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From partons to new physicsat the CERN Large Hadron Collider
Pavel Nadolsky
Michigan State University
March 3, 2008
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 1
Preparing for a discovery of unseen dimensions
¥ New phenomena occurring at Terascale energies provideinsights about the nature of fundamental symmetries,structure of space and time
¥ LHC is an experiment of extraordinary scope andsophistication that will look for these phenomena amidstabundant “known” Standard Model processes
¥ Its potential for success depends on the ability tounderstand hadronic dynamics in the new energy regimeand implement this dynamics in new physics searches
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 2
LHC: unprecedented richness of hadronic theory
¥ dominance of sea partonscattering
¥ small typical momentum fractionsx in several key searches(Higgs, lighter superpartners, ...)
¥ large QCD backgrounds
¥ complicated event signatures;reliance on differentialdistributions
¥ unique low-energy dynamics(underlying event, multipleinteractions...)
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
100
101
102
103
104
105
106
107
108
109
fixedtarget
HERA
x1,2
= (M/14 TeV) exp(±y)Q = M
LHC parton kinematics
M = 10 GeV
M = 100 GeV
M = 1 TeV
M = 10 TeV
66y = 40 224
Q2
(GeV
2 )x
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 3
Perturbative QCD computations
Other experiments:HERA, Tevatron,fixed target, ...
mass effectsCharm and bottom
Stability ofperturbation theory
compositionParton flavor
Multi−scaleregimes
Resummations
saturation?...DGLAP? BFKL?
Combined withelectroweak corrections
Fragmentationfunctions
Power−suppressedcontributions
Predictions for LHC observablesperturbative X−sections
Hard scattering:
Universality
Renormalizationgroup invariance
(N)NLO radiativecorrections
nonperturbative inputSoft scattering:
Partondistributions
(PDFs)
Globalanalysis
to LHC dataComparison
Parton showeringmodels
freedomAsymptotic Confinement
Factorization
observablesProof for individual
Small−xeffects
A relevant, yet incomplete, picture
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 4
Perturbative QCD computations
nonperturbative inputSoft scattering:
freedomAsymptotic Confinement
Factorization
Other experiments:HERA, Tevatron,fixed target, ...
Globalanalysis
Small−xeffects
mass effectsCharm and bottom
Stability ofperturbation theory
(N)NLO radiativecorrections
compositionParton flavor
observablesProof for individual
to LHC dataComparison
Multi−scaleregimes
Parton showeringmodels
Resummations
saturation?...DGLAP? BFKL?
Combined withelectroweak corrections
Partondistributions
(PDFs)
Fragmentationfunctions
Power−suppressedcontributions
Predictions for LHC observablesperturbative X−sections
Hard scattering:
Universality
Renormalizationgroup invariance
Global interconnections can be as important as (N)NLOperturbative contributions; are different at the LHC and Tevatron
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 4
Perturbative QCD computations
saturation?...DGLAP? BFKL?
Combined withelectroweak corrections
Fragmentationfunctions
Power−suppressedcontributions
Predictions for LHC observablesperturbative X−sections
Hard scattering:
Universality
Renormalizationgroup invariance
(N)NLO radiativecorrections
nonperturbative inputSoft scattering:
Partondistributions
(PDFs)
Globalanalysis
to LHC dataComparison
Parton showeringmodels
freedomAsymptotic Confinement
Factorization
observablesProof for individual
Small−xeffects
Other experiments:HERA, Tevatron,fixed target, ...
Resummations
Stability ofperturbation theory
Multi−scaleregimes
compositionParton flavor
mass effectsCharm and bottom
Global interconnections can be as important as (N)NLOperturbative contributions; are different at the LHC and Tevatron
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 4
Examples of global connections
¥ Correlations between collider cross sections through sharedparton distribution functions
based on
Implications of CTEQ6.6 global analysis for colliderobservables
with Cao, Huston, Lai, Pumplin, Stump, Tung, Yuan; arXiv:0802.0007
¥ Constraints on Higgs boson sector from direct searches andprecision measurements
I QCD backgrounds for Higgs → γγ (with Balazs, Berger, Yuan)
I W boson mass at the Tevatron and LHC(with Berge, Konychev, Olness, Tung, Yuan, and others)
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 5
PDF-induced correlations in hadron scattering
10-510-4 10-3 0.010.02 0.05 0.1 0.2 0.5 0.7x in 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
xin
gat
Q=
85.G
eV
Correlations between CTEQ6.6 PDF’s
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 6
PDF-induced correlations in hadron scattering
¥ Dependence on the PDF’s isstrongly correlated for some pairsof cross sections andanti-correlated for other pairs
¥ I will discuss the origin of thecorrelations, especially for W, Z, ttcross sections
⇒ implications for the monitoring ofparton and collider luminosities,determination of new physicsparameters
Noteworthy correlations
Range of PDF uncertainties (CTEQ6.1)σ
totNLO * KNNLO at the LHC
~4%
~4%
1.875 1.9 1.925 1.95 1.975 2 2.025ΣHp p −> Z −> e eL @nbD
−
18.5
19
19.5
20
20.5
ΣHp
p −>
W −>
eΝeL
@nb
D
σ(W) (nb)182 184 186 188 190 192 194
σ(tt
) (p
b)
-
LHC41 CTEQ6.1 PDFs
Campbell, Huston, Stirling
760
765
770
775
780
785
790
795
800
805
182 184 186 188 190 192 194760
765
770
775
780
785
790
795
800
805
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 7
Theoretical uncertainties on σW , σZ , σtt
0.9 1 1.1 1.2 1.3
W+
W-
Z0
W+h0H120LW-h0H120L
t t-
H171Lgg®h0H120L
h+H200L
Σ±∆ΣPDF in units of ΣHCTEQ66MLLHC,NLO
CTEQ6.6CTEQ6.1IC-Sea
KNNLO
18.5 19. 19.5 20. 20.5 21. 21.5 22.ΣtotHpp®HW±®{ΝLXL HnbL
1.9
1.95
2.
