6.3 Systematic Eects
6.3.1 Correlated Errors
The LEP Beam Energy Uncertainty
The LEP beam energy is used as an absolute energy scale in the kinematic
t. The uncertainty of the beam energy willthus aect the reconstructed mass
spectrum. Since the beam energy of LEP is known with an accuracy of 20
MeV for the 1998 data period [104], the inuence of this uncertainty onthe W
mass t results can be estimated by changing the beam energy in the range of
this uncertainty. This isstudiedwithMonte Carloevents by changingthe beam
energy before performing the kinematic ts and comparing the mass t results
fordierentbeamenergies. Anerrorof17MeVisisassignedassystematicerror.
Initial State Radiation
The eects of the initial state radiation are not included in the kinematic ts.
average M inv [GeV]
number of events / GeV
● Data qqeν M w fit result MC background
0 5 10 15
70 80 90
average M inv [GeV]
number of events / GeV
● Data qqµν M w fit result MC background
0 5 10 15
70 80 90
average M inv [GeV]
number of events / GeV
● Data qqτν M w fit result MC background
0 5 10 15
70 80 90
average M inv [GeV]
number of events / GeV
● Data qqlν M w fit result MC background
0 20 40
70 80 90
Abbildung 6.22: Reconstructed mass distributions for the data at 183
GeV:qqe ; qq ; qq andqql, thecombinationofthe threechannels. The
solid curves and light shading display the results of the ts of M
W
to the
indicated nalstates. The backgrounditselfisindicated by the darkshaded
region.
qqeν
slope = 1.00 ± 0.05 offset = 0 ± 4 GeV
80.283 ± 0.377 GeV
80.163 ± 0.376 GeV
M W _true [ GeV ] M W _fit [ GeV ]
80 80.5 81
80 80.5 81
qqµν
slope = 0.95 ± 0.05 offset = 4 ± 4 GeV
80.783 ± 0.411 GeV
80.553 ± 0.432 GeV
M W _true [ GeV ] M W _fit [ GeV ]
80 80.5 81 81.5
80 80.5 81 81.5
qqτν
slope = 0.85 ± 0.07 offset = 13 ± 6 GeV 81.152 ± 0.558 GeV
80.824 ± 0.659 GeV
M W _true [ GeV ] M W _fit [ GeV ]
80 80.5 81 81.5
80 80.5 81 81.5
Abbildung 6.23: Mean of the tted masses versus generated mass for
Monte Carlo subsamples with ve dierent input masses. The solid line
through the points show the linear two parameter ts used to obtain the
biascorrections. The resultsofttedandcorrectedmassesareshown forthe
semileptonicnal states.
qqqq 1st pairing slope = 0.93 ± 0.03 offset = 6 ± 2 GeV 80.682 ± 0.217 GeV
80.671 ± 0.234 GeV
M W _true [GeV]
M W _fit [ GeV ]
80 80.5 81
80 80.5 81
qqqq 2nd pairing slope = 0.98 ± 0.11 offset = 2 ± 9 GeV
80.803 ± 0.538 GeV
80.922 ± 0.552 GeV
M W _true [GeV]
M W _fit [ GeV ]
80 80.5 81 81.5
80 80.5 81 81.5
Abbildung 6.24: Mean of the tted masses versus generated mass for
Monte Carlo subsamples with ve dierent input masses. The solid line
through the points show the linear two parameter ts used to obtain the
biascorrections. Theresultsofttedandcorrected massesare shownforthe
semileptonic nal states.
callythe reconstructed invariantmass, the ttedmasses are higher. This bias is
taken into accountin both the reweighting and MC calibrationt method. But
the correlated bias is only as accurate as the simulations in the Monte Carlo.
There is still some systematic uncertainty due to incomplete modelling of ISR.
To estimate this eect, a comparison is made between the Monte Carlo
gene-rators KORALW and EXCALIBUR, implementing dierent radiation schemes.
The dierences are 10MeV, and they are shown in Table 6.12.
