Hard Probes 2008
Illa de A Toxa, Spain, June 8-14, 2008
Jet production at low Bjorken-x from HERA
S. Levonian
• HERA and low x physics
• Inclusive Forward jets
• Forward jets in multijet configurations
• Azimuthal correlations in dijet system
Low x ≤ 5 · 10−3
2 The HERA Collider
Days of running
H1
Inte
grat
ed L
umin
osity
/ p
b-1
Status: 1-July-2007
0 500 1000 15000
100
200
300
400electronspositronslow E
HERA-1
HERA-2
• HERA upgrade: L × 3, Polarised e+/e−
(Exp. improvements: silicon trackers, triggering, ...)
• Final Data samples H1+ZEUS: 2 × 0.5 fb−1
HERA-1 (1993-2000) ≃ 120 pb−1
HERA-2 (2003-2007) ≃ 380 pb−1
last 3 months - low Ep run to measure F p
L
(Ep = 460; 575 GeV, L = 20pb−1)
3 Small x domain of HERA
y=1
(HERA √s
=320
GeV
)
x
Q2 (
GeV
2 )
Fixed Target Experiments
D0 Inclusive jets η<3
CDF/D0 Inclusive jets η<0.7
ZEUS
H1
10-1
1
10
10 2
10 3
10 4
10 5
10-6
10-5
10-4
10-3
10-2
10-1
1
p
e
x
Q2
• ep DIS: clean QCD laboratorywith high resolving power Q2 ⇒ 0.001fm
• Low x ≤ 10−3: new kinematic domain at HERA
⇒ any sign of novel parton dynamics?
4 Small x domain of HERA
y=1
(HERA √s
=320
GeV
)
x
Q2 (
GeV
2 )
Fixed Target Experiments
D0 Inclusive jets η<3
CDF/D0 Inclusive jets η<0.7
ZEUS
H1
10-1
1
10
10 2
10 3
10 4
10 5
10-6
10-5
10-4
10-3
10-2
10-1
1
p
e
x
Q2
• ep DIS: clean QCD laboratorywith high resolving power Q2 ⇒ 0.001fm
• Low x ≤ 10−3: new kinematic domain at HERA
⇒ any sign of novel parton dynamics?
H1 and ZEUS Combined PDF Fit
HE
RA
Str
uctu
re F
unct
ions
Wor
king
Gro
upA
pril
2008
x = 0.000032, i=22x = 0.00005, i=21
x = 0.00008, i=20x = 0.00013, i=19
x = 0.00020, i=18x = 0.00032, i=17
x = 0.0005, i=16
x = 0.0008, i=15x = 0.0013, i=14
x = 0.0020, i=13
x = 0.0032, i=12
x = 0.005, i=11
x = 0.008, i=10
x = 0.013, i=9
x = 0.02, i=8
x = 0.032, i=7
x = 0.05, i=6
x = 0.08, i=5
x = 0.13, i=4
x = 0.18, i=3
x = 0.25, i=2
x = 0.40, i=1
x = 0.65, i=0
Q2/ GeV2
σ r(x,
Q2 )
x 2i
HERA I e+p (prel.)Fixed TargetHERA I PDF (prel.)
10-3
10-2
10-1
1
10
10 2
10 3
10 4
10 5
10 6
10 7
1 10 102
103
104
105
• NLO DGLAP is still perfectly OK for F p2 (too inclusive?)
5 Small x domain of HERA
y=1
(HERA √s
=320
GeV
)
x
Q2 (
GeV
2 )
Fixed Target Experiments
D0 Inclusive jets η<3
CDF/D0 Inclusive jets η<0.7
ZEUS
H1
10-1
1
10
10 2
10 3
10 4
10 5
10-6
10-5
10-4
10-3
10-2
10-1
1
p
e
x
Q2
• ep DIS: clean QCD laboratorywith high resolving power Q2 ⇒ 0.001fm
• Low x ≤ 10−3: new kinematic domain at HERA
⇒ any sign of novel parton dynamics?
