Vector Mesons and Deeply Virtual Compton Scattering at HERA€¦ · Deeply Virtual Compton...

$: Vector Mesons and Deeply Virtual Compton Scattering at HERA€¦ · Deeply Virtual Compton Scattering at HERA Niklaus Berger 6th Small x and Diffraction Workshop. Niklaus Berger Vector$
Vector Mesonsand

Deeply Virtual ComptonScatteringat HERA

Niklaus Berger

6th Small x and Diffraction Workshop

Niklaus Berger Vector Mesons and DVCS Small x 2007

2

Overview

• Results on vector meson production: • Trajectory measurements • Comparisons to pQCD models

• Results on Deeply Virtual Compton Scattering

• Conclusion and outlook

t

e e

p p

γ γ*W

Q2

t

e e

p p

γ*

W

Q2

VM


3

Diffractive Vector Meson Production

“Soft” processes well described by Regge Theory (Soft Pomeron) vs.“Hard” processes calculable in pQCD

Hard scale can be set by:• Q2 (electroproduction)● VM mass (J/ψ, ϒ)• t

Soft: Pomeron trajectory Hard: Gluon densities, evolution equations, s-channel helicity non-conservation

t

e e

p p

γ*

W

Q2

VM

P

t

e e

p p

γ*

W

Q2

VM


4

ρ - extracting the pomeron trajectory • ZEUS: measure at large W, in bins of t, combine with OMEGA data at low W• Fit σ ∝ W4(α(t)-1) in each t bin• Large lever arm, but large uncertainty due to relative normalisation ZEUS: Eur.Phys.J. C 14 (2000) 213

• H1: Determine trajectory from a single experiment• Smaller lever arm but NO relative normalistaion uncertainty H1 Preliminary 06-011 (DIS 2006)

W [GeV]

20 30 40 50 60 70 100

]2b/

GeV

µp)

[0 ρ

→p γ

/dt (

σd

-110

1

10

210

H1 PRELIMINARY

Photoproduction0ρElastic ]2-t [GeV

0.010 2.0×,

0.035 1.2×, 0.0690.1230.189

0.26

0.38

0.58

H1 '05 PreliminaryH1 '05 fitZEUS '94ZEUS '94 LPSZEUS '95


5

ρ - pomeron trajectory • ZEUS result:αP(0) = 1.096±0.021α’P = 0.125±0.038 GeV-2

• H1 preliminary result:αP(0) = 1.093±0.003+0.008

α’P = 0.116±0.027+0.036 GeV-2

• Results compatible, half the Donnachie-Landshoff shrinkage

-0.007

-0.046

]2 t [GeV-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 -0.0 0.2

(t)α 0.90

0.95

1.00

1.05

1.10

1.15

1.20

H1 PRELIMINARY

Photoproduction0ρElastic

H1 '05 Preliminary

H1 '05 fitZeus '95Zeus '95 fitDonnachie-Landshoff


6

J/ψ - extracting the pomeron trajectory

● Determine dependence of cross section on W in bins of t

• Fit σ ∝ W4(α(t)-1) in each t bin

• Photo- and electroproduction

H1: Eur.Phys.J. C46 (2006) 585ZEUS: Nucl. Phys. B 695 (2004) 3 (DIS) Eur.Phys.J. C 24 (2002) 345 (γp)

Wγp [GeV]

dσ/

dt(

γp →

J/ψ

p) [

nb

/GeV

2 ]

50 100 300

10

100

1000

⟨|t|⟩[GeV2]

0.03

0.10

0.22

0.43

0.83

⟨Q2⟩ = 0.05 GeV2

FitData

H1

a)

Wγp [GeV]

dσ/

dt(

γp →

J/ψ

p) [

nb

/GeV

2 ]

50 100 200

10

100

⟨|t|⟩

[GeV2]

0.05

0.19

0.64

⟨Q2⟩ = 8.9 GeV2b)


7

J/ψ - pomeron trajectory ● Alternatively: do a 2-D fit• J/ψ harder than predicted by soft pomeron (γp):αP(0) = 1.224±0.010±0.012α’P = 0.164±0.028±0.030 GeV-2