2.05
2.1
2.15
2.2
Σto
tHpp®HZ
0®{{-
LXLHn
bL
W± & Z cross sections at the LHC
H1
MRST’02
MRST’04
ZEUS-TRZEUS-ZM
ZEUS-ZJ
Alekhin’02
MSTW’06
AMP’06
CTEQ6.6
NNLL-NLO ResBos
NLO PDF’sNNLO PDF’s
σW,Z
I NNLO PQCD: (Hamberg et al; Harlander, Kilgore;
Anastasiou et al.): σNNLO − σNLO = −2%
I PDF dependence: & 3%at ≈ 90% c.l.
σtt
INLO scale dependence: 11%(to be reduced at NNLO soon)
Imt dependence: 2− 3% formt = 172±1 GeV
I PDF dependence: 3%
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 8
“Standard candle” processes: W, Z, tt production
¥ Event rates for pp → W±X, pp → Z0X at the LHC can bemeasured with accuracy δσ/σ ∼ 1% (tens of millions ofevents even at low luminosity)
¥ These measurements will be employed to tightly constrainPDF’s and monitor the LHC luminosity L in real time(Dittmar, Pauss, Zurcher; Khoze, Martin, Orava, Ryskin; Giele, Keller’;...)
I other methods will initially give δL = 10− 20%
¥ tt event rate can be potentially measured with accuracy≈ 5%
Tevatron: the accuracy of luminosity monitoring in pp elastic scattering is oforder 5%
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 9
Cross section ratios
¥ LHC collaborations will normalize many cross sections σ tothe “standard candle” cross sections σsc (i.e., measurer = σ/σsc)
I dependence on L and other systematics may cancel in r
I PDF uncertainties cancel in r for strongly correlated crosssections; add up in anticorrelated cross sections
¥ Similar cancellations may occur in S/√
B, asymmetries, etc.
It helps to find a correlated “standard candle” cross section foreach interesting LHC cross section
For example, it is better to normalize σHiggs to σZ (σtt) if σHiggs iscorrelated (anticorrelated) with σZ
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 10
A mini-poll: Z production at the LHC
Choose all that apply and select the x range
The PDF uncertainty in σZ is mostly due to...
1. u, d, u, d PDF’sat x < 10−2 (x > 10−2)
2. gluon PDFat x < 10−2 (x > 10−2)
3. s, c, b PDF’sat x < 10−2 (x > 10−2)
Leading order
Z0q
q e
e
Next-to-leading order
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 11
An inefficient application of the error analysis
Ì Compute σZ for 40 (now 44)extreme PDF eigensets
Ì Find eigenparameter(s)producing largest variation(s),such as #9, 10, 30 0 2 4 6 8 10121416182022242628303234363840
PDF set number
1.86
1.88
1.9
1.92
1.94
1.96
1.98
Σto
t
pp®ZX,�!!!
s=14 TeV; 40 CTEQ6.1 extreme PDF sets
Î It is not obvious how to relate abstract eigenparameters tophysical PDF’s u(x), d(x), etc.
