from partons to new physics at the cern large hadron collider€¦ · at the cern large hadron...

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


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


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





Factorization


Globalanalysis

Small−xeffects









Resummations



Partondistributions

(PDFs)




Hard scattering:

Universality


Global interconnections can be as important as (N)NLOperturbative contributions; are different at the LHC and Tevatron








Hard scattering:

Universality




Partondistributions

(PDFs)

Globalanalysis




Factorization


Small−xeffects


Resummations





Global interconnections can be as important as (N)NLOperturbative contributions; are different at the LHC and Tevatron


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)


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


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


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%


“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%


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


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


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.


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)


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



a+ia−

i aiai0

∆χ2

χ20

χ2

¥ Establish a confidenceregion for {ai} for a giventolerated increase in χ2



ai

χ2

Pitfalls to avoid

¥ “Landscape”

I disagreements betweenthe experiments



ai

χ2 Pitfalls to avoid

¥ Flat directions

I unconstrainedcombinations of PDFparameters

I dependence on the PDFparametrization, freetheoretical parameters(factorization scale, etc.)



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



χ2

ai



0


0 (mini-landscape)


The likelihood is approximately described by a quadratic χ2 witha revised tolerance condition ∆χ2 ≤ T 2



∆χ2

ai0 a+ia−

i

χ2

ai



0


0 (mini-landscape)


The likelihood is approximately described by a quadratic χ2 witha revised tolerance condition ∆χ2 ≤ T 2


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


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


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


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


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


-1 -0.5 0 0.5 1

Cos j

Can you explain why the gluon correlation pattern looks sodifferent?



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


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


-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



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


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


-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


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


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


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 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


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


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


-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


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


Gluons at Q = 85 GeV arecorrelated with gluons atQ = 2 GeV and larger xbecause of DGLAP evolution


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


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


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


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


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


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


Correlations between σ(gg → H0), σZ , σtt


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


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)


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!


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

«


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


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


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


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 )

]



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)



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)


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


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


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


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)


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


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


Compact Muon Solenoid as seen by BBC


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


Backup slides


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}



(b)



~∇X

~zm

PDF error for a physical observable X is given by

∆X = ~∇X · ~zm =∣∣∣~∇X

∣∣∣ = 12

√∑Ni=1

(X

(+)i −X

(−)i

)2



(b)



~∇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

)


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


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


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


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


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


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)


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


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 ′, ...)


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


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