collider phenomenology and global analysis of parton...

C.-P. YuanMichigan State University

Collider phenomenology and

Global analysis of Parton Distribution Functions

New Physics signal found?

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High-x gluon not well known

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ET (GeV)Phys. Rev. Lett. 77, 438 (1996)

known…can be accommodated

in the Standard Model

Cross sections at the LHCExperience at the Tevatron is very useful, but scattering at the LHC is not necessarilyat the LHC is not necessarily just “rescaled” scattering at the TevatronSmall typical momentum fractions x in many key searches

dominance of gluon and sea quark scatteringsea quark scatteringlarge phase space for gluon emissionintensive QCDintensive QCD backgroundsor to summarize,…lots of Standard Model to wade BFKL??

through to find the BSM pony

LHC Parton Kinematics

Sensitive to new region ofx and Q values.

Need better determination of PDFs

Need new kind of global analysis,such as

“The Combined PDF and PT Fits”

News from CTEQ-TEA PDF analysis

Pavel Nadolsky

Southern Methodist UniversityDallas, TX, U.S.A.

in collaboration withM. Guzzi, J. Huston, H.-L. Lai, Z. Li,

J. Pumplin, D. Stump, and C.-P. Yuan

April 11, 2010

Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 1

x-410 -310 -210 -110 1

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CT10 PDF plotsLow Scale

High Scale

CTEQ-Tung Et Al.: ongoing activities

¥ CT10 and CT10W general-purpose NLO PDF sets

¥ NNLO CTEQ global analysis (in progress)

I Validation of O(α2s) heavy-quark contributions to DIS is

completed (details by M. Guzzi in the HQ WG session)

¥ Effects of new experimental data on PDFsI W lepton asymmetry, Fn

2 /F p2 , comparisons with the LHC data

I dependence on the PDF parametrization form (J. Pumplin,today)

¥ DGLAP factorization in DIS at small x


CT10 parton distribution functions (PRD82, 074024 (2010))

¥ General-purpose NLO PDFs

¥ Adequate for the majority ofPQCD applications

¥ includes combined HERA-1 DISand Tevatron Run-2 inclusive jetdata

¥ detailed analysis of the TevatronRun-2 W asymmetry (A`) data

I CT10 and CT10W sets, withdifferent treatment of A`

¥ no LHC data yet10-3

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σNC

r (

x,Q

2 ) ⋅

2i e+ P

→ e

+ X

Q2 [GeV2 ]

x=6.18⋅ 10-5 , i=20

x=9.5⋅ 10-5 , i=19x=2⋅ 10-4 , i=18

x=3.2⋅ 10-4 , i=17x=5⋅ 10-4 , i=16

x=8⋅ 10-4 , i=15

x=1.3⋅ 10-3 , i=14

x=2⋅ 10-3 , i=13

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x=0.13, i=4

x=0.18, i=3

x=0.25, i=2

x=0.4, i=1

x=0.65, i=0

Shifted HERA-1 data (circles)CT10 NLO theory (lines)


CT10 family

� Two series of PDFs are produced:

I CT10: no D0 Run-2 W asymmetry data are included

I CT10W: include D0 Run-2 W asymmetry, with an extra weight

C.-P. Yuan (MSU) BNL June 24, 2010 9

Agreement between data sets� Good overall agreement: χ2/d.o.f. = 1.1 (out of ~2800 data

points)

� Noticable observations on the quality of the fit:

I Tevatron single-inclusive jet production: Run-1 and Run-2 setsare moderately compatible (arXiv:0904.2424)

I Tevatron Run-2 Z rapidity: D0 well described; CDF acceptable(higher stat.)

I Tevatron Run-2 W lepton asymmetry♦ is precise; constrains d(x)/u(x) at x → 1

♦ apparently disagrees with existing constraints on d/u, mainlyprovided by the NMC F d

2 /F p2 and Run-1 W lepton asymmetry

data; minor tension against BCDMS F d2 data


Agreement between data sets

� Reaonable fits to electron (e) asymmetry data are possiblewithout NMC and BCDMS; and vice versa

� No acceptable fit to D0 II e asymmetry and NMC/BCDMSdata can be achieved, if they are included on the samefooting

