News from CTEQ-TEA PDF analysis · ¥ NNLO CTEQ global analysis (in progress) I Validation of O(α2...
Transcript of News from CTEQ-TEA PDF analysis · ¥ NNLO CTEQ global analysis (in progress) I Validation of O(α2...
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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
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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
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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
10-2
10-1
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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
x=3.2⋅ 10-3 , i=12
x=5⋅ 10-3 , i=11
x=8⋅ 10-3 , i=10
x=1.3⋅ 10-2 , i=9
x=2⋅ 10-2 , i=8
x=3.2⋅ 10-2 , i=7
x=5⋅ 10-2 , i=6
x=8⋅ 10-2 , i=5
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)
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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
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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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Σto
tHpp®HZ
0®{{-
LXLHn
bL
W± & Z cross sections at the LHC
CTEQ6.6 (GM)
CTEQ6.1 (ZM)
NNLL-NLO ResBos
G. Watt, PDF4LHC mtg, 26.03.2010
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NNLO global PDF analysis
NNLO DIS contributions are fullyimplemented in the S-ACOTscheme, the defaultfactorization scheme ofCTEQ6.6 and CT10 PDFs
18.5 19 19.5 20 20.5 21 21.5 22ΣtotHpp®HW±®{ΝLXL HnbL
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Σto
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LXLHn
bL
W± & Z cross sections at the LHC
CTEQ6.6 (GM)
CTEQ6.1 (ZM)
NNLL-NLO ResBos
G. Watt, PDF4LHC mtg, 26.03.2010
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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
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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
ò
ò
òò
ò
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
0.5
1.0
1.5
2.0
2.5
3.0
x
103x0.
5F
2c H
x,QL
NLO, Q = 2 GeV, mc = 1.41 GeV
2009 Les Houches HQ benchmarkswith toy PDFs; default µ = Q
G. Watt, PDF4LHC mtg, 26.03.2010
W, Z cross sections;mc = 1.3 GeV in CTEQ6.6
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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
10-5 10-4 10-3 0.01 0.02 0.05 0.1 0.20.0
0.5
1.0
1.5
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x
103x0.
5F
2c H
x,QL
LH PDFs Q=2 GeV, mc=1.414 GeV
¥ ACOT formalism provides recipe-like formulasfor implementing NNLO in the GM scheme (⇒Guzzi)
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New: F(c)2 (x,Q2) in S-ACOT scheme at NNLO
Preliminary
GM ACOT-Χ NNLO
FFNS Nf=3 NNLO
ZM NNLO
0.00
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0.10
0.15
0.20
0.25
F2
hHx
,QL
x=0.01
10.5.2. 20.3. 30.1.5 15.7.0.60.70.80.91.01.11.21.3
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
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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.
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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
0 0.5 1 1.5 2 2.5 3
)e
(y
eA
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> 25 GeVeT
p
=1.96 TeVS+X ν ± e→ ± W→pp
> 25 GeVνTE
)-1D0 electron data (0.75 fbCT10W (Solid band)CTEQ6.6 (Hatched band)
(GeV)JJM200 400 600 800 1000 1200 1400
JJ
/dM
σR
ati
o o
f d
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< 0.4max
|y|
Scale = 0.5 average pT of jets
CTEQ6.6 / CT10.00
CT10 / CT10.00
CT10W / CT10.00
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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
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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)
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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)
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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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Solid band: CTEQ6.6 uncertaintyHatched band: CT10W uncertainty
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ioto
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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
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Why difficulties with fitting A`(y`)?
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
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Why difficulties with fitting A`(y`)?
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)
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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
0.5 1 1.5 2 2.5 3y{
-0.6
-0.4
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asym
met
ry
25 < pT{ < 35 GeV, CTEQ65
Resummed
NLOLO
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ry
35 < pT{ < 45 GeV, CTEQ65
NNLL�NLO
NLO
LO
PN, 2007, unpublished; arXiv:1101.0561
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CT10(W) vs. A` at the LHC
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0.35=7 TeV)sData 2010 (
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
|η|0 0.5 1 1.5 2 2.5 3
W c
har
ge
asym
met
ry
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CT10W
CMS electron
CMS muon
NNLL−NLO+K, ResBos
PRELIMINARY
Zhao Li, 2011
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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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CT10W
LHCBNNLL−NLO+K, ResBos
PRELIMINARY
