Work in progress, updated 4-Nov-97
FD Luminosity, 1997 pass 3
The FD luminosity for 1997 is determined using the method described in
OTN 376 , 'FD Luminosity at LEP 1.5'.
The on-peak CUBED cross section
The cross section for CUBED Bhabha scattering events in the FD was determined
from the p83 on-peak calibration data, excluding runs before 8072, for which
the tube chambers were not operational.
A CUBED cross section of
12.829 +- 0.140 nb
was calculated using the on peak TKMH cross section of 30.08nb ( Ref OTN 282 ).
The statistical error is 1.1%, from the number of CUBED and TKMH candidates
in 988/nb of data with good FD and TKMH detector status.
This value is 3% higher than the
best estimate for 1996. However, 2% of this change is due to the recovery
of 2 tube chamber quadrants during the 1996/97 shutdown.
The most recent comparable value is 12.675 +- 0.050 nb determined
from p70 pass 3;
1SD lower than the 1997 value.
Since these two values are compatible, they may be combined. If the error on
the p70 value is doubled to 0.100 nb, ( an arbitrary allowance for possible
changes in operating conditions since 1995 )
the weighted mean cross section becomes
12.727 +- 0.140 nb
where the statistical error is calculated using the 1997 p83 data only.
The effect of averaging with the p70 result is to decrease the cross-section by
0.8% , or 0.75 of the quoted statistical error.
Extrapolation to higher energy
The FD smear MonteCarlo has been rerun, generating 2*10**6 events at 185 and
205 GeV/c, using Bhlumi 4.01.
When these new points are combined with the previous runs at 165, 135 and
Z-peak, the cross section is found to be ~1% higher ( at 205 Gev ) than would
be expected from the nominal 1/s**2 dependence.
The deviation is an approximately linear
function of Ebeam.
This energy dependence will be included in a future version of ROLUFD.
Currently the database stores the cross section values at the
nominal beam energy points,
and extrapolates to the exact beam energy using 1/s**2.
Comparison with SW
Data from p84-88 was analysed, requiring that the SW, FD and TKMH status was
good.
The SW luminosity returned by ROCROS was scaled by
0.9918 to use the current best estimate of the
SWRL cross section.
The recommended beam energy correction of 0.997 was NOT applied to SW, since
it had not been applied to FD.
Comparison of FD and SW Luminosity ( 1./nb),
showing statistical errors only.
| Period
| 84 | 85 | 86 | 87
| Sum |
|---|
| LuSW
| 6236 +- 37 | 7415 +- 40 | 6776.7 +- 54.8 | 2302.6 +- 22.7
| 22729 +- 76 |
|---|
| LuCu
| 6201 +- 43 | 7235 +- 47 | 6670.5 +- 45.4 | 2283.1 +- 18.9
| 22389 +- 80 |
|---|
| Diff.
| 35 +- 56 | 180 +- 62 | 106.1 +- 71.1 | 19.5 +- 29.5
| 340 +- 110 |
|---|
The SW luminosity is systematically 1.5% higher than the FD ( CUBED ) values,
or ~ 1.5 times the quoted FD systematic error of 1.1%.
Had the p70 cross section been excluded, the difference would be 2%, or twice
the FD systematics.
Conversely, using the p70 cross section alone, the difference is only 0.4%.
( Several small contributions to the error have been neglected -
- Extrapolation of the FD ceross section to higher energy
- SW systematic error of 0.25%
- 'Theory' error ( Bhlumi ) of 0.25%, assumed to be common
Conclusion
Given that a major change to the FD detector ( such as the failure of 2 out of
8 tube quadrants ) cause only a 2% changes in cross section, and that changes
in the detector positions ( from 96 to 97 ) change the luminosity by less than
0.5% , it seems reasonable to use the p70 estimate, although the weight it
should receive in the calculation is rather arbitrary.
Even if the p70 data is ignored, the FD and SW Luminosities agree to 2SD.
If one accepts that the p70 data should be included, then a reasonable
assesment of the combined cross section indicates agreement at the 1.5 SD
level.