� Tension between Run-2 e asymmetry and µ asymmetry

� Good agreement between Run-2 e W asymmetry data andZ y data

� With special emphasis on D0 II e asymmetry data (weight>1),it is possible to obtain a reasonable agreement for Wasymmetry (χ2/d.o.f. = 1− 2) , with some remaining tensionwith NMC & BCDMS data, especially at x > 0.4


CT10 parton distribution functions (PRD82, 074024 (2010))

¥ 53 CT10/CT10W eigenvector sets for αs(MZ) = 0.118

I 4 CT10AS/CT10WAS PDFs for αs(MZ) = 0.116− 0.120

♦ The correlated PDF+αs uncertainty on an observable X iscomputed by

∆XPDF+αs =q

∆X2PDF, CT10 + ∆X2

αs, CT 10AS ,

as explained in PRD 82,054021 (2010)

I CT10/CT10W PDFs with 3 and 4 active flavors

¥ In the LHADPF library and at http://hep.pa.msu.edu/cteq/public/index.html


NNLO global PDF analysis¥ Time is ripe for producingNNLO PDFs

¥ Accuracy of many EW, DIS, jetdata becomes comparable toNNLO contributions

¥ Heavy-quark mass effects inDIS at Q ≈ mQ is the key chal-lenge for NNLO global fits

⇒ 5-7% differences in σW,Z

at the LHC (Tung et al., hep-ph/0611254)

¥ For comparison, NNLO hard-scattering correction to σW,Z is≈2%

18.5 19 19.5 20 20.5 21 21.5 22ΣtotHpp®HW±®{ΝLXL HnbL

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W± & Z cross sections at the LHC

CTEQ6.6 (GM)

CTEQ6.1 (ZM)

NNLL-NLO ResBos

G. Watt, PDF4LHC mtg, 26.03.2010


NNLO global PDF analysis

NNLO DIS contributions are fullyimplemented in the S-ACOTscheme, the defaultfactorization scheme ofCTEQ6.6 and CT10 PDFs


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NNLL-NLO ResBos



Simplified Aivazis-Collins-Olness-Tung schemeACOT, PRD 50 3102 (1994); Collins, PRD 58 (1998) 094002; Kramer, Olness, Soper, PRD (2000) 096007

¥ Derivation is based upon, and closely follows, the proof ofQCD factorization for DIS with massive quarks (Collins, 1998)

¥ Relatively simple

I One value of Nf (and one PDF set) in each Q range

I Straightforward matching based on kinematical rescaling

I Sets mQ = 0 in ME with incoming c or b

¥ Reduces to the ZM MS scheme at Q2 À m2Q, without

additional renormalization

¥ Reduces to the FFN scheme at Q2 ≈ m2Q

I has reduced dependence on tunable parameters at NNLO


New: F(c)2 (x,Q2) in S-ACOT scheme at NNLO

Preliminary

GM ACOT-Χ NNLO

FFNS Nf=3 NNLO

ZM NNLO

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Q HGeVL

Rat

ioto

GM

NNLO calculationfor F c

2,L(x,Q) isimplemented inthe CTEQ fit (Guzzi, Lai,

P.N., Yuan, in preparation)

ACOT reducesto FFNS at Q ≈ mc

and to ZM at Q À mc

Les Houches toyPDFs, evolved at

NNLO withthreshold matching

terms


CTEQ PDFs vs. the latest data: LHCAgreement with many LHC measurements

Figures are from ATLAS. Similar results from CMS

+data on σW /σZ , tt, γγ, etc.


CTEQ PDFs vs. the latest data: Tevatron

Outstanding puzzles:1. Run-2 W charge asymmetry

(constraining d(x,Q)/u(x,Q)at x > 0.1)

2. Inclusive (di)jet production(constraining g(x,Q) atx > 0.1)

In both processes, experimentalaccuracy is high enough to startfeeling effects beyond NLO andof resummations

ey

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CTEQ6.6 / CT10.00

CT10 / CT10.00

CT10W / CT10.00


The puzzle of the CDF/D0 W lepton asymmetry

¥ CT10W set reasonably agrees with 3 pT` bins of Ae(ye) andone bin of Aµ(yµ) from D0 Run-2 (2008).

¥ NNPDF 2.0 (arXiv:1012.0836) agrees with Aµ(yµ), disagrees with twopTe bins of Ae(ye).

¥ CT10, many other PDFs fail.

