Jet production at low Bjorken-x from HERA

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?


y=1

(HERA √s

=320

GeV

)

x

Q2 (

GeV

2 )




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




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?)


y=1

(HERA √s

=320

GeV

)

x

Q2 (

GeV

2 )




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





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


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(


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


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


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


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


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


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


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


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



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

Documents

Jet production at low Bjorken-x from HERA