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 12
CTEQ6.6 theoretical framework(Michigan State/Taiwan/Washington)
¥ A full NLO analysis (NNLO is nearly completed)
¥ 2700 data points from 35 experiments on DIS, Drell-Yanprocess, jet production
¥ Recent improvements in treatment of heavy quark masses inDIS, etc. (CTEQ6.5), with important impact on W, Z crosssections
I a general-mass factorization scheme with fulldependence on mc,b
I free parametrization for strange quarks (constrained by CCFR,NuTeV charged-current DIS data)
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 13
CTEQ6.6 PDF’s
10-5 10-4 10-3 0.01 0.02 0.05 0.1 0.2 0.5 0.7x
0.8
0.85
0.9
0.95
1
1.05
1.1
Rat
ioto
CT
EQ
6.6M
g at Q=85. GeV
10-5 10-4 10-3 0.01 0.02 0.05 0.1 0.2 0.5 0.7x
0.8
0.85
0.9
0.95
1
1.05
1.1
Rat
ioto
CT
EQ
6.6M
d at Q=85. GeV
10-5 10-4 10-3 0.01 0.02 0.05 0.1 0.2 0.5 0.7x
0.8
0.85
0.9
0.95
1
1.05
1.1
Rat
ioto
CT
EQ
6.6M
g at Q=85. GeV
10-5 10-4 10-3 0.01 0.02 0.05 0.1 0.2 0.5 0.7x
0.8
0.85
0.9
0.95
1
1.05
1.1
Rat
ioto
CT
EQ
6.6M
s at Q=85. GeV dashes:CTEQ6.1M
¥ CTEQ6.6 u, d are above CTEQ6.1 by 2-4%
I The result of suppressed charm contribution to F2(x,Q) atHERA in the general-mass scheme
¥ very different strange PDF’sPavel Nadolsky (MSU) Southern Methodist University March 3, 2008 14
Multi-dimensional PDF error analysis
aiai0
χ20
χ2
¥ Minimization of a likelihoodfunction (χ2) with respectto ∼ 30 theoretical (mostlyPDF) parameters {ai} and> 100 experimentalsystematical parameters
I partly analytical andpartly numerical
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 15
Multi-dimensional PDF error analysis
a+ia−
i aiai0
∆χ2
χ20
χ2
¥ Establish a confidenceregion for {ai} for a giventolerated increase in χ2
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 15
Multi-dimensional PDF error analysis
ai
χ2
Pitfalls to avoid
¥ “Landscape”
I disagreements betweenthe experiments
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 15
Multi-dimensional PDF error analysis
ai
χ2 Pitfalls to avoid
¥ Flat directions
I unconstrainedcombinations of PDFparameters
I dependence on the PDFparametrization, freetheoretical parameters(factorization scale, etc.)
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 15
Multi-dimensional PDF error analysis
χ2
ai
The actual χ2 function shows
¥ a well pronounced globalminimum χ2
0
¥ weak tensions betweendata sets in the vicinity ofχ2
0 (mini-landscape)
¥ some dependence onassumptions about flatdirections
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 15
Multi-dimensional PDF error analysis
χ2
ai
The actual χ2 function shows
¥ a well pronounced globalminimum χ2
0
¥ weak tensions betweendata sets in the vicinity ofχ2
0 (mini-landscape)
¥ some dependence onassumptions about flatdirections
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 15
Multi-dimensional PDF error analysis
χ2
ai
The actual χ2 function shows
¥ a well pronounced globalminimum χ2
0
¥ weak tensions betweendata sets in the vicinity ofχ2
0 (mini-landscape)
¥ some dependence onassumptions about flatdirections
The likelihood is approximately described by a quadratic χ2 witha revised tolerance condition ∆χ2 ≤ T 2
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 15
Multi-dimensional PDF error analysis
χ2
ai
The actual χ2 function shows
¥ a well pronounced globalminimum χ2
0
¥ weak tensions betweendata sets in the vicinity ofχ2
0 (mini-landscape)
¥ some dependence onassumptions about flatdirections
The likelihood is approximately described by a quadratic χ2 witha revised tolerance condition ∆χ2 ≤ T 2
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 15
Multi-dimensional PDF error analysis
∆χ2
ai0 a+ia−
i
χ2
ai
The actual χ2 function shows
¥ a well pronounced globalminimum χ2
0
¥ weak tensions betweendata sets in the vicinity ofχ2
0 (mini-landscape)
¥ some dependence onassumptions about flatdirections
The likelihood is approximately described by a quadratic χ2 witha revised tolerance condition ∆χ2 ≤ T 2
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 15
Correlation analysis for collider observables(J. Pumplin et al., PRD 65, 014013 (2002); P.N. and Z. Sullivan, hep-ph/0110378)
A technique based on the Hessian method to relate the PDFuncertainty in physical cross sections to PDF’s of specific flavorsat known (x, µ)
For 2N PDF eigensets and two cross sections X and Y :
∆X =1
2
√√√√N∑
i=1
(X
(+)i −X
(−)i
)2
cosϕ =1
4∆X ∆Y
N∑
i=1
(X
(+)i −X
(−)i
) (Y
(+)i − Y
(−)i
)
X(±)i are maximal (minimal) values of Xi tolerated along the i-th PDF
eigenvector direction; N = 22 for the CTEQ6.6 setPavel Nadolsky (MSU) Southern Methodist University March 3, 2008 16
Correlation angle ϕ
Determines the parametric form of the X − Y correlation ellipse
X = X0 + ∆X cos θ
Y = Y0 + ∆Y cos(θ + ϕ)
δX
δY
δX
δY
δX
δY
cos ϕ ≈ 1 cos ϕ ≈ 0 cos ϕ ≈ −1
X0, Y 0: best-fitvalues
∆X, ∆Y : PDF errors
cosϕ ≈ ±1 :cosϕ ≈ 0 :
Measurement of X imposestightloose
constraints onY
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 17
Types of correlations
X and Y can be
¥ two PDFs f1(x1, Q1) and f2(x2, Q2)(plotted as cosϕ vs x1 & x2)
¥ a physical cross section σ and PDFf(x,Q) (plotted as cosϕ vs x)
¥ two cross sections σ1 and σ2
10-510-4 10-3 0.010.02 0.05 0.1 0.2 0.5 0.7x in u at Q=85. GeV
10-5
10-4
10-3
0.01
0.02
0.05
0.1
0.2
0.5
0.7
xin
u-
atQ=
85.G
eV
Correlations between CTEQ6.6 PDF’s
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 ΣZHLHCL and fHx,Q=85. GeVL
d-
u-
gudscb
0.82 0.84 0.86 0.88 0.9
ΣtotHpp->t t-
XL HnbL
2.