• Significant t dependence in photoproduction: 4σ evidence for shrinkage, but also 2σ below soft pomeron• Electroproduction: compatible with no shrinkageαP(0) = 1.183±0.054±0.030α’P = 0.019±0.139±0.076 GeV-2

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

0 0.2 0.4 0.6 0.8 1 1.2|t| [GeV2]

α(t)

PhotoproductionElectroproduction

1D-Fit 2D-Fit

Soft Pomeron

H1

a)

0.9

1

1.1

1.2

1.3

0 0.5 1 1.5|t| [GeV2]

α(t)

H1ZEUS2D-Fit

⟨Q2⟩ = 0.05 GeV2 H1b)

0.9

1

1.1

1.2

1.3

0 0.5 1 1.5|t| [GeV2]

α(t)

H1ZEUS2D-Fit

⟨Q2⟩ = 8.9 GeV2 H1c)


8

Summary of trajectory measurements

• Intercept rises with scale

• Slope more difficult to measure

• Data consistent with being flat at ~0.13 GeV-2

• Data inconsistent with Donnachie-Landshoff slope of 0.25 GeV-2

[GeV]2 + Q2VMM

2 4 6 8 10 12 14 16 18 20

(0)

α

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

[GeV]2 + Q2VMM

2 4 6 8 10 12 14 16 18 20

]-2

' [G

eVα

-0.2

-0.15

-0.1

-0.05

-0

0.05

0.1

0.15

0.2

0.25

0.3

0ρH1 0ρZEUS

φZEUS

ψH1 J/

ψZEUS J/

DL


9

J/ψ - testing gluon densities? ● High J/ψ mass provides a hard scale - calculable in QCD• Measure cross section as a function of Q2, W, compare to models• Phenomenological fit (Q2+M2)-n

Martin, Ryskin and Teubner: pQCD model based on kT factorisa-tion and a parton-hadron duality ansatz(Phys.Rev.D 62 (2000) 014022)

• Prediction normalised to data - shape comparison can constrain gluon density

σ(γp

→ J

/ψp

) [n

b]

1

10

100

H1ZEUSFit

Wγp= 90 GeV

H1

a)

0

0.5

1

1.5

Q2 [GeV2]

σ /

Fit

0.1 1 10

Fit + fit uncertaintyMRT (MRST02)MRT (CTEQ6M)MRT (ZEUS-S)MRT (H1 QCD Fit)

b)


10

J/ψ - testing gluon densities! ● Even more prominent in W dependence• Normalise predictions at W = 90 GeV, compare shapes• Access to gluon densities in regions poorly constrained by inclusive DIS data (very low x)• Uncertainties on Gluon distributions not taken ito accountTheoretical alternative: Dipole model by Frankfurt, McDermott and Strikman (FMS)(JHEP 0103 (2001) 045)H1: Eur.Phys.J. C46 (2006) 585ZEUS: Nucl. Phys. B 695 (2004) 3 (DIS) Eur.Phys.J. C 24 (2002) 345 (γp)

0

50

100

150

200

50 100 150 200 250 300

Wγp [GeV]

σ(γp

→ J

/ψp

) [n

b]

H1ZEUS

Fit

⟨Q2⟩ = 0.05 GeV2

a)

H1

0

1

2

3

50 100 150 200 250 300Wγp [GeV]

σ /

Fit

Fit + exp. uncertaintyMRT (H1 QCD Fit)FMS (CTEQ4L, λ=4)MRT (ZEUS-S)MRT (CTEQ6M)MRT (MRST02)

b)

H1

0

1

2

3

50 100 150 200 250 300Wγp [GeV]

σ /

Fit

Fit + fit uncertaintyMRT (H1 QCD Fit)FMS (CTEQ4L, λ=4)MRT (ZEUS-S)MRT (CTEQ6M)MRT (MRST02)

b)


11

J/ψ at high t ● ZEUS higher and steeper than H1• BFKL better than DGLAP

ZEUS: Preliminary, Lepton-Photon 2005 (291)H1: Phys.Lett. B 568 (2003), 205

ZEUS

10-2

10-1

1

10

10 2

0 2 4 6 8 10 12 14 16 18 20|t| (GeV2)

dσ(γ

p→J/

ψY

)/d|

t| (n

b/G

eV2 )

