Tevatron bunch length studies at CDF

Abstract

A luminous interaction region can be described by the distribution in (x, y, z) over which p{bar p} interactions are observed in a detector. The spatial size of this distribution can be written in terms of expressions that involve only combinations of the proton and anti-proton bunch sizes. Hence, it is not possible to determine the sizes of the proton and anti-proton bunches independently by fitting the distribution of (x, y, z) from the recorded events. If, in addition to the coordinates (x, y, z) at which p{bar p} interactions occur, the times at which the interactions took place are also measured, then it becomes possible to measure the lengths of the proton and anti-proton bunches separately. This sensitivity is due to a correlation between z and t that arises from the fact that the proton and anti-proton bunches travel in opposite directions. The derivation presented in section 2 quantifies this correlation, resulting in an expression for the probability density as a function of z and t for p{bar p} interactions. By fitting the distributions observed at CDF using this model, we measure the lengths of the proton and anti-proton bunches at times throughout several Tevatron stores. From this analysismore » the evolution of the bunch lengths can be studied. We attempt to correlate these with other measures of the bunch length obtained using different experimental techniques.« less