2.025
2.05
2.075
2.1
2.125
2.15
Σto
tHpp->HZ
0->
e+e-LXLHn
bL
Z0 vs tt-
production at the LHC at NLO
mt=Μ=171 GeV
CTEQ6.6
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 18
Correlations between f1(x1, Q) and f2(x2, Q) at Q = 85 GeV
Figures from http://hep.pa.msu.edu/cteq/public/6.6/pdfcorrs/Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 19
Correlations between f(x1, Q) and f(x2, Q) at Q = 85 GeV
u(x1, Q) vs. u(x2, Q)
10-510-4 10-3 0.010.02 0.05 0.1 0.2 0.5 0.7x in f1at Q=85. GeV
10-5
10-4
10-3
0.01
0.02
0.05
0.1
0.2
0.5
0.7
xin
f1at
Q=
85.G
eV
Correlations between CTEQ6.6 PDF’s
g(x1, Q) vs. g(x2, Q)
10-510-4 10-3 0.010.02 0.05 0.1 0.2 0.5 0.7x in g at Q=85. GeV
10-5
10-4
10-3
0.01
0.02
0.05
0.1
0.2
0.5
0.7
xin
gat
Q=
85.G
eV
Correlations between CTEQ6.6 PDF’s
-1 -0.5 0 0.5 1
Cos j
Can you explain why the gluon correlation pattern looks sodifferent?
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 20
Correlations between f(x1, Q) and f(x2, Q) at Q = 85 GeV
u(x1, Q) vs. u(x2, Q)
10-510-4 10-3 0.010.02 0.05 0.1 0.2 0.5 0.7x in f1at Q=85. GeV
10-5
10-4
10-3
0.01
0.02
0.05
0.1
0.2
0.5
0.7
xin
f1at
Q=
85.G
eV
Correlations between CTEQ6.6 PDF’s
g(x1, Q) vs. g(x2, Q)
10-510-4 10-3 0.010.02 0.05 0.1 0.2 0.5 0.7x in g at Q=85. GeV
10-5
10-4
10-3
0.01
0.02
0.05
0.1
0.2
0.5
0.7
xin
gat
Q=
85.G
eV
Correlations between CTEQ6.6 PDF’s
-1 -0.5 0 0.5 1
Cos j
¥ Momentum sum rule:
∫ 1
0xg(x)dx +
Nf∑
i=1
∫ 1
0x [qi(x) + qi(x)] dx = 1
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 20
Correlations between f(x1, Q) and f(x2, Q) at Q = 85 GeV
u(x1, Q) vs. u(x2, Q)
10-510-4 10-3 0.010.02 0.05 0.1 0.2 0.5 0.7x in f1at Q=85. GeV
10-5
10-4
10-3
0.01
0.02
0.05
0.1
0.2
0.5
0.7
xin
f1at
Q=
85.G
eV
Correlations between CTEQ6.6 PDF’s
g(x1, Q) vs. g(x2, Q)
10-510-4 10-3 0.010.02 0.05 0.1 0.2 0.5 0.7x in g at Q=85. GeV
10-5
10-4
10-3
0.01
0.02
0.05
0.1
0.2
0.5
0.7
xin
gat
Q=
85.G
eV
Correlations between CTEQ6.6 PDF’s
-1 -0.5 0 0.5 1
Cos j
Correlation patterns look similar for g, c, b PDF’s(no intrinsic charm here!)