Agreement of Source orPQCD with D0 Ae(ye) χ2/npt comments

CTEQ6.6, NLO 191/36=5.5 Our study;

CT10W, NLO 78/36=2.2 Resbos, NNLL-NLO

With Aµ(yµ): 88/47=1.9ABKM’09, NNLO 540/24=22.5 Catani, Ferrera, Grazzini,

MSTW’08, NNLO 205/24=8.6 JHEP 05, 006 (2010)

JR09VF, NNLO 113/24=4.7


Why difficulties with fitting A`(y`)?

1. A`(y`) is very sensitive to the average slope sdu ofd(x, MW )/u(x, MW )

A`(y`) ∼ A`(yW )|LO ∝1

x1 − x2

[d(x1)

u(x1)− d(x2)

u(x2)

]; x1,2 =

Q√se±yW

Berger, Halzen, Kim, Willenbrock, PRD 40, 83 (1989); Martin, Stirling, Roberts, MPLA 4, 1135 (1989); PRD D50, 6734 (1994);Lai et al., PRD 51, 4763 (1995)

2. Constraints on sdu by fixed-target F d2 (x,Q)/F p

2 (x,Q) areaffected by nuclear and higher-twist effectsAccardi, Christy, Keppel, Monaghan, Melnitchouk, Morfin, Owens, PRD 81, 034016 (2010)


Challenges with fitting A`(y`)

Small changes in sdu causesignificant variations in A`

Lai et al., PRD 51, 4763 (1995)

Alternative constraints on d/uby F d

2 (x,Q)/F p2 (x,Q) from

fixed-target DIS are affectedby nuclear and higher-twisteffectsAccardi, Christy, Keppel, Monaghan, Melnitchouk,Morfin, Owens, PRD 81, 034016 (2010)


d(x,Q)/u(x,Q) at Q = 85 GeV

Solid band: CTEQ6.6 uncertaintyHatched band: CT10 uncertainty

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EQ

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d/u at µ = 85 GeV

Solid band: CTEQ6.6 uncertaintyHatched band: CT10W uncertainty

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EQ

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d/u at µ = 85 GeV

¥ CT10W prefers a larger slope of d/u, has a smaller uncertaintythan CTEQ6.6 or CT10

¥ CT10W shows tension with NMC, BCDMS F p,d2 data



3. Existing parametrizations underestimate the PDF uncertaintyon d/u

PDFs based on Chebyshovpolynomials improveagreement with D0 Run-2 Ae,but are outside of currentCTEQ/MSTW bands (Pumplin)

This ambiguity is reduced byA`(y`) at the LHC, whichconstrains d/u and d/u atx ∼ 0.01.

Band: CT10 uncertainty

Long dash: Chebyshov, dbar/ubar->1 at x->0

Short dash: Chebyshov, free dbar/ubar at x->0

Solid: MSTW’2008NLO

PRELIMINARY



4. Experimental A` with lepton pT` cuts is sensitive to dσ/dqT of Wboson at transverse momentum qT → 0.

¥ Fixed-order (N)NLO calculations (DYNNLO, FEWZ, MCFM,...)predict a wrong shape of dσ/dqT at qT → 0.

¥ Small-qT resummation correctly predicts dσ/dqT in this limit.

¥ CT10(W) PDFs are fitted using a NNLL-NLO+K resummedprediction for A` (ResBos); must not be used with fixed-orderpredictions for A`.

For example:

χ2(CT10W+ResBos) = 1.9Npt (us);

χ2(CT10W+DYNNLO) = 8.4Npt (NNPDF)


Charge asymmetry in peT bins (CDF Run-2, 207 pb−1)

Without the peT cut (FEWZ):

Anastasiou et al., 2003

y

y of W boson

With pTe cuts imposed, Ach(ye) is sensitive to small-QT resummation

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NNLL�NLO

NLO

LO

PN, 2007, unpublished; arXiv:1101.0561


CT10(W) vs. A` at the LHC

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MC@NLO, CTEQ 6.6MC@NLO, HERA 1.0MC@NLO, MSTW 2008

-1 L dt = 31 pb∫

νµ →W

ATLAS

CT10(W) agrees well with theLHC A`; some differencesbetween NLO and NNLL+NLO

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W c

har

ge

asym

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ry

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CT10W

CMS electron

CMS muon

NNLL−NLO+K, ResBos

PRELIMINARY

Zhao Li, 2011


CT10(W) vs. A`: LHC-B

|η|1.5 2 2.5 3 3.5 4 4.5

W c

harg

e as

ymm

etry

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CT10

CT10W

LHCBNNLL−NLO+K, ResBos

PRELIMINARY

Zhao Li, 2011

LHC-B marginally prefers CT10W


Conclusions

¥ In the CTEQ-TEA fit, an NNLO calculation for F c,b2,L in the

S-ACOT scheme is demonstrated to be viable.