ZEUS (prel.) 96-00H1 96-00

BFKL LL (fixed αs)BFKL LL + nonL (fixed αs)BFKL LL + nonL (running αs)DGLAP LL

10-1

1

10

10 2

20 40 60 80 100 120 140 160 180 200W (G eV )

σ(γp

→J/

ψY

) (n

b)

BFKL

(fixed

αs)BFKL

+ nonL

(fixed

αs)

DGLAP LL

|t| (GeV2 )

1-2

2-5

5-10

10-20

x 2

ZEUS (pr el.) 96-00H1 96-00


12

High t ρ0 in photoproduction

Q2 < 0.01 GeV2

75 < W < 95 GeV1.5 < |t| < 20 GeV2

MY < 5 GeV

fits data well

n = 4.26 ± 0.06 + 0.06

• Two gluon models don’t describe data• BFKL model gives reason- able description (G.G. Poludnikowski et al., JHEP 312 (2003) 002)

) 2|t| (GeV1 2 3 4 5 6 7 8 9 10

)-2

/ d|

t| (G

eVσ

dσ1/

-410

-310

-210

-110

1

Yρ e→ep

2 < 0.01 GeV 2Q

75 < W < 95 GeV

< 5 GeV YM

H1

BFKL)sαtwo gluon (fixed

)sαtwo gluon (running +0.08-0.07, n = 4.26

-nA|t|

H1 Collab., A. Aktas et al. Phys. Lett. B 638 (2006) 422

dσ dt

∝ |t|-n

- 0.04


13

High t ρ0: Angular distributions

MesonProduction

LeptonScattering

Meson Decay Plane

Decay in MesonRest Frame

π

π

π

γe

ρ

ρ−

−

+e’

Φθ∗

φ

Plane Plane π+

∗

Look for s-channel helicity NON-conservation (departure from Vector Dominance)

Photoproduction: e escapes through beampipe; only φ* and θ* accessible

*θcos-1 -0.5 0 0.5 1

*θ/d

cos

σ dσ

1/

0

0.2

0.4

0.6

0.8

1

21.5 < |t| < 2.2 GeV

H1 a)

*θcos-1 -0.5 0 0.5 1

*θ/d

cos

σ dσ

1/

0

0.2

0.4

0.6

0.8

1

22.2 < |t| < 3.5 GeV

c)

*θcos-1 -0.5 0 0.5 1

*θ/d

cos

σ dσ

1/

0

0.2

0.4

0.6

0.8

1

23.5 < |t| < 10.0 GeV

e)

* (deg)φ0 100 200 300

)-1

* (d

egφ

/dσ dσ

1/

0

0.001

0.002

0.003

0.004

0.005

21.5 < |t| < 2.2 GeV

Fit SCHC b)

* (deg)φ0 100 200 300

)-1

* (d

egφ

/dσ dσ

1/

0

0.001

0.002

0.003

0.004

0.005

22.2 < |t| < 3.5 GeV

d)

* (deg)φ0 100 200 300

)-1

* (d

egφ

/dσ dσ

1/

0

0.001

0.002

0.003

0.004

0.005

23.5 < |t| < 10.0 GeV

f)


14

High t ρ0: SCH-Non-Conservation Matrix elements 0 for SCHCCompare to 2-gluon and BFKL models

r04 in accordance with SCHC

r04 and Re[r04] violate SCHC

• Two gluon model fails• BFKL based model describes r04, has difficulties with r04 and fails for Re[r04]

) 2|t| (GeV

0 1 2 3 4 5 6

04 00r

0

0.2

0.4

0.6

0.8

H1ZEUS

a)

) 2|t| (GeV

0 1 2 3 4 5 6

04 1-1

r

-0.4

-0.2

0BFKL two gluon SCHC

b)

)2|t| (GeV

0 1 2 3 4 5 6

]04 10

Re[

r

-0.4

-0.2

0

c)

00

1-1 10

10

00

1-1


15

J/ψ - Helicity Analysis

|φ*| [°]

dσ/d

|φ*|

[nb/

°]

1

10

0 90 180

[GeV2]⟨Q2⟩

0.05

3.2

7.0

22.4

Fit ∝ 1+r1-1cos2φ* 04

SCHC

b)