H1 and ZEUS Combined PDF Fit
HE
RA
Str
uctu
re F
unct
ions
Wor
king
Gro
upA
pril
2008
x = 0.000032, i=22x = 0.00005, i=21
x = 0.00008, i=20x = 0.00013, i=19
x = 0.00020, i=18x = 0.00032, i=17
x = 0.0005, i=16
x = 0.0008, i=15x = 0.0013, i=14
x = 0.0020, i=13
x = 0.0032, i=12
x = 0.005, i=11
x = 0.008, i=10
x = 0.013, i=9
x = 0.02, i=8
x = 0.032, i=7
x = 0.05, i=6
x = 0.08, i=5
x = 0.13, i=4
x = 0.18, i=3
x = 0.25, i=2
x = 0.40, i=1
x = 0.65, i=0
Q2/ GeV2
σ r(x,
Q2 )
x 2i
HERA I e+p (prel.)Fixed TargetHERA I PDF (prel.)
10-3
10-2
10-1
1
10
10 2
10 3
10 4
10 5
10 6
10 7
1 10 102
103
104
105
• NLO DGLAP is still perfectly OK for F p2 (too inclusive?)
0
0.2
0.4
0.6
0.8
1
-410 -310 -210 -110 10
0.2
0.4
0.6
0.8
1
HERA-I PDF (prel.)
exp. uncert.
model uncert.
x
xf 2 = 10 GeV2Q
vxu
vxd
0.05)×xS (
0.05)×xg (
vxu
vxd
0.05)×xS (
0.05)×xg (
HE
RA
Str
uctu
re F
unct
ions
Wor
king
Gro
upA
pril
2008
H1 and ZEUS Combined PDF Fit
0
0.2
0.4
0.6
0.8
1
• There is a lot of glue in proton at low x!⇒ gluodynamics in high energy limit of QCD (W 2 ≈ Q2/x)
6 QCD at low x
e+
p
e+
γ*
q
q
Q2
x
x0, k⊥ 0
xi, k⊥ i
xi+1, k⊥ i+1
Lots of glue in the proton ⇒ long gluon cascade at low x. Perturbative expansion
of evolution equations ∼∑
mn Amn ln(Q2)m ln(1/x)n hard to calculate explicitely
⇒ approximations needed
DGLAP: resums ln(Q2)n terms, neglecting ln(1/x)n terms
strong kT ordering in partonic cascade
BFKL: resums ln(1/x)n terms
no kT ordering in partonic cascade ⇒ more hard gluons
are radiated far from the hard interaction vertex
CCFM: angular ordered parton emission ⇒
reproduces DGLAP at large x and BFKL at x → 0
• How long is partonic cascade at HERA, at small x?
• Do the ln(1/x)n terms play a major role in parton dynamics as suggested by BFKL?
⇒ Look at (multi)jet final states at low x in different configurations
7 Low x phenomenology
NLO 2-jet NLO 3-jet
, ..., , ...,DISENT, NLOJET++ NLOJET++
Fixed order
QCD calculations
Rapgap Dir Rapgap Res Cascade Lepto (CDM)
DGLAP
DGLAP
DGLAP
CCFM
CDM
LO ME + PS
MC models
kt−ordered gluon radiation angular ordering random walk in kt
(DGLAP) (BFKL like)(DGLAP ⇐⇒ BFKL)
8 Forward jets
xBj
evolution from large
forward jet
x = Ejet
jetEp
Bj (small)x
to small x
(large)p
e e’
γ Strategy
Eventselection
(Ejett )2 ≈ Q2 ⇒ suppress phase space
for DGLAP evolution
large xjet >>xBj ⇒ enhance BFKL evolution
10−4 <x<4·10−3 5 < Q2 < 85GeV2
Ejett >3.5GeV 7o < θjet < 20o
xjet > 0.035 0.5 < (Ejett )2/Q2 < 2
9 Forward jets
xBj
evolution from large
forward jet
x = Ejet
jetEp
Bj (small)x
to small x
(large)p
e e’
γ
H1
E scale uncert
NLO DISENT 1+δHAD0.5µr,f<µr,f<2µr,f
PDF uncert.
