QCD:
from the Tevatron to the LHC
James Stirling
IPPP, University of Durham
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Overview
Perturbative QCD – precision physics
‘Forward’ (non-perturbative) processes
Summary
Scattering processes at high energy
hadron colliders can be classified as
either HARD or SOFT
Quantum Chromodynamics (QCD) is
the underlying theory for all such
processes, but the approach (and the
level of understanding) is very different
for the two cases
For HARD processes, e.g. W or highET jet production, the rates and event
properties can be predicted with some
precision using perturbation theory
Calculate,
& Test
For SOFT processes,
e.g. thePredict
total
cross section or diffractive processes,
the rates and properties are dominated
by non-perturbative QCD effects, which
are much less well understood
Model, Fit, Extrapolate
& Pray!
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the QCD factorization theorem for hard-scattering
(short-distance) inclusive processes
where X=W, Z, H, high-ET jets, SUSY sparticles, black hole, …, and Q
is the ‘hard scale’ (e.g. = MX), usually F = R = Q, and ^ is known …
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to some fixed order in pQCD and EWpt, e.g.
P
•
or in some leading logarithm approximation antiproton
(LL, NLL, …) to all orders via resummation
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jet
x1P
x2P
P
proton
jet
3
momentum fractions x1 and x2
determined by mass and rapidity
of X
x dependence of fi(x,Q2)
determined by ‘global fit’ (MRST,
CTEQ, …) to deep inelastic
scattering (H1, ZEUS, …) data*,
Q2 dependence determined by
DGLAP equations:
DGLAP evolution
* F2(x,Q2) = q eq2 x q(x,Q2) etc
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examples of ‘precision’ phenomenology
jet production
W, Z production
NNLO QCD
NLO QCD
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what limits the precision of the predictions?
3.6
3.4
• the order of the
W
3.2
Tevatron
(Run 2)
Z(x10)
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(nb)
2.4
NNLO
NLO
2.6
CDF D0(e) D0()
CDF D0(e) D0()
2.2
2.0
LO
1.8
1.6
24
23
W
LHC
Z(x10)
22
21
 . Bl (nb)
perturbative expansion
• the uncertainty in the
input parton distribution
functions
• example: σ(Z) @ LHC
σpdf  ±3%, σpt  ± 2%
→
σtheory  ± 4%
whereas for gg→H :
σpdf << σpt
2.8
 . Bl
3.0
20
NLO
NNLO
19
18
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16
15
14
LO
4% total error
(MRST 2002)
partons: MRST2002
NNLO evolution: van Neerven, Vogt approximation to Vermaseren et al. moments
NNLO W,Z corrections: van Neerven et al. with Harlander, Kilgore corrections
6
not all NLO corrections are known!
the more external
coloured particles,
the more difficult
the NLO pQCD
calculation
Example:
pp →ttbb + X
bkgd. to ttH
t
t
b
b
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Nikitenko, Binn 2003
7
John Campbell, Collider Physics Workshop, KITP, January 2004
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NNLO: the perturbative frontier
The NNLO coefficient C is not
yet known, the curves show
guesses C=0 (solid), C=±B2/A
(dashed) → the scale
dependence and hence  σth
is significantly reduced
Tevatron jet inclusive cross section at ET = 100 GeV
Other advantages of NNLO:
• better matching of partons
hadrons
• reduced power corrections
• better description of final
state kinematics (e.g.
transverse momentum)
Glover
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jets at NNLO
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2 loop, 2 parton final state
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| 1 loop |2, 2 parton final state
• 1 loop, 3 parton final states
or 2 +1 final state
•

soft, collinear
tree, 4 parton final states
or 3 + 1 parton final states
or 2 + 2 parton final state
rapid progress in last two years [many authors]
• many 2→2 scattering processes with up to one off-shell leg now calculated
at two loops
• … to be combined with the tree-level 2→4, the one-loop 2→3 and the selfinterference of the one-loop 2→2 to yield physical NNLO cross sections
• this is still some way away but lots of ideas so expect progress soon!
