factor of a string.