On The Shape of the Betatron Side-Band

The shape of the betatron side-band is sensitive to the transverse rms size of colliding bunches. It is shown in this note that the transverse rms of the beam can be inferred from the shape of the betatron line. Analysis is presented which takes into account the tilt angle of the beams at the collision point and their offset. The authors discuss other effects which can change the shape of the betatron line in the spectrum