absolute cross section notes 1

I'm attempting to assemble the information necessary to calculate the absolute cross section of the BHT3 trigger in the 2009 500GeV running.

 

By assuming the transverse profiles of the beams are gaussian, we can come up with an analytic formula for the number of events recorded in BHT3:

Neve(d)=xs*Kb*Frev*Nb*Ny/(2*pi*sqrt((sigbx^2*sigyx^2)*(sigby^2*sigyy^2))) * exp(-d^2/(2*(sigbx^2+sigyx^2)))

xs is the BHT3 cross section.

Kb is the number of bunches.

Frev is the revolution frequency.

Nb and Ny are the number of protons in the blue beam and yellow beam bunches, respectively.  Some complexity appears when the numbers aren't the same bunch-to-bunch, but previous papers have bounded this as a small contribution, and I see no reason that shouldn't apply here as well.

sigQW is the width of the gaussian in the W direction in the Q beam.

d is the displacement of the beams from full-on collision during the vernier scan.

The equation is written for displacements in the x direction, but the equivalent y direction equation should be obvious.

 

A fit of the recorded Neve as a function of d can give us a value for (xs*Kb*Frev*Nb*Ny).  We can presumably get all of the constants from the collider, and so we can solve for xs.

 

I have contacted Bill Christie and Angelika (real first name Kirsten, which would have been nice to know in advance so I could find her email more easily) to get ahold of the vernier scan data, and am trying to find out who did the similar work in the last jet cross section measurement.

 

The cross section will also be complicated by the fact that the barrel status changes over time.  This will have to be treated carefully.  When calculating, we will have to mask any towers that were hot during the vernier scan.  I expect we can scale the absolute cross section by the number of good towers in a given run, divided by the number of good towers during the vernier scan, or something along these lines.

Other changes, like drifting pedestals, seem like they might cause more trouble.