¥ This is the most challenging component of the NNLO CTEQPDF analysis, to be made available soon.

¥ Progress in understanding of new Tevatron and LHC datasets, PDF parametrization issues

¥ arXiv:1101.0561: synopsis of recent CTEQ-TEA publications

I CT10W fit to Run-2 W charge asymmetry;PDFs for leading-order showering programs; constraints oncolor-octet fermions


Backup slides


CT10 & CT10W predictions for the near futureTotal cross sections

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t (t-channel)

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VBF H (160)

VBF H (250)

LHC 7 TeV

CT10CTEQ6.6CT10W

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-HW

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HZ

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Z

Z’ (300)

Z’ (600)

tt

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H (160)→gg

H (250)→gg

t (t-channel)

VBF H (120)

VBF H (160)

VBF H (250)

Tevatron

CT10CTEQ6.6

CT10W


S-ACOT input parameters

At Q ≈ mc, F c2 depends significantly on

1. Charm mass: mc = 1.3 GeV in CT10

2. Factorization scale: µ =√

Q2 + κm2c ; κ = 1 in CT10

3. Rescaling variable ζ(λ) for matching in γ∗c channels(Tung et al., hep-ph/0110247; Nadolsky, Tung, PRD79, 113014 (2009))

Fi(x,Q2) =∑

a,b

∫ 1

ζ

dξ

ξfa(ξ, µ) Ca

b,λ

(ζ

ξ,Q

µ,mi

µ

)

x = ζ/(

1 + ζλ · (4m2c)/Q2

), with 0 ≤ λ . 1

CT10 usesζ(0) ≡ χ ≡ x

(1 + 4m2

c/Q2),

motivated by momentum conservation

1+ ��Mf

2

Q2 Ζ=ΧACOT HΛ=0L

Ζ=x HΛ®¥L

Λ=0.1

Λ=0.2

Λ=1 Phy

sica

lthr

esho

ld:W=

Mf;Ζ=

1

10-4 0.001 0.01 0.1 1

1

x

Res

calin

gfa

ctorΖ�x


Input parameters of the S-ACOT schemeAt NLO, the charm mass mc, factorization scale µ, and rescalingvariable ζ of CTEQ PDFs are tuned to best describe the DIS data

ç

ç

çç

ç

à

à

à

à

à

æ

æ

æ æ

æ

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òò

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S-ACOT band, from top:

Μ2=Q2+4mc

2,Λ=0.2Μ

2=Q2+mc

2,Λ=0 (default)Μ

2=Q2,Λ=0

Dashed: NF=3, NNLO

ç MSTW08-NLOà MSTW08-NLO-Χò FONNL-A-Χæ FONLL-B-Χ

10-5 10-4 10-3 0.01 0.02 0.05 0.1 0.20.0

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5F

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x,QL

NLO, Q = 2 GeV, mc = 1.41 GeV

2009 Les Houches HQ benchmarkswith toy PDFs; default µ = Q


W, Z cross sections;mc = 1.3 GeV in CTEQ6.6


NNLO results for F(c)2 (x,Q2) - Preliminary

At NNLO and Q ≈ mc:

S-ACOT-χ (Nf = 4) ≈ FFN (Nf = 3)

without tuning

¥ S-ACOT is numerically closeto other NNLO schemes

¥ NNLO expressions are closeto the FONLL-C scheme(Forte, Laenen, Nason, arXiv:1001.2312).

ò

ò

ò

ò

æ

æ

æ æ

æ

scale dependence

blue: S-ACOT-Χ NLO

green: S-ACOT-Χ NNLO

magenta: FFNS NNLO Nf=3

ò MSTW08-NNLO-Χ

æ FONNL-C-Χ

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x,QL

LH PDFs Q=2 GeV, mc=1.414 GeV

¥ ACOT formalism provides recipe-like formulasfor implementing NNLO in the GM scheme (⇒Guzzi)


CT10(W): radiative contributions to A`(y`)

¥ Default calculation: A`(y) at NNLL-NLO, using lookup tablesfor σ(p`

T , y`)NNLL+NLO/σ(p`T , y`)LO from ResBos [Balazs, Yuan, PRD 56, 5558

(1997); Landry, Brock, P.N. Yuan, PRD67, 073016 (2003)].