LO DISENT1+δHAD
H1 forward jet data
xBj
dσ
/ dx B
j (n
b)
a)
0
500
1000
0.001 0.002 0.003 0.004
H1E. scale uncert.RG-DIR
CDMRG-DIR+RES
H1 forward jet data
xBj
dσ
/ dx B
j (n
b)
c)
0
500
1000
0.001 0.002 0.003 0.004
Strategy
Eventselection
(Ejett )2 ≈ Q2 ⇒ suppress phase space
for DGLAP evolution
large xjet >>xBj ⇒ enhance BFKL evolution
10−4 <x<4·10−3 5 < Q2 < 85GeV2
Ejett >3.5GeV 7o < θjet < 20o
xjet > 0.035 0.5 < (Ejett )2/Q2 < 2
• Huge improvement from
LO to NLO, but still
insufficient at low x
• Resolved γ component in
DGLAP MC helps
(”breaks” kt ordering)
• CDM and RG(d+r) provide
similar description
⇒ inconclusive
10 Forward jets against CCFM Monte Carlo
ZEUS
0
10
20
50 100
Q2 (GeV2)
dσ/d
Q2 (
pb/G
eV2 )
(a)
CASCADE s.1
CASCADE s.2
0
1000
2000
3000
x 10 2
0.0025 0.005
xBjdσ
/dx B
j (pb
)
Energy Scale UncertaintyZEUS 82 pb-1
(b)
1
10
10 2
5 10
(c)
Ejet
T (GeV)
dσ/d
Eje
t T (
pb/G
eV)
0
200
400
600
2 4
(d)
ηjet
dσ/d
ηjet (
pb)
3
• extended forward range
2 < ηjet < 4.3
Ejett > 5GeV, xjet > 0.036
• Jet rate is OK, butshapes of the distributionsare not described
• Clear sensitivity to uPDF
11 Jet multiplicity
5 < Q2 < 80 GeV2
10−4 < x < 10−2
Jets: E∗t,jet > 4 GeV
−1 < η < 2.5
Njet ≥ 3
• Gluon radiation is frequent at low x
• O(α3s) QCD can only predict up to 4 jets
• RG d+r (DGLAP type of MC)
underestimates high jet multiplicities
• CDM (BFKL like MC) is just perfect!
10−2
10−1
1
10
10 2
10 3
10 4
1 2 3 4 5 6
Datacorr. errorO(αs
3)
NJet
dσ/
dNJe
t [pb
]
CDMRG d+r
H1
12 Two and Three Jet production vs NLO QCD
01
Bjx-410×2 -310 -310×2
-1
01
(p
b)
Bj
/dx
σd
310
410
510
610
) < 1T
2E+2/(Q
r2µ1/16 <
jet energy scale uncertainty
-1ZEUS 82 pb
dijets
trijets
had C⊗) s2αNLOjet: O(
had C⊗) s3αNLOjet: O(
theo
ryd
ata
- th
eory
Bjx-410×2 -310 -310×2
-0.2
0
0.2
dije
tσ/
trije
tσ
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
) < 1T
2E+2/(Q
r2µ1/16 <
jet energy scale uncertainty
-1ZEUS 82 pbtri-/dijets
)s2α)/O(s
3αNLOjet: O(
theo
ryd
ata
- th
eory
• NLO QCD is OK in this domain (x > 2·10−4, Ej1t > 7GeV, E
j2(3)t > 5GeV)
⇒ Try even higher jet multiplicities and look for specific jet topologies
13 3-jet samples with different topologies
1 forward jet + 2 central jets
10 3
10 4
10 5
10−4
10−3
Datacorr. errorO(αs
3)O(αs
2)
x
dσ/
dx [p
b] H1
2 forward jets + 1 central jet
10 3
10 4
10 5
10−4
10−3
Datacorr. errorO(αs
3)O(αs
2)
x
dσ/
dx [p
b] H1
Jet Jet
Jet Jet
Jet Jet
Central jets:
−1 < ηjet < 1
Forward jets:
ηfj1 > 1.73
xfj1 > 0.035
ηfj2 > 1
All jets:
E∗t,jet > 4 GeV
• Large deficit at small x for 2-forward jet topology! There O(α3s) calculation is insufficient
14 3- and 4-jet distributions vs LO+PS Monte Carlo
3-jet
4-jet
10−2
10−1
1
10
10 20 30 40 50 60
corr. error Data
corr. errorCDM (norm.)RG d+r (norm.)
