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Total Cross Section

The luminosity independent method [46] is the best way to measure the total cross section using the FPD, since it does not require very low |t| acceptance. This method combines the definition of the total cross section (Eq. 11)
 equation981
with the optical theorem
 equation988
and the relation tex2html_wrap_inline4854 to obtain
 equation996
where tex2html_wrap_inline4856 is the extrapolated number of elastic events, tex2html_wrap_inline4858 is the number of inelastic events, B is the slope of the elastic |t| distribution, and tex2html_wrap_inline4864 is the ratio of the real to imaginary part of the elastic scattering amplitude.

In a low luminosity special run with extra beam scraping, it will be possible to obtain a tex2html_wrap_inline4866 GeVtex2html_wrap_inline3030. CDF and E710 are in very good agreement for the elastic slope in the region |t|<0.15 GeVtex2html_wrap_inline3030 (tex2html_wrap_inline4874), with a virtually identical central value yielding a world average measurement of tex2html_wrap_inline4876 GeVtex2html_wrap_inline4878. For a 50,000 event special run, the largest error in the measurement should be about 1.5% from the extrapolation to t=0. The contribution of the tex2html_wrap_inline4864 error to the cross section is small, and the Level Ø counters will be used to accurately measure tex2html_wrap_inline4858. The slope in the region 0.15<|t|<0.6 GeVtex2html_wrap_inline3030 (tex2html_wrap_inline4890) is flatter than tex2html_wrap_inline4874, and is measured to be tex2html_wrap_inline4894 GeVtex2html_wrap_inline4878 [46]. This 3% error could be reduced to about 0.5% during this run.

The elastic cross section is roughly 20 mb, and about 8% of the events have |t|>0.15 GeVtex2html_wrap_inline3030, giving an effective cross section of 1.6 mb. Assuming a tex2html_wrap_inline2820 acceptance of 20% and a luminosity of tex2html_wrap_inline4904 cmtex2html_wrap_inline4098 gives a rate of 3 Hz. A five hour run will thus give 50,000 elastic events. Note that this will be a one-time run which could be done after all of the properties of the FPD are well-understood, and would consequently not require any dedicated setup time. With a data sample of 50,000 good elastic events it should be possible to measure the total cross section to an accuracy of about 2%.


next up previous contents
Next: Run-by-run Luminosity Monitor Up: Luminosity Measurement Previous: Luminosity Measurement

Gilvan Alves
Tue Mar 17 12:50:26 GRNLNDST 1998