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 2

PDF uncertainty and inclusive jet production

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 8

PDF uncertainty — the method

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 16

PDF uncertainty for W/Z production

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 25

Why calculations don’t agree

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 31

The BLNY fit to E288, E605, CDF Z, and D0 Z data

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

October 2004 CTEQ Meeting 37

More work needs to be done to obtain a final uncertainty range for g2.

Our larger goal is to include pT cross sections in the global analysis; i.e., simultaneously to fit PDF parameters and resummation parameters, for both W and Z production.