october 2004cteq meeting1 parton distribution uncertainty and w and z production at hadron colliders...
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October 2004 CTEQ Meeting 1
Parton distribution uncertaintyand
W and Z production at hadron colliders
Dan StumpDepartment of Physics and Astronomy
Michigan State University
October 2004 CTEQ Meeting 3
PDF uncertainty and the cross section for inclusive jet production at the Tevatron.Run 1:CTEQ6.1, central fit and 40 Eigenvector Basis Sets
October 2004 CTEQ Meeting 4
Comparing the CDF data (Run 1) and the NLO calculation with CTEQ6.1Green: 1 + 40 alternative sets; Red: full uncertainty range
October 2004 CTEQ Meeting 5
The “master equation” for the Hessian method
2
10
2
d
kk XXX )()()( , aa
asymmetric errors,or one could use the Sullivan-Nadolsky formula
October 2004 CTEQ Meeting 6
Inclusive jet cross section for Run 2, in 5 rapidity bins, predicted by CTEQ6.1.
Red: central prediction;Blue: full uncertainty range
October 2004 CTEQ Meeting 7
Inclusive jet cross section for the LHC,predicted by CTEQ6.1.
central prediction+ 40 alternatives
October 2004 CTEQ Meeting 9
Uncertainties of Parton Distribution Functions—a major challenge for global analysis
The total cross sections for W and Z production were among the first examples to which we applied the new methods of uncertainty analysis.
W and Z were good test cases.
October 2004 CTEQ Meeting 10
Estimate the uncertainty on the predicted cross section for ppbar W+X at the Tevatron collider.
global 2
local 2’s
October 2004 CTEQ Meeting 11
Each experiment defines a “prediction” and a “range”. This figure shows the 2 = 1 ranges.
October 2004 CTEQ Meeting 12
This figure shows broader ranges for each experiment based on the “90% confidence level” (cumulative distribution function of the rescaled 2).
October 2004 CTEQ Meeting 13
The final result is an uncertainty range for the prediction of W.
Survey of wBl predictions (by R. Thorne, 2002)
PDF set energy wBln [nb] PDF uncert
Alekhin Tevatron 2.73 0.05
MRST2002 Tevatron 2.59 0.03
CTEQ6 Tevatron 2.54 0.10
Alekhin LHC 215. 6.
MRST2002 LHC 204. 4.
CTEQ6 LHC 205. 8.
October 2004 CTEQ Meeting 14
Each experiment defines a “prediction” and a “range”.This figure shows the 2 = 1 ranges for the value of S.Particle data group (shaded strip) is 0.1170.002.
The fluctuations are larger than expected for normal statistics. The vertical lines have 2
global=100;s(MZ)=0.11650.0065.
October 2004 CTEQ Meeting 15
How well can we determine the value of S( MZ ) from Global Analysis?
For each value of S, find the best global fit. Then look at the 2 value for each experiment as a function of S.
October 2004 CTEQ Meeting 17
Inclusive Z production at the Tevatron, Run 2(K factor for NNLO/NLO = 1.045 has been applied)
Red: 1 + 40 alternatives Blue: full uncertainty range 0.258 0.008 nbGreen: Latest CDF value Purple: Latest D0 value 0.25390.00330.00460.0152 nb 0.26490.00390.00990.0172 nb
October 2004 CTEQ Meeting 18
Inclusive W production at the Tevatron, Run 2(K factor for NNLO/NLO = 1.037 has been applied)
Red: 1 + 40 e.v. basis sets Blue: full uncertainty range 2.63 0.09 nbOrange: MRST prediction 2.690.11 nbGreen: Latest CDF value 2.7800.0140.0600.167 nbPurple: Latest D0 value 2.8650.0080.0750.186 nb
October 2004 CTEQ Meeting 19
Red: 1 + 40 e.v. basis setsPurple: Full uncertainty range (error ellipse)Blue: Uncorrelated ranges, roughly 3% each
The error ellipse for W and Z production at the Tevatron, Run 2
October 2004 CTEQ Meeting 20
Are the “up” and “down” displacements along the eigenvector directions symmetric?