c vs. c
10-510-4 10-3 0.010.02 0.05 0.1 0.2 0.5 0.7x in c at Q=85. GeV
10-5
10-4
10-3
0.01
0.02
0.05
0.1
0.2
0.5
0.7
xin
cat
Q=
85.G
eV
Correlations between CTEQ6.6 PDF’s
b vs. b
10-510-4 10-3 0.010.02 0.05 0.1 0.2 0.5 0.7x in b at Q=85. GeV
10-5
10-4
10-3
0.01
0.02
0.05
0.1
0.2
0.5
0.7
xin
bat
Q=
85.G
eV
Correlations between CTEQ6.6 PDF’s
c vs. g
10-510-4 10-3 0.010.02 0.05 0.1 0.2 0.5 0.7x in g at Q=85. GeV
10-5
10-4
10-3
0.01
0.02
0.05
0.1
0.2
0.5
0.7
xin
cat
Q=
85.G
eV
Correlations between CTEQ6.6 PDF’s
b vs. c
10-510-4 10-3 0.010.02 0.05 0.1 0.2 0.5 0.7x in c at Q=85. GeV
10-5
10-4
10-3
0.01
0.02
0.05
0.1
0.2
0.5
0.7
xin
bat
Q=
85.G
eV
Correlations between CTEQ6.6 PDF’s
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 20
Correlations between f1(x1, Q) and f2(x2, Q) at Q = 85 GeV
d vs u
10-510-4 10-3 0.010.02 0.05 0.1 0.2 0.5 0.7x in u at Q=85. GeV
10-5
10-4
10-3
0.01
0.02
0.05
0.1
0.2
0.5
0.7
xin
dat
Q=
85.G
eV
Correlations between CTEQ6.6 PDF’s
s vs u at Q=2 GeV
10-510-4 10-3 0.010.02 0.05 0.1 0.2 0.5 0.7
x in u-
at Q=2. GeV
10-5
10-4
10-3
0.01
0.02
0.05
0.1
0.2
0.5
0.7
xin
sat
Q=
2.G
eV
Correlations between CTEQ6.6 PDF’s
s vs. g
10-510-4 10-3 0.010.02 0.05 0.1 0.2 0.5 0.7x in g at Q=85. GeV
10-5
10-4
10-3
0.01
0.02
0.05
0.1
0.2
0.5
0.7
xin
sat
Q=
85.G
eV
Correlations between CTEQ6.6 PDF’s
-1 -0.5 0 0.5 1
Cos j
Sometimes there is a clear physics reason behind the correlation(e.g., sum rules, assumed Regge behavior, data constraints);sometimes not
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 21
Correlations between g(x1, 2 GeV) and g(x2, 85 GeV)
10-510-4 10-3 0.010.02 0.05 0.1 0.2 0.5 0.7x in 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
xin
gat
Q=
85.G
eV
Correlations between CTEQ6.6 PDF’s
Gluons at Q = 85 GeV arecorrelated with gluons atQ = 2 GeV and larger xbecause of DGLAP evolution
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 22
Correlations between W, Z cross sections and PDF’s
Tevatron Run-2
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
CTEQ6.6: correlation between Σtot and fHx,Q=85. GeVL
d-
u-
gudscb
pp-
®ZX,�!!!
s=1.96 TeV
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
CTEQ6.6: correlation between Σtot and fHx,Q=85. GeVL
d-
u-
gudscb
pp-
®WX,�!!!
s=1.96 TeV
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 ΣZHLHCL and fHx,Q=85. GeVL
d-
u-
gudscb
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 ΣW± HLHCL and fHx,Q=85. GeVL
d-
u-
g
udscb
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 23
Correlations of Z and tt cross sections with PDF’s
LHC Z, W cross sections arestrongly correlated with g(x), c(x),b(x) at x ∼ 0.005
∴ they are strongly anticorrelatedwith processes sensitive to g(x) atx ∼ 0.1(tt, gg → H for MH > 300 GeV)
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 ΣZHLHCL and fHx,Q=85. GeVL
d-
u-
gudscb
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
CTEQ6.6: correlation between s tot and fHx,Q=85. GeVL
d-
u-
gudscb
ppfi t t-
X,� !!!
s=14 TeVmt=m=171 GeV
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 24
tt vs Z cross sections at the LHC
0.82 0.84 0.86 0.88 0.9
ΣtotHpp->t t-
XL HnbL
2.
2.025
2.05
2.075
2.1
2.125
2.15
Σto
tHpp->HZ
0->
e+e-LXLHn
bL
Z0 vs tt-
production at the LHC at NLO
mt=Μ=171 GeV
CTEQ6.6
Measurements of σtt and σZ probe the same (gluon) PDFdegrees of freedom at different x values
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 25
Correlations between σ(gg → H0), σZ , σtt
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 26
Other topics explored in the CTEQ6.6 paper
¥ Strong sensitivity of σZ/σW to the strangeness PDF andσW+/σW− to uV − dV
¥ Potential role of σtt as a standard candle observable
¥ Origin of PDF uncertainties in single-top production
¥ Correlation cosines for various Higgs production channels inSM and MSSM
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 27
LHC studies of electroweak symmetry breaking
P(x2; ~kT2)
P(x1; ~kT1)S HH�
(GeV/c)T
* qγZ/0 5 10 15 20 25 30
-1 (
GeV
/c)
T/d
qσ
d× σ1/
0.02
0.04
0.06
0.08
0.1|y|>2
ResBos with small-x effectResBos without small-x effectDØ data
DØ, 0.98 fb-1
(b)
¥ A new aspect: multi-scale factorization (resummation)
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 28
Higgs sector in SM and MSSM¥ Standard Model: 1 Higgs doublet, one scalar field H
I Direct search: mH > 114 GeV at 95% c.l.
I indirect: MH = 80+39−28 GeV at 68% c.l.
¥ Minimal Supersymmetric Standard Model:2 Higgs doublets; h0, H0, A0, H±
I mh ≤ mZ | cos 2β|+ rad. corr. . 135 GeV
¥ In these models, expect one or more Higgs bosons with massbelow 140 GeV
¥ Many other possibilities for EW symmetry breaking exist!
