Progress in PDFs

Conspirators: P. Nadolsky, S. Berge, I Schienbein,

J.-Y. Yu, W. Tung, S. Kretzer, J. Owens, S. Kuhlmann, J. Pumplin, H. LaiJ. Morfin, C. Keppel, V. Radescu, D. Mason

Fred Olness

SMU

Workshop on Intersections of

Nuclear Physics with

Neutrinos and Electrons

4 May 2006

Special thanks to Jeff Owens for his APS 2005 material

PDF StatusEvolutionNuclear CorrectionsTarget Mass Corrections

Strange Quark PDFDrell-YanHeavy Quark Effects

PDF STATUS

Many different experiments are required for Global Fit to proton structure

Data points used for global PDF fit

QCUT

1 / (Momentum Fraction)

Ener

gy S

cale

(GeV

)

Q > 2 GeVW > 3.5 GeV

Kinematics&

Evolution

Low Q & Hi-x: Feeds down to Hi Q & intermediate x

Tevatronx range for LHCborrowed from R. Thorne, et al., hep-ph/0507015

Nuclear Corrections

| eη|0 0.5 1 1.5 2 2.5

Cor

rect

ed A

sym

met

ry

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5 < 35 GeV T25 < E

Run II data from CDF (170pb-1)

Run II improved statistics

Nuclear Corrections at Large-x

�Tevatron W-Asymmetry data constrains d/u out to x ≈0.3�DIS data extends to higher x, but Nuclear Corrections important�Time to revisit

Large x parton distributions.S. Kuhlmann, et al.,Phys.Lett.B476:291-296,2000

0.1

1

1 10 100 1000

F 2(x

,Q2 )

Q2 (GeV/c)2

x=0.015 (X3)

x=0.045 (X1.8)

x=0.080 (X1.3)

x=0.125x=0.175x=0.225

x=0.275

x=0.35

x=0.45

x=0.55

x=0.65

x=0.75NuTeVCCFR

CDHSWNuTeV fit

0.1

1

10

1 10 100

xF3(

x,Q

2 )

Q2 (GeV/c)2

x=0.08

(x40)x=0.015

x=0.045

(x1.2)

(x2)

(x3.5)

(x1.5)

(x12)

(x6)

x=0.125

x=0.175

x=0.225

x=0.275

x=0.35

x=0.45

x=0.55

x=0.65

x=0.75NuTeV

CCFR 97CDHSW

NuTeV fit

NuTeV Structure Functions

NuTeV higher at large-xImplications for valence PDF

Nuclear Corrections important at large-x

Parton X0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Mea

n D

ata/

Th

eory

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4No Nuclear Correction

NMC Nuclear Correction

Kulagin/Petti Nuclear Correction

No Nuclear Correction

NMC Nuclear Correction

Kulagin/Petti Nuclear Correction

NuTeV Neutrino Data, NLO QCD, CTEQ6.1M

Nuclear Corrections for Neutrino Data

NMC too large at both small & large-x

K/P does better

Shape not ideal

Large-x not too bad

Small-x: what to do??

K/P depends on F123

Should correction depend on NC/CC???In progress: NuTeV Cross section data analysis

TargetMass

Corrections

1) Nachtmann variable ξ

2)p- ≠ ξP- results in mixing partonic & hadronic F's

(diagonal in helicity basis)

3) Transverse momentum (kT) effects

4) Threshold effects as x → 1

�=2x

1��1�4M2 x2

Q2

Sources of Target Mass Corrections

F.M. Steffens, W. Melnitchouk, nucl-th/0603014

Target Mass Corrections:

Size of TMC vs. Q and X

Strange

Quark PDF

What is relative uncertainty on PDFs' ???

u-quark

x

Gluon

x

Previously, s(x) was tied to u-bar and d-bar via kappa:

s�x�= �s�x�= ��u �x ���d �x �

2

Question: Do we really know the s-quark PDF to 5%???

0.01 0.03 0.1 0.3 0.70.6

0.8

0.9

1.

1.1

1.2

1.4

s-quark

x

40 CTEQ6M PDF sets

5% uncertainty???

Ratio

to C

TEQ

6

40 PDF Sets explore parameter space

Gluon important for Higgs production

Hi-x behavior constrained by DIS data

CTEQ6: Pumplin, Stump, Huston, Lai, Nadolsky, Tung, JHEP 0207, 012 (2002)

PDF Uncertainty band compared to

CTEQ6M

What is true uncertainty on s-quark PDF???

0.01 0.03 0.1 0.3 0.70.6

0.8

0.9

1.

1.1

1.2

1.4

s-quark

x

5% uncertainty???

Warning: The Director General has determined the band of PDF's can greatly

underestimate the true uncertainty

0.01 0.03 0.1 0.3 0.70.6

0.8

0.9

1.