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summary of NNLO calculations
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p + p → jet + X *; in progress, see previous
p + p → γ + X; in principle, subset of the jet calculation
but issues regarding photon fragmentation, isolation etc
p + p → QQbar + X; requires extension of above to nonzero fermion masses
p + p → (γ*, W, Z) + X *; van Neerven et al, Harlander and
Kilgore corrected (2002)
p + p → (γ*, W, Z) + X differential rapidity distribution *;
Anastasiou, Dixon, Melnikov (2003)
p + p → H + X; Harlander and Kilgore, Anastasiou and Melnikov
(2002-3)
Note: knowledge of processes * needed for a full NNLO
global parton distribution fit
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interfacing NnLO and parton showers
+
Benefits of both:
NnLO
correct overall rate, hard scattering
kinematics, reduced scale, dependence, …
PS
complete event picture, correct treatment of
collinear logarithms to all orders, …
→ see talk by Bryan Webber
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HO corrections to Higgs cross section
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•
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the HO pQCD corrections
to (gg→H) are large (more
diagrams, more colour)
can improve NNLO
precision slightly by
resumming additional
soft/collinear higher-order
logarithms
example: σ(MH=120 GeV)
@ LHC
g
t
g
H
Catani et al,
hep-ph/0306211
σpdf  ±3%, σptNNL0  ± 10%,
σptNNLL  ± 8%,
→
σtheory  ± 9%
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top quark production
awaits full NNLO pQCD calculation;
NNLO & NnLL “soft+virtual”
approximations exist (Cacciari et al,
Kidonakis et al), probably OK for
Tevatron at ~ 10% level (> σpdf )
Tevatron
NNLO(S+V)
NLO
… but such approximations
work less well at LHC energies
LO
Kidonakis and Vogt, hep-ph/0308222
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HEPCODE: a
comprehensive list of
publicly available
cross-section codes
for high-energy
collider processes,
with links to source or
contact person
www.ippp.dur.ac.uk/HEPCODE/
•
Different code types, e.g.:
– tree-level generic (e.g. MADEVENT)
– NLO in QCD for specific processes
–
–
(e.g. MCFM)
fixed-order/PS hybrids (e.g. MC@NLO)
parton shower (e.g. HERWIG)
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pdfs from global fits
Formalism
NLO DGLAP
MSbar factorisation
Q0 2
functional form @ Q02
sea quark (a)symmetry
etc.
Data
DIS (SLAC, BCDMS, NMC, E665,
CCFR, H1, ZEUS, … )
Drell-Yan (E605, E772, E866, …)
High ET jets (CDF, D0)
W rapidity asymmetry (CDF)
N dimuon (CCFR, NuTeV)
etc.
fi (x,Q2)   fi (x,Q2)
αS(MZ )
Who?
Alekhin, CTEQ, MRST,
GKK, Botje, H1, ZEUS,
GRV, BFP, …
http://durpdg.dur.ac.uk/hepdata/pdf.html
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(MRST) parton distributions in the proton
1.2
up
down
antiup
antidown
strange
charm
gluon
MRST2001
1.0
2
2
Q = 10 GeV
2
x f(x,Q )
0.8
0.6
0.4
0.2
0.0
10
-3
10
-2
10
x
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-1
10
0
Martin, Roberts, S, Thorne
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uncertainty in gluon distribution (CTEQ)
then fg → σgg→X etc.
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pdf uncertainties
encoded in parton-parton
luminosity functions:
with  = M2/s, so that for
ab→X
solid = LHC
dashed = Tevatron
Alekhin 2002
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Tevatron parton kinematics
LHC parton kinematics
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10
10
x1,2 = (M/1.96 TeV) exp(y)
Q=M
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10
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10
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M = 1 TeV
10
6
5
2
Q (GeV )
10
4
M = 100 GeV
10
M = 1 TeV
10
longer Q2
extrapolation
5
10
4
M = 100 GeV
10
2
2
2
M = 10 TeV
7
10
Q (GeV )
x1,2 = (M/14 TeV) exp(y)
Q=M
3
3
10
10
y=
2
10
2
4
0
2
4
y=
M = 10 GeV
10
1
fixed
target
HERA
10
1
10
0
10
-7
10
6
4
2
0
2
4
6
2
M = 10 GeV
smaller x
fixed
target
HERA
0
10
-6
-5
10
10
-4
-3
10
10
-2
10
-1
10
0
x
10
-7
10
10
-6
10
-5
-4
10
10
-3
10
-2
-1
10
0
10
x
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Higgs cross section: dependence on pdfs
Djouadi & Ferrag, hep-ph/0310209
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Djouadi & Ferrag, hep-ph/0310209
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the differences between pdf sets
needs to be better understood!