H1
p*T1 [GeV]
dσ/
dp* T
1 [p
b⋅ G
eV−1
]
10−3
10−2
10−1
1
10
5 10 15 20 25 30 35 40 45
corr. error Data
corr. errorCDM (norm.)RG d+r (norm.)
H1
p*T1 [GeV]
dσ/
dp* T
1 [p
b⋅ G
eV−1
]
0
50
100
150
−3 −2 −1 0 1 2 3
corr. error Data
corr. errorCDM (norm.)RG d+r (norm.)
H1
η1− η2
dσ/
d(η 1−
η 2) [p
b]
0
5
10
15
20
25
−3 −2 −1 0 1 2 3
corr. error Data
corr. errorCDM (norm.)RG d+r (norm.)
H1H1
η1− η4
dσ/
d(η 1−
η 4) [p
b]
0
100
200
300
400
−1 −0.5 0 0.5 1
corr. error Data
corr. errorCDM (norm.)RG d+r (norm.)
H1
cos θ’
dσ/
dcos
θ’ [p
b]
0
10
20
30
40
50
60
70
−1 −0.5 0 0.5 1
corr. error Data
corr. errorCDM (norm.)RG d+r (norm.)
H1
cos θ’
dσ/
dcos
θ’ [p
b]
• CDM describes well all distributions except high pT tail where it is too hard
• DGLAP MC (RG dir+res) fails both in shapes and normalization (3j×1.55, 4j×2.9)
15 Azimuthal correlations in di-jet system
0 0.5 1 1.5 2 2.5 3-1
0
1
2
|dx
(pb
)H
CM
jet1
,2φ∆
/d|
σ2d
210
310
410
510
610
710 < 0.0003Bj0.00017 < x
theo
ryd
ata
- th
eory
0.5 1 1.5 2 2.5 3
< 0.0005Bj0.0003 < x
|HCM
jet1,2φ ∆|
0.5 1 1.5 2 2.5 3
< 0.001Bj0.0005 < x
) < 1T
2E+2/(Q
r2µ1/16 <
jet energy scaleuncertainty
-1ZEUS 82 pbdijets
had C⊗) s2αNLOjet: O(
had C⊗) s3αNLOjet: O(
Collinear factorisation scheme:
jets are back-to-back at LO, hence
∆Φ∗ < 180o are only possible at higher orders
kt factorisation scheme:
∆Φ∗ < 180o already at LO
Sensitive to details of parton dynamics
ZEUS vs NLO DGLAP
O(α3s) calculations
describes the data
reasonably well
(although with still large
scale uncertainty)
16 Azimuthal correlations vs CCFM
10 2
10 3
10 4
10 5
10 6
10 7 d
2 σ/d
xd|∆
φ| (
pb
)
1.7 10-4 < x < 3 10-4 3 10-4 < x < 5 10-4 5 10-4 < x < 1 10-3
-2
0
2
1 2 3
∆φ
(th
eo-d
at)/
dat
1 2 3
∆φ
1 2 3
∆φ * (n
b/d
eg.)
φ∆dB
j/d
xσ2
d
1
10
210
-410× < 3Bj < x-510× 8H1 data (prel.)
Cascade (A0)
Cascade (J2003)
* (n
b/d
eg.)