¥ Cross check: include NNLO corrections at QT ≈ MW [Arnold &

Reno, 1989]; A`(y`) changes by a few percent at the highest y`

and pT > 35 GeV

I magnitude of changes is comparable with full NNLO terms(Catani, Ferrera, and Grazzini, JHEP 05, 006 (2010))

I changes are small compared to the experimental errors


CT10 and CT10W predictions for Ae(ye) (D0 Run-2)

ey

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A

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> 25 GeVνTE

)-1D0 electron data (0.75 fbCT10 (Solid band)CTEQ6.6 (Hatched band)

ey

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) e (y e

A

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25 GeV < p

=1.96 TeVS+X ν ± e→ ± W→pp

> 25 GeVνTE


ey

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) e (y e

A

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> 25 GeVνTE


ey

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) e (y e

A

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> 25 GeVνTE


ey

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) e (y e

A

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< 35 GeVeT

25 GeV < p

=1.96 TeVS+X ν ± e→ ± W→pp > 25 GeVν

TE


ey

0 0.5 1 1.5 2 2.5 3

) e (y e

A

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

> 35 GeVeT

p

=1.96 TeVS+X ν ± e→ ± W→pp

> 25 GeVνTE



Di-jet at Tevatron

• Large scale dependence

• PDF uncertainty

CT10 and CTEQ6.6 differ from MSTWwith larger uncertainty

Do CTEQ PDFs disagree with D0 (di)-jet data?Pumplin et al., PRD 80 (2009) 014019: no significant tension betweenCTEQ PDFs and incl. jet data; D0 presentation exaggerates the“discrepancy”

Data and NLO theory, from the D0 paper and CT09 analysis

D0 Coll., arXiv:0802.2400 (700 pb−1)

0.5

1.0

1.5

|y| < 0.4

DØ Run II-1L = 0.70 fb

= 0.7coneR

50 100 200 3000.0

0.5

1.0

1.5

1.2 < |y| < 1.6

NLO scale uncertainty

0.4 < |y| < 0.8

T = p

Fµ =

RµNLO pQCD

+non-perturbative corrections

50 100 200 300

1.6 < |y| < 2.0

CTEQ6.5M with uncertainties

MRST2004

0.8 < |y| < 1.2

DataSystematic uncertainty

50 100 200 300

2.0 < |y| < 2.4

(GeV)T

p

data

/ th

eory

(GeV)T

p

data

/ th

eory

(GeV)T

p

data

/ th

eory

(GeV)T

p

data

/ th

eory

(GeV)T

p

data

/ th

eory

(GeV)T

p

data

/ th

eory

“Discrepancy”?

(Shifted D0-Run 2 data)/CT09

Good agreement


Jet production: issues to consider

¥ Significant scaledependence

I Comparisons to CT10 PDFsmust use µ = pjet

T /2 , thesame scale as in the CT10fit

¥ Differences between NLOcodes; sensitivity toresummation of jetdifferential distributions(Alioli et al., arXiv:1012.3380)

(GeV)JJM200 400 600 800 1000 1200 1400

JJ

/dM

σR

atio

of

d

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

< 0.4max

|y|


CTEQ6.6 / CT10.00

CT10 / CT10.00

CT10W / CT10.00

(GeV)JJM200 400 600 800 1000 1200 1400

JJ

/dM

σR

atio

of

d

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

< 2.0max

1.6 < |y|


CTEQ6.6 / CT10.00

CT10 / CT10.00

CT10W / CT10.00

¥ Correlated systematic shifts reconcile the data with a widerrange of PDFs than in the standalone experimental analysis


Theory uncertainties on jets @ LHC 7TeV

1900 1950 2000 2050 2100 2150 2200 2250 2300

(fb/

GeV

)jj

/dM

d

0

20

40

60

80

100

120

140

160

180

200

CT10.00CT10 PDF uncertaintyhalf scaledouble scale

di-jet @ LHC 7 TeV < 2200 GeVjj2000 GeV < M

|y| < 2.8 R = 0.6

280 300 320 340 360 380 400 420

/dy

(pb/

GeV

)T

/dp

d

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

CT10.00CT10 PDF uncertainty

half scaledouble scale

Inclusive Jet @ LHC 7 TeV

< 400 GeVT

310 GeV < p

2.1 < |y| < 2.8 R = 0.6

PDF uncertainty dominates.Can further constrain PDFs.