Djouadi & Ferrag, hep-ph/0310209
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why do ‘best fit’ pdfs and errors differ?
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different data sets in fit
•
different choice of
– different subselection of data
– different treatment of exp. sys. errors
– tolerance to define   fi (CTEQ: Δχ2=100, Alekhin: Δχ2=1)
– factorisation/renormalisation scheme/scale
– Q0 2
– parametric form Axa(1-x)b[..] etc
– αS
– treatment of heavy flavours
– theoretical assumptions about x→0,1 behaviour
– theoretical assumptions about sea flavour symmetry
– evolution and cross section codes (removable differences!)
→ see ongoing HERA-LHC Workshop PDF Working Group
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resummation
Z
Kulesza
Sterman
Vogelsang
Work continues to refine the
predictions for ‘Sudakov’
processes, e.g. for the Higgs or
Z transverse momentum
distribution, where
resummation of large
logarithms of the form
qT (GeV)
n,m αSn log(M2/qT2)m
Bozzi
Catani
de Florian
Grazzini
is necessary at small qT, to be
matched with fixed-order QCD
at large qT
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•
comparison of
resummed / fixed-order
calculations for Higgs (MH
= 125 GeV) qT distribution
at LHC
Balazs et al, hep-ph/0403052
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differences due mainly
to different NnLO and
NnLL contributions
included
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Tevatron d(Z)/dqT
provides good test of
calculations
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αS measurements at hadron colliders
• in principle, from an absolute cross section
measurement…
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•
  αSn
but problems with exp. normalisation
uncertainties, pdf uncertainties, etc.
or from a relative rate of jet production
(X + jet) / (X)  αS
but problems with jet energy measurement, noncancellation of pdfs, etc.
or, equivalently, from ‘shape variables’ (cf. thrust
in e+e-)
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S. Bethke
inclusive b
cross section
UA1, 1996
hadron collider
measurements
prompt photon
production
UA6, 1996
{
inclusive jet
cross section
CDF, 2002
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D0 (1997): R10= (W + 1 jet) / (W + 0 jet)
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BFKL at hadron colliders
Andersen, WJS
Production of jet pairs with equal
and opposite large rapidity
(‘Mueller-Navelet’ jets) as a test
of QCD BFKL physics
cf. F2 ~ x as x →0 at HERA
many tests:
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y dependence, azimuthal
angle decorrelation,
accompanying minjets etc
jet
jet
• replace forward jets by forward
W, b-quarks etc
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forward physics
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‘classical’ forward physics – σtot , σel , σSD, σDD, etc – a challenge for
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non-perturbative QCD models. Vast amount of low-energy data (ISR,
Tevatron, …) to test and refine such models
output → deeper understanding of QCD, precision luminosity
measurement (from optical theorem L ~ Ntot2/Nel)
‘new’ forward physics – a potentially important tool for precision QCD
and New Physics Studies at Tevatron and LHC
p + p → p  X  p or p + p → M  X  M
where  = rapidity gap = hadron-free zone, and X = χc, H, tt, SUSY
particles, etc etc
advantages? good MX resolution from Mmiss (~ 1 GeV?) (CMS-TOTEM)
disadvantages? low event rate – the price to pay for gaps to survive the
‘hostile QCD environment’
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‘rapidity gap’ collision events
Typical event
D
Hard single diffraction
Hard double pomeron
Hard color singlet
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For example: Higgs at LHC (Khoze, Martin,
Ryskin hep-ph/0210094)
couples
to gluons
MH = 120 GeV, L = 30 fb-1 , Mmiss = 1 GeV
 Nsig = 11, Nbkgd = 4

3σ effect ?!
selection
rules
Note: calibration possible via X = quarkonia
or large ET jet pair
new
Observation of
p + p → p + χ0c (→J/ γ) + p
by CDF?
QCD challenge: to refine and
test such models & elevate to
precision predictions!