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 29
Higgs sector in SM and MSSM
160 165 170 175 180 185mt [GeV]
80.20
80.30
80.40
80.50
80.60
80.70
MW
[GeV
]
SM
MSSM
MH = 114 GeV
MH = 400 GeV
light SUSY
heavy SUSY
SMMSSM
both models
Heinemeyer, Hollik, Stockinger, Weber, Weiglein ’07
experimental errors 68% CL:
LEP2/Tevatron (today)
Tevatron/LHC
SM band: 114 ≤ MH ≤ 400 GeVSUSY band: random scan
¥ the goal of direct and indirectmeasurements is toover-constrain the Higgs sector inSM, greatly constrain SUSY
¥ indirect constraints stronglydepend on MW , mt values,hence require accurate QCDpredictions for W and tproduction
For example, in SMMW = 80.3827− 0.0579 ln
„MH
100 GeV
«− 0.008 ln2
„MH
100 GeV
«
+0.543
„mt
175 GeV
«2
− 1
!− 0.517
∆α
(5)had(MZ)
0.0280− 1
!− 0.085
„αs(MZ)
0.118− 1
«
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 29
pp → (H → γγ)X: resummation for signal and backgroundwith Balazs, Berger, Yuan; PLB 635, 235 (2006); PRD 76, 013008 & 013009 (2007)
8000
6000
4000
2000
080 100 120 140
Q = Mγγ (GeV)
Higgs signal
Eve
nts
/ 500
MeV
for
105
pb-
1
D_D
_105
5c
CMS, 105 pb-1
Signal and background in H → γγ
¥ To find the narrow Higgsresonance, it is useful tounderstand differences betweenfully differential distributions of theHiggs signal and large QCDbackground
¥ resummation is needed forlogarithmic corrections of severaltypes from all orders in αs
I e.g., αns lnk(QT /Q) at QT ¿ Q
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 30
NNLL/NLO distributions for Higgs → γγ signal andbackground (ResBos, normalized; MH = 130 GeV, 128 < Q < 132 GeV)
QT andyγ1 − yγ2 in thelab frame
Decay anglesθ∗, ϕ∗ in theγγ rest frame
no singularities,in contrast tothe fixed-orderrate
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
pp → γγX, √S = 14 TeV
cos(θ*)
dσ/d
cos(
θ* )/σ
Signal
Background
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
-3 -2 -1 0 1 2 3
pp → HX → γγX, √S = 14 TeV
yhard - ysoft
σ-1 d
σ/d∆
y
Signal
Background
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 0.5 1 1.5 2 2.5 3
pp → γγX, √S = 14 TeV
φ* (rad)
dσ/d
φ* /σ (1
/rad)
Signal
Background
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 31
Transverse energy distribution in H → γγ
¥ A typical γγ pair recoilsagainst many mini-jets with small~kTi, rather than against a fewjets with large ~kTi
¥ leading mini-jet contributionsmust be summed to all orders inαs to obtain reliable predictions
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 32
Overview of the resummation procedure
pp_ → γγX, √S = 1.96 TeV
QT (GeV)
dσ/d
QT (
pb/G
eV)
Finite-order (NLO)CDF, 207 pb-1
10-1
1
0 5 10 15 20 25 30 35 40
Q2T ∼ Q2
jHj2f(x2; Q)
f(x1; Q)
Collinear factorization at NLO;unstable at Q2
T ¿ Q2
dσ
dQ2dydQ2T
=∑
partons
∫dx1dx2fa(x1, Q)fb(x2, Q) |H(ab → V )|2
(dσ
dQ2T
)
Q2T¿Q2
≈∞∑
k=0
αks
[ckδ( ~QT ) + Q−2
T ·2k−1∑
n=0
dnk lnn(Q2/Q2T )
]
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 33
Overview of the resummation procedure
pp_ → γγX, √S = 1.96 TeV
QT (GeV)
dσ/d
QT (
pb/G
eV)
Resummed (NNLL)Finite-order (NLO)CDF, 207 pb-1
10-1
1
0 5 10 15 20 25 30 35 40
Q2T ¿ Q2
P(x2; ~kT2)
P(x1; ~kT1)S HH�
Factorization in terms of a soft factor S,~kT -dependent PDF’s Pa, and LO hardvertex HLO
ab
dσ
dQ2dydQ2T
=∑
partons
∣∣HLOab
∣∣2∫
d~kTsd~kT1d~kT2δ[~QT − ~kTs − ~kT1 − ~kT2
]
× S(~kTs, Q)Pa(x1,~kT1)Pb(x2,~kT2)
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 33
Overview of the resummation procedure
pp_ → γγX, √S = 1.96 TeV
QT (GeV)
dσ/d
QT (
pb/G
eV)
Resummed (NNLL)Finite-order (NLO)CDF, 207 pb-1
10-1
1
0 5 10 15 20 25 30 35 40
Q2T . Q2
P(x2; ~kT2)
P(x1; ~kT1)S HH� jHj2
f(x2; Q)
f(x1; Q)
P(x2; ~kT2)
P(x1; ~kT1)S HH�
NLO
+ −
Add small-QT and large-QT
X-sections, subtract the overlap
We include large-QT Xsection at NLO, resummed perturbativecoefficients up to three loops (NNLL)
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 33
Resummation for gg + gq → γγX at O(α3s)
1-loop 2 → 3 diagrams
¥ obtained in the helicity amplitude formalism(Bern, Dixon, Kosower)
¥ checked against the “sector decomposition”calculation (Binoth, Guillet, Mahmoudi, 2003)
¥ soft and collinear limits derived in the splittingamplitude method (Bern, Chalmers, Dixon, Dunbar, Kosower;...)
