The acceptance of Upsilon decays depends on the polarization of the Upsilon.  We do not have enough statistics to measure the polarization.  It is also not clear even at higher energies if there is a definite pattern: there are discrepancies between CDF and D0 about the polarization of the 1S.  The 2S and 3S show different polarizations trends than the 1S. So for the purposes of the paper, we will estimate the uncertainty due to the unknown Upsilon polarization using two extremes: fully transverse and fully longitudinal polarization.  This is likely an overestimate, but the effect is not the dominant source of uncertainty, so for the paper it is good enough.

There are simulations of the expected acceptance for the unpolarized, longitudinal and transverse cases done by Thomas:

http://www.star.bnl.gov/protected/heavy/ullrich/ups-pol.pdf

Using the pT dependence of the acceptance for the three cases (see page 9 of the PDF) we must then apply it to our measured upsilons.  We do this by obtaining the pT distribution of the unlike sign pairs (after subtracting the like-sign combinatorial background) in the Upsilon mass region and with |y|<0.5.  This is shown below as the black data points.

The data points are fit with a function of the form A p_T²  exp(-p_T/T), shown as the solid black line (fit result: A=18.0 +/- 8.3, T = 1.36 +/- 0.16 GeV/c).  We then apply the correction for the three cases, shown in the histograms (with narrow line width).  The black is the correction for the unpolarized case (default), the red is for the longitudinal and the blue is for the transverse case.  The raw yield can be obtained by integrating the histogram or the function.  These give 89.7 (histo) and 89.9 (fit), which given the size of the errors is a reasonable fit.  We can obtain the acceptance corrected  yield (we ignore all other corrections here) by integrating the histograms, which give:

• Unpol: 158.9 counts
• Trans: 156.4 counts
• Longi: 163.6 counts

We estimate from this that fully transverse Upsilons should have a yield lower by -1.6% and fully longitudinal Upsilons should have a higher yield by 2.9%.  We use this as a systematic uncertainty in the acceptance correction. 

In addition, the geometrical acceptance can vary in the real data due to masked towers which are not accounted for in the simulation.  We estimate that this variation is of order 25 towers (which is used in the 2007 and 2008 runs as the number of towers allowed to be dynamically masked). This adds 25/4800 = 0.5% to the uncertainty in the geometrical acceptance.