Jet Measurement
The MC calibration and reweighting procedures rely on the Monte Carlo
assu-ming an accurate jet measurement. The uncertainty in the simulation of the
energies and anglesof jetsand of theirresolutions caninuence the tresultsof
the W mass and is therefore a source of systematic error. The uncertainties in
the simulation of jet properties as energies and angles are carried out studying
s = 183 GeV
Process Fitted Corrected Expected stat.
mass [GeV] mass [GeV] error[GeV]
qqe() 80:283 0:377 80:163 0:376 0:361
qq() 80:783 0:411 80:553 0:432 0:376
qq() 81:152 0:558 80:824 0:659 0:586
qqq q() 1st 80:682 0:217 80:671 0:234 0:253
qqq q() 2nd 80:803 0:538 80:922 0:552 0:838
qql() 80:408 0:261 0:238
qqq q() 80:709 0:215 0:242
f
ff
f() 80:587 0:166 0:170
Tabelle 6.4: Summary of t results and Monte Carlo corrections to M
W
for the BW t method using the data collected at183 GeV. The errors are
purely statistical. There isa smalloverlap of events between channels.
that they are consistent with ajet energy scalingby 0.1GeV,a smearingof the
jet energies by 1% and a smearingof the jet positions by 0:5 Æ
. To estimate the
systematicerror of the measured W mass, the jet properties are changedbefore
the kinematic ts and the variation of the tted mass values are determined.
The change of the tted mass values are regarded as systematicerrors, and the
totalerror is obtained addingthe errorsfrom allthesechecks in quadrature,see
Table 6.6. This is the dominant experimental systematicerror.
p
s = 183 GeV
Process Fitted mass [GeV]
qqq q()(before BE correction) 80.709 0.215
qqq q()(after BE correction) 80.616 0.215
f
ff
f()(after BE correction) 80.532 0.166
Tabelle 6.5: Final tresults of M
W
using data collected at183 GeV after
the correction of Bose-Einstein models mentioned above. The errors are
statisticalonly.
s = 189 GeV
Observed M
W
shift inMeV
qqe qq qq qqq q
E
jet
smearing by 5 % -3 -10 1 +6
E
jet
+ 0.2GeV +10 +48 +28 0
E
jet
+ 1.0GeV +45 +201 +129 -2
E
jet
- 0.2 GeV -10 -30 -23 0
E
jet
- 1.0 GeV -45 -182 -133 -6
Jetangle smearingby 0:5 Æ
-2 +1 +5 +1
Jet angle smearingby 2 Æ
+5 +7 -16 +3
Rescaled errors
E
jet
smearing by 1 % 1 2 1 1
E
jet
scale 0.1 GeV 5 20 15 1
Jetangle smearingby 0:5 Æ
1 2 5 1
total systematic 5 20 15 1
Tabelle 6.6: Systematicerrors injet measurements
Fragmentation and Decay
Fragmentation and particle decays are simulated using string fragmentation as
implemented inthe PYTHIA MonteCarloprogram. The inuence ofthe choice
ofthe hadronisationmodelontheresultsof thettedmassisstudiedby
compa-ring the string fragmentation and the cluster fragmentation as implemented in
the HERWIG MonteCarlo program[67, 68]. The dierenceinthe tted masses
is taken as anestimatefor the systematicerror, and this error isdetermined for
each channel separately. The errors range from20to 70MeV depending onthe
channels.
Fitting Method
The tting method itself may have some bias. Since the the events are binned,
thebin sizeisvariedand halfofthemaximaleectwithrespecttothecalibrated
mass is taken as systematic error, see Table 6.7. The uncertainty on the wrong
pairing fraction doesn't substantially aect the measured W mass, since the
s = 189 GeV
Bin size Observed M
W
shift inMeV
[GeV] qqe qq qq qqq q
0.25 +32 +18 +62 +16
0.50 0 0 0 0
1.00 +42 +10 +26 +4
total systematic 20 10 30 10
Tabelle 6.7: Systematic errors inthe tting method