¥ resummed to all orders in αs
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 34
MW measurement at hadron colliders
¥ The Tevatron (LHC) collaborations intend to measure MW
with accuracy 15 MeV (5 MeV)
¥ Several theoretical factors contribute at this level ofaccuracy
I NNLO QCD+NLO EW perturbative contributions
I PDF dependencewith Lai, Pumplin,Tung
I small-pT resummationwith Brock, Konychev, Landry, Yuan
I small-x effectswith Berge, Olness, Yuan
I dependence on mc,bwith Berge, Olness
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 35
Small-x broadening of QT distributions
Complicated small-x dynamics may result in harder QTdistributions at the LHC than predicted by conventional CSSresummation (Berge, PN, Olness, Yuan, 2004)
⇒ Consequences for MW measurement
pp → Z0 X → e+e− X (√ S = 14 TeV)
0
10
20
30
40
50
0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25
qT [GeV]
dσ/d
q T [
pb/G
eV]
| ye | < 2.5pTe > 25 GeV
ρ(x) = 0ρ(x) ≠ 0, c0 = 0.013, x0 = 0.005
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 36
Small-x broadening of QT distributions
New D0 measurements in pp → (γ∗, Z)X (arXiv:0712.0803) provide firstconstraints on the magnitude of small-x broadening
All Z rapidities
(GeV/c)T
* qγZ/0 5 10 15 20 25 30
-1 (
GeV
/c)
T/d
qσ
d× σ1/
0.02
0.04
0.06
0.08 ResBos
DØ data
DØ, 0.98 fb-1
(a)
|yZ | > 2
(GeV/c)T
* qγZ/0 5 10 15 20 25 30
-1 (
GeV
/c)
T/d
qσ
d× σ1/
0.02
0.04
0.06
0.08
0.1|y|>2
ResBos with small-x effectResBos without small-x effectDØ data
DØ, 0.98 fb-1
(b)
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 36
Correlations between PDF’s and nonperturbativepT function (Lai, P.N., Pumplin, Tung, Yuan, in progress)
The PDF dependence of the power-suppressed resummedcontribution to dσ/dQT is analyzed in a combined PDF+pT fit;leads to a somewhat larger MW value extracted from the data
MW/2
10 20 30 40 50 60pT
e HGeVL
10
20
30
40
50
60
dΣ
����������������
dp
TeH
pb
���������������
Ge
VL
pp-
®HW+®e+ΝeLX,�!!!
s=1.96 TeV, NNLL�NLO, MW=80.423 GeV
PDF+PT fitKN1, CT6.5MKN1, CT6.1M
PRELIMINARY
25 30 35 40 45 50pT
e HGeVL
0.98
0.99
1
1.01
1.02
Fra
ctio
na
ld
iffe
ren
ce
inth
esh
ap
e
pp-
®HW+®e+ΝeLX,�!!!
s=1.96 TeV, NNLL�NLO, MW=80.423 GeV
PDF+PT fitKN1, CT6.5MKN1, CT6.1MPDF+PT fit ;MW±50 MeV
PRELIMINARY
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 37
Conclusions
¥ It is exciting to explore rich global connections between theLHC cross sections and diverse domains of the StandardModel
I to calibrate the LHC detectors, monitor LHC luminosity
I to explore new forms of QCD factorization (resummations)and merge them with important EW contributions
I to precisely test the Standard Model, understand the EWSBmechanism
I to impose limits on new physics parameters using hadroncollider data
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 38
Compact Muon Solenoid as seen by BBC
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 39
Compact Muon Solenoid as seen by BBC
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 39
Compact Muon Solenoid as seen by BBC
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 39
Compact Muon Solenoid as seen by BBC
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 39
Credibility of LHC discoveries must be supported by dependablenumerical tools implementing a realistic theoretical framework
The phenomenological “Q Branch” that develops this frameworkwill be in a high demand for a long time
Ì
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 40
Backup slides
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 41
Tolerance hypersphere in the PDF space
(a)
Original parameter basis
(b)
Orthonormal eigenvector basis
zk
Tdiagonalization and
rescaling by
the iterative method
ul
ai
2-dim (i,j) rendition of N-dim (22) PDF parameter space
Hessian eigenvector basis sets
ajul
p(i)
s0s0
contours of constant c2global
ul: eigenvector in the l-direction
p(i): point of largest ai with tolerance T
s0: global minimump(i)
zl
A hyperellipse ∆χ2 ≤ T 2 in space of N physical PDF parameters{ai} is mapped onto a hypersphere of radius T in space of Northonormal PDF parameters {zi}
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 42
Tolerance hypersphere in the PDF space
(b)
Orthonormal eigenvector basis
2-dim (i,j) rendition of N-dim (22) PDF parameter space
~∇X
~zm
PDF error for a physical observable X is given by
∆X = ~∇X · ~zm =∣∣∣~∇X
∣∣∣ = 12
√∑Ni=1
(X
(+)i −X
(−)i
)2
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 42
Tolerance hypersphere in the PDF space
(b)
Orthonormal eigenvector basis
2-dim (i,j) rendition of N-dim (22) PDF parameter space
~∇X
~∇Y
ϕ
Correlation cosine for observables X and Y :
cosϕ =~∇X·~∇Y∆X∆Y = 1
4∆X ∆Y
∑Ni=1
(X
(+)i −X
(−)i
)(Y
(+)i − Y
(−)i
)
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 42
tt production as a standard candle process
Uncertainties in σtt for mt = 171 GeV
Type Current Projected Assumptions
Scale 11% ∼ 3− 5%? mt/2 ≤ µ ≤ 2mt
dependence (NLO) (NNLO+resum.)PDF 2% 1%? 1σ c.l.
