C.-P. YuanMichigan State University
Collider phenomenology and
Global analysis of Parton Distribution Functions
New Physics signal found?
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Systematic uncertainties
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CDFNLO QCD
1/ ∫
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/(dE
Td
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Excitement at 10 years agoxT
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Systematic uncertainties
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/GeV
GeV
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Systematic uncertainties
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GeV
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0 50 100 150 200 250 300 350 400 450
GeV
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10-6
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1
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0 100 200 300 400
CDFNLO QCD
1/ ∫
d2
/(dE
Td
) dnb
/GeV
GeV
CDF Run 1A Data (1992-93)
High-x gluon not well known
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0 50 100 150 200 250 300 350 400 450
GeV
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10-6
10-4
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1
10 2
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0 100 200 300 400
CDFNLO QCD
1/ ∫
d2
/(dE
Td
) dnb
/GeV
GeV
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
)2xf(x,Q
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
s
u
g/10
u
d
dc
x-410 -310 -210 -110 1
)2xf(x,Q
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
s
u
g/10
u
d
d
c
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
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 2
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
1
10
102
103
104
105
106
107
10 102 103 104 105
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)
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 3
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
C.-P. Yuan (MSU) BNL June 24, 2010 7
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
C.-P. Yuan (MSU) BNL June 24, 2010 8
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
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 3
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
1.85
1.9
1.95
2
2.05
2.1
2.15
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
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 4
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
1.85
1.9
1.95
2
2.05
2.1
2.15
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
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 4
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
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 5
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
0.05
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
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 8
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.
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 9
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
-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)
(GeV)JJM200 400 600 800 1000 1200 1400
JJ
/dM
σR
ati
o o
f 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
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 10
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
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 11
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)
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 12
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)
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 13
d(x,Q)/u(x,Q) at Q = 85 GeV
Solid band: CTEQ6.6 uncertaintyHatched band: CT10 uncertainty
10-5 10-4 10-3 0.01 0.02 0.05 0.1 0.2 0.5 0.70.7
0.8
0.9
1.0
1.1
1.2
1.3
x
Rat
ioto
CT
EQ
6.6M
d/u at µ = 85 GeV
Solid band: CTEQ6.6 uncertaintyHatched band: CT10W uncertainty
10-5 10-4 10-3 0.01 0.02 0.05 0.1 0.2 0.5 0.70.7
0.8
0.9
1.0
1.1
1.2
1.3
x
Rat
ioto
CT
EQ
6.6M
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
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 14
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
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 15
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)
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 16
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
-0.2
0
0.2
Cha
rge
asym
met
ry
25 < pT{ < 35 GeV, CTEQ65
Resummed
NLOLO
0.5 1 1.5 2 2.5 3y{
-0.4
-0.2
0
0.2
0.4
Cha
rge
asym
met
ry
35 < pT{ < 45 GeV, CTEQ65
NNLL�NLO
NLO
LO
PN, 2007, unpublished; arXiv:1101.0561
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 17
CT10(W) vs. A` at the LHC
|µη|0 0.5 1 1.5 2
µA
0.15
0.2
0.25
0.3
0.35
|µη|0 0.5 1 1.5 2
µA
0.15
0.2
0.25
0.3
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
0.1
0.15
0.2
0.25
0.3
0.35 CT10
CT10W
CMS electron
CMS muon
NNLL−NLO+K, ResBos
PRELIMINARY
Zhao Li, 2011
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 18
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
-0.6
-0.4
-0.2
0
0.2
0.4
CT10
CT10W
LHCBNNLL−NLO+K, ResBos
PRELIMINARY
Zhao Li, 2011
LHC-B marginally prefers CT10W
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 19
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
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 22
Backup slides
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 24
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
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
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 25
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
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 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
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
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)
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 7
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
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 26
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)
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 27
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
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 28
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
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 29
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)
C.-P. Yuan (MSU) BNL June 24, 2010 3
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
Pavel Nadolsky (SMU) XIX DIS workshop, Newport News April 11, 2010 31
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
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)
18.5 19 19.5 20 20.5 21 21.5 22ΣtotHpp®HW±®{ΝLXL HnbL
1.85
1.9
1.95
2
2.05
2.1
2.15Σ
totH
pp®HZ
0®{{-
LXLHn
bL
W± & Z cross sections at the LHC
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
Pavel Nadolsky (SMU) DIS’2009 workshop, Spain April, 26 2009 26
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
Pavel Nadolsky (SMU) DIS’2009 workshop, Spain April, 26 2009 24