October 2004 CTEQ Meeting 21
Z production at the LHC
Red: 1 + 40 e.v. basis sets Blue: Full uncertainty range 1.95 0.07 nb
October 2004 CTEQ Meeting 22
W production at the LHC
Red: 1 + 40 e.v. basis sets Blue: Full uncertainty range 19.5 0.8 nbOrange: MRST prediction 20.00.8 nb
October 2004 CTEQ Meeting 23
Error ellipse for W and Z production at the LHC
Red: 1 + 40 e.v. basis setsBlue: uncorrelated rangesPurple: Full uncertainty range(error ellipse)
October 2004 CTEQ Meeting 24
The PDF uncertainty in the ratioratio Z/W is very small possible test for new physics.
October 2004 CTEQ Meeting 26
W production at the Tevatron; MRST calculations from their paper on Theoretical Errors
CTEQ2.630.09 nb
October 2004 CTEQ Meeting 27
W production at the LHC; MRST calculations from their paper on Theoretical Errors
CTEQ19.50.8 nb
October 2004 CTEQ Meeting 28
Other theoretical uncertainties
• Branching ratio• Treatment of W width (off shell W)• EW parameter values, e.g., CKM matrix• Treatment of heavy quark mass effects
may lead to differences of order 1 %
October 2004 CTEQ Meeting 29
A survey of results from different programs(Pavel Nadolsky, C P Yuan)
Program Cross sec (nb)
CTEQ6M MRST2002
Tev’n Run 2
SigmaTot1 (W -> l 2526 2548
wttot (W)0.1068
2539 2562
wttot (W)0.1084
2577 2601
ResBos (W -> l 25886 26066
MRST’02 (W)0.1068
2600
LHC
SigmaTot1 (W -> l 20022 19944
wttot (W)0.1068
20137 20066
wttot (W)0.1084
20439 20367
ResBos (W -> l 2061652 20690 52
MRST’02 (W)0.1068
20400
s = 1.96 TeV
s = 14 TeV
October 2004 CTEQ Meeting 30
PT dependence of vector boson production
Collins, Soper and Sterman (CSS) formalism for pT resummation, schematically,
2
22222
3
1 )/( with )()()( and
)()(
max
**bb
bbbWbWbW
YbWebdMQdydQdQ
d
NPpert
bTiQV
T
BLNY parametrization
22131021 1002 bxxggQQggbWNP )ln()/ln(exp)(
(Brock, Landry, Nadolsky, Yuan)
i.e., 4 N.P. parameters (g1,g2,g3,bmax)
October 2004 CTEQ Meeting 32
Standard 2 = 1 parameter errors
2GeV
2GeV
2GeV
GeV
..
..
..
.max
050600
010680
010210
50
3
2
1
1
g
g
g
b
… but are such small uncertainties realistic?
October 2004 CTEQ Meeting 33
Reassess the parameter uncertainties, using the methods that we have used for PDF uncertainties.
The most interesting parameter, and which should have the largest uncertainty, is g2.
Method•Scan the BLNY fit versus g2 values.• For a range of g2 values, construct the best fit to g1 and g3.• Then look how 2 varies with g2.
October 2004 CTEQ Meeting 34
A 2 “parabola” for each experiment…
… implies an allowed range for the value of g2 for each experiment.
bmax = 0.5 GeV-1
October 2004 CTEQ Meeting 35
A 2 “parabola” for each experiment…
… implies an allowed range for the value of g2 for each experiment.
bmax = 1.12 GeV-1
October 2004 CTEQ Meeting 36
Comparison of CDF Z and D0 Z data (Run 1) to resummation calculation with BLNY parametrization