Uncertainty induced by αs in the PDF analyses

� Questions addressed:

I Two leading theoretical uncertainties in LHC processes aredue to αs and the PDFs; how can one quantify theircorrelation?

I Which central αs(MZ) and which error on αs(MZ) are to beused with the existing PDFs?

I What are the consequences for key LHC processes(gg → H0, etc.)?

� recent activities on this issue:

I MSTW (arXiv:0905.3531)I NNPDF (in 2009 Les Houches Proceedings, arXiv:1004.0962)I H1+ZEUS (arXiv:0911.0884)


Higgs predictions with different PDF sets

CT10 prediction is about the same as CTEQ6.6 for Higgs production

@LHC 7 TeV

Practical evaluation of the combined PDF+αs uncertainty

Several prescriptions of varying complexity for combining the PDFand αs uncertainties exist

In arXiv:1004.4624, we show that addition of the αs and PDFuncertainties in quadrature is entirely adequate in most practicalsituations

TheoremIn the quadratic approximation, the total αs+PDF uncertainty ∆σ forthe CT10 set, for αs(MZ) = 0.118± 0.002, is obtained by

∆X =√

∆X2CT10 + ∆X2

αs,

where¥ ∆XCT10 is the CTEQ6.6 PDF uncertainty from 44 PDFs with the same

αs(MZ) = 0.118

¥ ∆Xαs= (X0.120 −X0.116)/2 is the αs uncertainty computed with two

central CTEQ6.6AS PDFs for αs(MZ) = 0.116 and 0.120


Quadrature addition reproduces the exact PDF+αs uncertainty

Total PDF+αs errors ∆X are the same when found (a) from a fullfit with floating αs, or (b) by adding ∆XPDF and ∆Xαs inquadrature

10-5 10-4 10-3 0.01 0.02 0.05 0.1 0.2 0.5 0.7

0.6

0.8

1.0

1.2

1.4

x

CT

EQ

6.6A

S/C

TE

Q6.

6M

g at Q=2 GeV

10-5 10-4 10-3 0.01 0.02 0.05 0.1 0.2 0.5 0.7

0.6

0.8

1.0

1.2

1.4

x

CT

EQ

6.6A

S/C

TE

Q6.

6M

c at Q=2 GeV

¥ black – CTEQ6.6 PDFuncertainty

¥ Blue filled – PDF+αs

uncertainty of the fit withfloating αs(MZ)

¥ Green hatched – PDF+αs

uncertainty added inquadrature


Top Quark Pair production rates

At Tevatron Run-2, uncertainty Incduced by PDFs is sizable.

Uncertainty induced byfactorization (and renormalization) scale dependence is large at the LHC. Hence, NNLO calculation Is needed.

Use top quark pair production rate to determine the mass of top quark

What’s top mass?

What’s the top mass in a full event generator such as PYTHIA?generator, such as PYTHIA?

NOBODY KNOWS

Parton showers generate some higher order corrections in the event shapeorder corrections in the event shape,

but with approximations.

ResBos for Higgs Physicsq

q

V

H

VQuark initiated processes:

Gluon initiated processes:

• Rate and shape:at the same order of accuracy as Drell-Yan processes

t

tt

H

• Rate and shape:at the same order of accuracy as Drell-Yan processesconsistent with NNLO QCD rateinclude exact contribution in high PT

( )2Sα

arXiv:0909.2305

Shape changes from and variation of scales

( )2Sα

( )2Sα

( )1Sα

H

W+

W−

Predict different shapeResBos vs PYTHIA vs NLO hep-ph/0509100

b

b

H

MSSM Higgs boson

Consistent treatment of initial state parton mass with CTEQ6.6 PDFs, in GM scheme.(see Sally Dawson’s talk)

Di-Photon Productions

Backup Slides

CTEQ PDF parametrizationPDF’s (fa(x,Q)) are parametrized with a flexible form motivated by physics considerations (Regge behavior, spectator counting, for example) at fixed small Qo(1.3 GeV for CTEQ) and then evolved for Q>Qo by DGLAP

assume for most of the general analyses that the c and b distributions are zero at scales below their masses and are generated by QCD evolution above