φ∆dB
j/d
xσ2
d
1
10
210
0
1
2
* (deg.)φ∆0 20 40 60 80 100 120 140 160 180
MC
/Dat
a
H1 data vs CCFM based MC
• Although Cascade fail to describe the shape
of ∆Φ∗, 2 sets of uPDF (both describing
HERA F2) essentially cover the data
• large sensitivity to uPDF
ZEUS data vs CCFM based MC
• ”collinear approach” (HERWIG) fails
• Cascade based on kt factorisation
describes data much better
17 Implications for LHC predictions
• Large part of LHC phase space
is at low x
• Tevatron is at large x
⇒ SM predictions based on
fixed order calculations and
on DGLAP MC may not work
even if tuned to Tevatron data
• Low x dynamics has to be
implemented
• CDM and Cascade MC after
additional tuning are promissing
tools for LHC
18 Summary
� There is a lot of gluon radiation at small x.Hard gluons are often radiated forward, with large rapidity separation fromhard interaction vertex. This has an important implications for LHC!
� Fixed order QCD predictions based on DGLAP approachgive large improve-ment with every order in αs. Presently available calculations describe basicproperties of multijet production in DIS, however it still fails at lowest x andfor specific configurations with very forward jets.
� Color Dipole Model gives best description of jet production at HERA downto lowest x while models with kt-ordered gluon radiation fail completely.This provides a substantial indication for unordered gluon radiation at smallx as expected from ln(1/x) terms in evolution equations.
� Forward jet data and azimuthal correlations in dijet system show sensitivityto unintegrated PDFsand therefore can be used for their extraction.
BACKUP SLIDES...
20 H1 Forward jets: triple differential cross sections
0
5
10
0
0.5
1
1.5
2
0
0.02
0.04
0.06
0
1
2
0
0.2
0.4
0
0.01
0.02
0
0.05
0.1
0
0.01
0.02
5<Q2<10
12.2
5<p
t2 <35 H1
E scale uncert
1.2<r<7<r>=3.5
a)
NLO DISENT1+δHAD
0.5µr,f<µr,f<2µr,fPDF uncert.
10<Q2<20
0.6<r<3.5<r>=1.8
b)
LO DISENT1+δHAD
20<Q2<85
0.1<r<1.8<r>=0.8
c)
35<p
t2 <95
3.5<r<19<r>=8.1
d)
dσ
/ dxd
Q2 d
pt2
(nb
GeV
-4)
1.8<r<9.5<r>=4.2
e) 0.4<r<4.8<r>=1.8
f)
0.1 0.5 1
95<p
t2 <40
0
9.5<r<80<r>=22.2
g)
xBj × 1030.1 1 2
4.8<r<40<r>=11.3
h)
xBj × 1031 2 3 4
1.1<r<20<r>=4.9
i)
xBj × 103
0
0.001
0.002
21 H1 Forward jets vs NLL BFKL
(C.Royon, DIS-2008) d σ/dx dpT2 d Q2 - H1 DATA
0
2
4
6
8
0.025 0.05 0.075 0.1x 10
-2
5<Q2<10
12.2
5<p T
2 <35
.
x
0
0.2
0.4
0.6
0.8
0.05 0.1 0.15 0.2x 10
-2
10<Q2<20
x
0
0.01
0.02
0.03
0.04
0.05
0.001 0.002 0.003 0.004
20<Q2<85
x
0
0.5
1
1.5
2
0.025 0.05 0.075 0.1x 10
-2
x
35.<
p T2 <
95.
0
0.1
0.2
0.3
0.05 0.1 0.15 0.2x 10
-2
x
0
0.005
0.01
0.015
0.02
0.001 0.002 0.003 0.004x
0
0.05
0.1
0.025 0.05 0.075 0.1x 10
-2
x
95.<
p T2 <
400.
0
0.01
0.02
0.05 0.1 0.15 0.2x 10
-2
x
0
0.05
0.1
0.15
0.2
0.25
x 10-2
0.001 0.002 0.003 0.004x
22 Azimuthal correlations: Data vs NLOJET++
• NLO 3-jet is not in agreement with H1 data
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