Zhao Li, 2011
LHC-B marginally prefers CT10W
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Acut fits to combined HERA data
x-510 -410 -310 -210 -110 1
]2 [
GeV
2 T /
p2
/ M
2Q
1
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510
610 NMC-pdNMCSLACBCDMSHERAI-AVCHORUSFLH108NTVDMNZEUS-H2DYE886CDFWASYCDFZRAPD0ZRAPCDFR2KT
= 0.5cutA = 1.0cutA = 1.5cutA = 3.0cutA = 6.0cutA
NNPDF2.0 dataset
Fitting procedure:¥ Include only DIS data above an Acut line
¥ Compare the resulting PDFs with DIS data below the Acut
line, in a region that is “connected” by DGLAP evolutionPavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 20
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CT10: Acut fits to DIS data at Q > Q0 = 2 GeV>2
<d
0.5
1
1.5
2
2.5
3 = 1.5cutFit with A
Fit without cuts < 1.0 cutA
< 1.5cut1.0 < A
< 3.0cut1.5 < A
< 6.0 cut3.0 < A
> 6.0cutA
Caola, Forte, Rojo, arXiv:1007.5405v2
Q > 1.41 GeV
<1.0 1.0-1.5 1.5-3.0 3.0-6.0 >6.0
ææ
æ
ææ
à
à
à
àà
ì
ì
ì
ìì
CT10 fit
Fit 1 with Acut=1.5Fit 2 with Acut=1.5
Q > 2 GeV
N pts= 36 18 30 27 468Ags
ranges
0.5
1.0
1.5
2.0
2.5
3.0Χdata
2�Npts
Motivation
Search for deviations from DGLAP evolution at smallest x and Q
¥ Follow the procedure proposed by NNPDF (Caola, Forte, Rojo, arXiv:1007.5405)
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 21
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CT10: Acut fits to DIS data at Q > Q0 = 2 GeV>2
<d
0.5
1
1.5
2
2.5
3 = 1.5cutFit with A
Fit without cuts < 1.0 cutA
< 1.5cut1.0 < A
< 3.0cut1.5 < A
< 6.0 cut3.0 < A
> 6.0cutA
Caola, Forte, Rojo, arXiv:1007.5405v2
Q > 1.41 GeV
<1.0 1.0-1.5 1.5-3.0 3.0-6.0 >6.0
ææ
æ
ææ
à
à
à
àà
ì
ì
ì
ìì
CT10 fit
Fit 1 with Acut=1.5Fit 2 with Acut=1.5
Q > 2 GeV
N pts= 36 18 30 27 468Ags
ranges
0.5
1.0
1.5
2.0
2.5
3.0Χdata
2�Npts
CT10
Two CT10-like fits to data at Ags > 1.5, with differentparametrizations of g(x,Q)
χ2i =
(Shifted Data− Theory)2
σ2uncor
Large syst. shifts at Ags < 1.0, in apattern that could mimic aslower Q2 evolution
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CT10: Acut fits to DIS data at Q > Q0 = 2 GeV>2
<d
0.5
1
1.5
2
2.5
3 = 1.5cutFit with A
Fit without cuts < 1.0 cutA
< 1.5cut1.0 < A
< 3.0cut1.5 < A
< 6.0 cut3.0 < A
> 6.0cutA
Caola, Forte, Rojo, arXiv:1007.5405v2
Q > 1.41 GeV
<1.0 1.0-1.5 1.5-3.0 3.0-6.0 >6.0
ææ
æ
ææ
à
à
à
àà
ì
ì
ì
ìì
CT10 fit
Fit 1 with Acut=1.5Fit 2 with Acut=1.5
Q > 2 GeV
N pts= 36 18 30 27 468Ags
ranges
0.5
1.0
1.5
2.0
2.5
3.0Χdata
2�Npts
CT10, cont.
δχ2 ∼ 0 at Ags > 1.0[no difference]
δχ2 = 0− 1.5 at Ags < 1.0,with large uncertainty
⇒ Disagreement with the “DGLAP-connected” data atAgs < Acut is not supported by the CT10 fit
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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
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CT10 & CT10W predictions for the near futureTotal cross sections
0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2
+H
-HW
+HW
HZ
t (s-channel)
-W
+W
’ (300)+W
’ (600)+W
Z
Z’ (300)
Z’ (600)
tt
H (120)→gg
H (160)→gg
H (250)→gg
t (t-channel)
VBF H (120)
VBF H (160)
VBF H (250)
LHC 7 TeV
CT10CTEQ6.6CT10W
0.7 0.8 0.9 1 1.1 1.2 1.3
+H
-HW
+HW
HZ
t (s-channel)
+W
’ (300)+W
’ (600)+W
Z
Z’ (300)
Z’ (600)
tt
H (120)→gg
H (160)→gg
H (250)→gg
t (t-channel)
VBF H (120)
VBF H (160)
VBF H (250)
Tevatron
CT10CTEQ6.6
CT10W
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 23
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Backup slides
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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
ctor�x
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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
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CT10 and CT10W predictions for Ae(ye) (D0 Run-2)
ey
0 0.5 1 1.5 2 2.5 3
) e (y e
A
-0.8
-0.6
-0.4
-0.2
0
0.2
> 25 GeVeT
p
=1.96 TeVS+X ν ± e→ ± W→pp
> 25 GeVνTE
)-1D0 electron data (0.75 fbCT10 (Solid band)CTEQ6.6 (Hatched band)
ey
0 0.5 1 1.5 2 2.5 3
) e (y e
A
-0.8
-0.6
-0.4
-0.2
0
0.2
< 35 GeVeT
25 GeV < p
=1.96 TeVS+X ν ± e→ ± W→pp
> 25 GeVνTE
)-1D0 electron data (0.75 fbCT10 (Solid band)CTEQ6.6 (Hatched band)
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
)-1D0 electron data (0.75 fbCT10 (Solid band)CTEQ6.6 (Hatched band)
ey
0 0.5 1 1.5 2 2.5 3
) e (y e
A
-0.8
-0.6
-0.4
-0.2
0
0.2
> 25 GeVeT
p
=1.96 TeVS+X ν ± e→ ± W→pp
> 25 GeVνTE
)-1D0 electron data (0.75 fbCT10W (Solid band)CTEQ6.6 (Hatched band)
ey
0 0.5 1 1.5 2 2.5 3
) e (y e
A
-0.8
-0.6
-0.4
-0.2
0
0.2
< 35 GeVeT
25 GeV < p
=1.96 TeVS+X ν ± e→ ± W→pp > 25 GeVν
TE
)-1D0 electron data (0.75 fbCT10W (Solid band)CTEQ6.6 (Hatched band)
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
)-1D0 electron data (0.75 fbCT10W (Solid band)CTEQ6.6 (Hatched band)
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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
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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|
Scale = 0.5 average pT of jets
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|
Scale = 0.5 average pT of jets
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
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Resummation effects in inclusive (di)jetproduction
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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
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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
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 32