Parametrization of parton distributions at Qo used to obtain the CTEQ5 and CTEQ6 parton distributions contained 5 shape parameters (apart from normalization) for each flavor

global analysis data sets not sufficiently constraining to determine all of the parameters, so a number are frozen at some particular (motivated) values20 free parameters for CTEQ6.1/6.5 and 22 for CTEQ6.6 (see next slide)

For CTEQ6.5/6.6, adopt a simpler form with 4 shape parameters for the valence quarks uv(x), dv(x) and the gluon g(x)

a reasonable generalization of the conventional minimal form

which combines Regge behavior at x->0 and spectator counting at x->1Both forms above are positive definite and have simplified logarithmic derivatives

f (x) = aoxa1 (1− x)a2 ea3x+a4 x 2

f (x) = aox a1 (1− x)a2

CTEQ PDF Parametrization

Is this form flexible enough?Remember the lesson of Tevatron Run-1 jets, where low x and high x PDFs can easily be (artificially) tied together through the parametrization.We find that significantly better fits cannot be achieved by introducing additional parameters or changing the functional form

NB: prior to CTEQ6.6, the analysis generally assumed

that ansatz has been dropped in CTEQ6.6

s(x) = s (x)∝ d (x) + u (x)

Role of heavy flavors in the PDF analysisQCD factorization for heavy-quark scattering attracted Wu-Ki’sclose interest throughout his whole career

1987-2009: development of the general-mass (GM) SACOT-χ scheme,currently adopted by CTEQ and MSTW analyses

2006 (CTEQ6.5): realization that the GM (and not zero-mass) treatmentof c, b mass terms in DIS is essential for predicting precision W, Z, andother cross sections at the LHC

Threshold

suppression

x=0.05 µ2=Q

2+4 m

2

F2c

Q2 / GeV

2

χ=x(1+4 m2 / Q

2 )

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

1 10 102

103

NLO 3-flv

LO 3-flv : GF(1)

Naive LO 4-flv : c

(x)

LO

4-f

lv A

CO

T(c)

: c(c)


1.85

1.9

1.95

2

2.05

2.1

2.15Σ

totH

pp®HZ

0®{{-

LXLHn

bL


CTEQ6.6 (GM)

CTEQ6.1 (ZM)

NNLL-NLO ResBos

Pavel Nadolsky (SMU) DIS’2009 workshop, Spain April, 26 2009 25

Role of heavy quarks in the PDF analysisThis CTEQ6.5 observation triggered substantial activity, including

¥ revision/improvements inthe GM treatment of heavyquarks in the MSTW’2008analysis

¥ MSTW authors view theirpre-CTEQ6.5 PDF’s (such asMRST’2004) as obsolete andask not to use them

) (nb)ν± l→ ± B(W⋅ ±Wσ

20 20.5 21 21.5 22 22.5 23

) (

nb

)- l

+ l→ 0

B(Z

⋅ 0Zσ

1.9

1.92

1.94

1.96

1.98

2

2.02

2.04

2.06

2.08

2.1

W and Z total cross sections at the LHC

R(W/Z) = 10.5 10.6 10.7

MSTW08 NNLO

MRST06 NNLO

MRST04 NNLO

Alekhin02 NNLO

MSTW08 NLO

MRST06 NLO

MRST04 NLO

Alekhin02 NLO

CTEQ6.6 NLO

) (nb)ν± l→ ± B(W⋅ ±Wσ

20 20.5 21 21.5 22 22.5 23

) (

nb

)- l

+ l→ 0

B(Z

⋅ 0Zσ

1.9

1.92

1.94

1.96

1.98

2

2.02

2.04

2.06

2.08

2.1


Strangeness and σZ/σW at the LHC

10-5 10-4 10-3 0.01 0.02 0.05 0.1 0.2 0.5 0.7x

-1

-0.5

0

0.5

1

Cor

rela

tion

Correlation between ΣZ�ΣW± HLHCL and fHx,Q=85. GeVL

d-

u-

gudscb

The PDF uncertainty inσZ/σW is mostly driven bys(x,Q); increases by a factorof 3 compared to CTEQ6.1as a result of freestrangeness in CTEQ6.6

a stumbling block in the precision measurement of W bosonmass MW at the LHC


collider phenomenology and global analysis of parton...

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