dependencemt 5% < 3%
dependence δmt = 2 GeV δmt = 1 GeV
Total (theory) 12% ∼ 5%
Experiment 8% (CDF) 5%?
Measurements of σtt with accuracy ∼ 5% may be within reach;useful for monitoring of LLHC in the first years, normalization ofcross sections sensitive to large-x glue scattering
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 43
Z, W , tt cross sections and correlations
Table: Total cross sections σ, PDF-induced errors ∆σ, and correlationcosines cos ϕ for Z0, W±, and tt production at the Tevatron Run-2 (Tev2)and LHC, computed with CTEQ6.6 PDFs.
√s Scattering σ, ∆σ Correlation cos ϕ with
(TeV) process (pb) Z0 (Tev2) W±(Tev2) Z0 (LHC) W± (LHC)
pp → (Z0 → `+`−)X 241(8) 1 0.987 0.23 0.33
1.96 pp → (W± → `ν`)X 2560(40) 0.987 1 0.27 0.37
pp → ttX 7.2(5) -0.03 -0.09 -0.52 -0.52
pp → (Z0 → `+`−)X 2080(70) 0.23 0.27 1 0.956
pp → (W± → `ν)X 20880(740) 0.33 0.37 0.956 1
14 pp → (W + → `+ν`)X 12070(410) 0.32 0.36 0.928 0.988
pp → (W− → `−ν`)X 8810(330) 0.33 0.38 0.960 0.981
pp → ttX 860(30) -0.14 -0.13 -0.80 -0.74
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 44
Correlations with single-top cross sections
Table: Correlation cosines cosϕ between single-top, W, Z, and tt crosssections at the Tevatron Run-2 (Tev2) and LHC, computed withCTEQ6.6 PDFs.
Single-top Correlation cos ϕ with
production channel Z0 (Tev2) W±(Tev2) tt (Tev2) Z0 (LHC) W± (LHC) tt (LHC)
t−channel (Tev2) -0.18 -0.22 0.81 -0.82 -0.79 0.56
t−channel (LHC) 0.09 0.14 -0.64 0.56 0.53 -0.42
s−channel (Tev2) 0.83 0.79 0.18 0.22 0.27 -0.3
s−channel (LHC) 0.81 0.85 -0.42 0.6 0.68 -0.33
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 45
Correlations and ratio of W and Z cross sections
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
CTEQ6.1
NNLL-NLO ResBos
Free s=s-
HsolidL,
fixed s=s-
HdashesL
A. Cooper-Sarkar, 2007
σ(Z)/(σ(W+) + σ(W-))
PDF error band
Radiative contributions, PDF dependence have similar structurein W, Z, and alike cross sections; cancel well in Xsection ratios
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 46
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 remaining PDF uncertainty in σZ/σW is mostly driven by s(x);increases by a factor of 3 compared to CTEQ6.1 as a result offree strangeness in CTEQ6.6
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 47
σ(W+)/σ(W−)
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
ΣW+ �ΣW- at the LHC
uVHx,Q=85. GeVLdVHx,Q=85. GeVL
σ(W+)/σ(W−) = 1.36 + 0.016 (CTEQ6.6), 1.36 (MSTW’06NNLO),1.35 (MRST’04NLO)
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 48
An example of a small correlation with the gluon
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
CTEQ6.6: correlation between Σtot and fHx,Q=85. GeVL
d-
u-
gudscb
pp®t± X Hs-channelL�!!!!
s=14 TeV, mt=171 GeV
Single-top production (NLO)
Wb
tq
q′
¥ typical x ∼ 0.01
¥ mostly correlated with u, dPDF’s
PDF uncertainties in W, Z total cross sections are irrelevant forsome quark scattering processes (single-top, Z ′, ...)
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 49
cos ϕ for various NLO Higgs productioncross sections in SM and MSSM
Particle mass (GeV)100 150 200 250 300 350 400 450 500
Cor
rela
tion
cosi
ne
−1
−0.5
0
0.5
1sc + bc → h+LHC X-se tion:Correlation with pp → ZX (solid), pp → tt (dashes), pp → ZX (dots)
gg → h0 bb → h0 W+h0 h0 via WW fusiont- hannel single top:Z
tt : Z
W+ : W− : Z
Z (Tev-2): Z (LHC)t- hannel single top: tt
Pavel Nadolsky (MSU) Southern Methodist University March 3, 2008 50
top related