1.1

1.2

1.4

Additional sets with more general parameterization

s-quark

x

Ratio

to C

TEQ

6

Ratio

to C

TEQ

6

Curves shown are examples; this is not an exhaustive set

40 CTEQ6M PDF sets Closer to the true error

Dimuons are ideal signal of s(x)

di-muon NuTeV CCFR CombinedNeutrino 5012 5030 10042Anti-Nu 1458 1060 2518

∗ High stats & high precision data* Best constraints on strange quark

M. Goncharov et al., NuTeV Collaboration PRD 64:110226 (2001)

NuTeV Collaboration (D. Mason for the collaboration). Moriond 2004, hep-ex/0405037

FragmentationFunction

DecayDistribution

Charm Production

cross-section

Di-muon cross-section

d±�

�

dx dy= � d d�

d� c

dx dy d � Dc� � � �c ����E

±�5 GeV

Global Fit: vary s(x) distribution

CTEQ6M Constrained Mixed FreeCCFR Nu 1.02 0.85 0.79 0.72

CCFR Nu-bar 0.58 0.54 0.59 0.59NuTeV Nu 1.81 1.70 1.55 1.44

NuTeV Nu-bar 1.48 1.30 1.15 1.13BCDMS F2p 1.11 1.11 1.11 1.11BCDMS F2d 1.10 1.10 1.10 1.11

H1 96/97 0.94 0.95 0.94 0.94H1 98/99 1.02 1.03 1.03 1.03

ZEUS 96/97 1.14 1.14 1.14 1.15NMC F2p 1.52 1.50 1.51 1.49

NMC F2d/F2p 0.91 0.91 0.91 0.91

1.05 1.07 1.06 1.03CCFR F2 1.70 1.71 1.81 1.88CCFR F3 0.42 0.42 0.44 0.42

E605 0.82 0.82 0.82 0.83NA51 0.62 0.61 0.52 0.52

0.82 0.83 0.82 0.82E866 0.39 0.40 0.39 0.38

D0 Jets 0.71 0.65 0.70 0.67CDF Jets 1.48 1.48 1.48 1.47TOTAL 2173 2144 2142 2133

χ2 / DOF

NMC F2d/F2p <Q2>

CDF � Asym

CTEQ6: J. Pumplin, et al., JHEP 0207:012,2002

Reasonable χ2 values(CTEQ6 did not fit di-muon data)

More parameters, lower value of χ2

Only di-muon data is sensitive to s(x) !!!

∴Idea: ν and ν-bar data separately determine

s and s-bar distributionsTotal of 1991 data points

Only di-muon data is sensitive

to s(x) !!!

What does the ∆s(x) strange PDF look like?

10-5 .001 0.01 0.05 0.1 .2 .3 .4 .5 .6 .7

x

-2×10-3

0

2×10-3

4×10-3

6×10-3

8×10-3

S- (

= x

s- (x,Q

)) d

x/dz

Momentum Asymmetry

(scale: linear in z = x1/3

)

x [s(x) - s(x)]ν

NX

sc

µ

W

[S�]��0

1

x {s �x���s �x �}

�0.0040�[S�]��0.0010

General range of the asymmetry

Olness, Pumplin, Stump, Huston, Nadolsky, Lai, Kretzer, Owens, Tung, Eur.Phys.J.C40:145-156,2005Kretzer, Olness, Pumplin, Stump, Tung, Reno, PRL 93,041802 (2004)

∆s(x): large uncertainty affected by: � charm fragmentation� charm mass� PDF set

�0

1{s� x ���s � x �}=0

• Tremendous new information on BOTH s+s and s-s

• Work is ongoing: extend to higher orders

• Include this information in next generation PDF sets

Does this solve the SinθW problem???

D. Mason for the NuTeV Collaboration; AIP Conf.Proc.792:851-854,2005 S. Catani, D. de Florian, G. Rodrigo, W. Vogelsang; Phys.Rev.Lett. 93 (2004) 152003

� x �s��s ����5×10�4

Three-loop kernel generates asymmetry@ Q2 20GeV2

Kretzer, Mason, Olness PRD 65:074010 (2002)

Fixed Target Drell-Yan

FNAL-E866/NuSea Collaboration (J.C. Webb et al.) AIP Conf.Proc.549:532-535,2002 Al

The radiative corrections change both the normalization of the data w/respect to the theory, and the slope vs x1. The pp data are consistent with MRST w/in errors. The pd aren't.

Fixed Target Drell-Yan

Theory is uncomfortably high at large-x

Implications for valence...

Radiative Corrections in progress

Heavy Quark Effects

NuTeV F2, evaluated with S-ACOT heavy quark scheme, CTEQ6.1M PDFs, and EMC nuclear correction

NuTeV F2, evaluated with zero mass NLO QCD, CTEQ6.1M PDFs, and EMC nuclear correction

Preliminary:generated by Steve Kuhlmann

Preliminary:generated by Steve Kuhlmann

Effect of Fully Massive Calculation

Parton X0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Mea

n D

ata/

Th

eory

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4Quark Masses Neglected

Quark Masses Included

NuTeV Neutrino Data, NLO QCD with no Nuclear Correction, CTEQ6.1M

Effect of Fully Massive Calculation

Minimal effect for this kinematic range with inclusive quantityDoes make a difference for specific observables

Progress in PDFs

Conspirators: P. Nadolsky, S. Berge, I Schienbein,

J.-Y. Yu, W. Tung, S. Kretzer, J. Owens, S. Kuhlmann, J. Pumplin, H. LaiJ. Morfin, C. Keppel, V. Radescu, D. Mason

Fred Olness

SMU

Workshop on Intersections of

Nuclear Physics with

Neutrinos and Electrons

4 May 2006

Special thanks to Jeff Owens for his APS 2005 material

PDF StatusEvolutionNuclear CorrectionsTarget Mass Corrections

Strange Quark PDFDrell-YanHeavy Quark Effects