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summary
‘QCD at hadron colliders’ means …
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•
•
performing precision calculations (LO→NLO→NNLO ) for
signals and backgrounds, cross sections and distributions –
still much work to do! (cf. EWPT @ LEP)
refining event simulation tools (e.g. PS+NLO)
extending the calculational frontiers, e.g. to hard +
diffractive/forward processes, multiple scattering, particle
distributions and correlations etc. etc.
particularly important and interesting is p + p → p  X  p
– challenge for experiment and theory
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extra slides
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pdfs at LHC
• high precision (SM and BSM) cross
section predictions require precision pdfs:
th = pdf + …
• ‘standard candle’ processes (e.g. Z) to
– check formalism
– measure machine luminosity?
• learning more about pdfs from LHC
measurements (e.g. high-ET jets → gluon,
W+/W– → sea quarks)
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Full 3-loop (NNLO) non-singlet DGLAP splitting function!
new
Moch, Vermaseren and Vogt, hep-ph/0403192
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•
MRST: Q02 = 1 GeV2, Qcut2 =
2 GeV2
xg = Axa(1–x)b(1+Cx0.5+Dx)
– Exc(1-x)d
•
CTEQ6: Q02 = 1.69 GeV2,
Qcut2 = 4 GeV2
xg = Axa(1–x)becx(1+Cx)d
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tensions within the global fit?
2.00
1.75
systematic error
1.50
1.25

systematic error
1.00

2
Experiment A
0.75
0.50
0.25
0.00
Experiment B
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14
measurement #

•
with dataset A in fit, Δχ2=1 ; with A and B in fit, Δχ2=?
•
‘tensions’ between data sets arise, for example,
– between DIS data sets (e.g. H and N data)
– when jet and Drell-Yan data are combined with DIS data
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CTEQ αS(MZ) values from global analysis with Δχ2 = 1, 100
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as small x data are systematically removed from the MRST
global fit, the quality of the fit improves until stability is
reached at around x ~ 0.005 (MRST hep-ph/0308087)
Q. Is fixed–order DGLAP insufficient for small-x DIS data?!
Δ = improvement in χ2 to remaining data / # of data points removed
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the stability of the small-x fit can be
recovered by adding to the fit empirical
contributions of the form
... with coefficients A, B found to be O(1)
(and different for the NLO, NNLO fits);
the starting gluon is still very negative at
small x however
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extrapolation errors
8
7
6
5
f(x)
4
3
2
1
0
-1
-2
-3
-4
0.01
0.1
1
x
theoretical insight/guess:
f ~ A x as x → 0
theoretical insight/guess:
f ~ ± A x–0.5 as x → 0
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differences between
the MRST and
Alekhin u and d sea
quarks near the
starting scale
ubar=dbar
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3.4
W
3.2
Tevatron
(Run 2)
Z(x10)
(nb)
3.0
2.8
 . Bl
σ(W) and σ(Z) :
precision predictions
and measurements at
the LHC
3.6
2.4
NNLO
NLO
2.6
CDF D0(e) D0()
CDF D0(e) D0()
2.2
2.0
LO
1.8
1.6
24
MRST2002
204 ± 4 (expt)
CTEQ6
205 ± 8 (expt)
Alekhin02
215 ± 6 (tot)
W
LHC
Z(x10)
22
21
 . Bl (nb)
σNLO(W) (nb)
LHC
23
20
NLO
NNLO
19
18
17
LO
16
15
similar partons
different partons
different Δχ2
14
4% total error
(MRST 2002)
partons: MRST2002
NNLO evolution: van Neerven, Vogt approximation to Vermaseren et al. moments
NNLO W,Z corrections: van Neerven et al. with Harlander, Kilgore corrections
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ratio of W– and W+ rapidity distributions
dû(Wà )
dû(W+ )
=
d(x 1)u
ö(x 2)+ :::
u(x 1)dö(x 2)+ :::
1.0
x1=0.006
x2=0.006
x1=0.52
x2=0.000064
0.6
0.4
-
(note: MRST error = ±1½%)
+
–
ratio close to 1 because u  u etc.
d(W )/dy / d(W )/dy
0.8
sensitive to large-x d/u
––
and small x u/d ratios
0.2
MRST2002NLO
ALEKHIN02NLO
0.0
0
1
Q. What is the experimental precision?
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3
4
5
6
yW
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Note: CTEQ gluon ‘more
or less’ consistent with
MRST gluon
Note: high-x gluon should
become better determined
from Run 2 Tevatron data
Q. by how much?
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