-1 -0.5 0 0.5 1cosθ*

dσ/d

cosθ

* [n

b]

10

50

100

[GeV2]⟨Q2⟩

0.05

3.2

7.0

22.4

Fit ∝ 1+r00+(1-3r00)cos2θ* 04 04Data

H1

a)

|Φ| [°]

dσ/d

|Φ| [

nb/°

]

1

10

0 90 180

[GeV2]⟨Q2⟩

3.2

7.0

22.4

Fit ∝ 1-ε(r00+2r11)cos2Φ 1 1 ______ +√2ε(1+ε)(r00+2r11)cosΦ 5 5

SCHC

d)

MesonProduction

LeptonScattering

Meson Decay Plane

Decay in MesonRest Frame

µ

µ

µ

γe

J/Ψ

−

−

+e’

Φθ∗

φ

Plane Plane µ+

∗

J/Ψ

• All three angles accessible in electroproduction• Use also proton dissociative events to increase statistics


16

J/ψ - Helicity Analysis The 5 measured spin-density matrix elements are in agreement with SCHCFor SCHC, the ratio

R =

can be determined from r04

0

0.5 H1 a)r00 04

0

0.5b)

r1-1 04SCHC

0

0.5c)

r1-1 1

H1 PhotoproductionH1 ElectroproductionZEUS PhotoproductionZEUS Electroproduction

0

0.5d)

r00+2r11 5 5

Q2 [GeV2]

0

0.5

0.1 1 10

e)r00+2r11 1 1

0

0.5f)

r00 04

0

0.5g)

r1-1 04

0

0.5h)

r1-1 1

0

0.5i)

r00+2r11 5 5

|t| [GeV2]

0

0.5

0.1 1

j)r00+2r11 1 1

σL

σT

00

-0.5

0

0.5

1

1.5

2

Q2 [GeV2]

R=σ

L/σ T

0.1 1 10

H1ZEUSMRT(CTEQ6M)

H1a)


17

Vector Mesons: Summary • Intercepts increase with scale - slopes universal?

• J/ψ production calculable in pQCD, sensitive to gluon densities and evolution

• SCHC violated for high |t| ρ0, no evidence for violation in J/ψ production


18

Deeply Virtual Compton Scattering

Scattering of a virtual photon off the proton producing a realphoton: e + p → e + γ + p

In principle very clean channel:

• Factorisation theorem: First diffractive process fully calculable in QCD

• No uncertainty due to VM wave-function

• Clean final state

t

e e

p p

γ γ*W

Q2

NLO leading twist calculation by A. Freund and M. McDermott Eur. Phys. J. C23 (2002) 651Factorisation Theorem:Collins & Freund Phys.Rev.D 59 (1999) 074009Ji & Osborne Phys.Rev. D 58 (1998) 094018

H1: Eur.Phys.J. C 44 (2005) 1 (HERA I) Preliminary ICHEP 2006 (HERA II)ZEUS: Phys.Lett. B 573 (2003) 46


19

DVCS and Bethe-Heitler

DVCS has the same final state as the Bethe-Heitler process:

• Interference gives access to amplitudes via asymmetries (angles, beam charge)

• DVCS cross section via sub- traction of B-H (calculable in QED) - Interference cancels in integration over angles

e

e

p p

γ

γ

*

e e

p p

γγ

*

e e

p p

γ γ*DVCS

Bethe-Heitler


20

DVCS: Data selection

Expect one photon, one electron and nothing else in detector

Two samples:

• Electron in barrel, photon in backward direction (Mainly Bethe-Heitler)

• Photon in barrel, electron in backward direction (DVCS and Bethe-Heitler)

Use first sample to understand detector response

Control Sample

γ Sample

e →

e →

← p

← p

39.7 pb-1 (2004 e+)


21

DVCS: t dependence• H1 has first result with HERA-II data, more to come

• Exponential fit in t: dσ/dt ∝ e-bt

b = 5.83 ± 0.27 ± 0.50 GeV-2 at Q2 = 8 GeV, W = 82 GeV

• Compatible with old measurement

• Constrains theory normalisation ]2|t| [GeV

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1]

2 p

) /dt

[nb/

GeV

γ →

p

* γ (σd

-110

1

10

H1 04 Prel. H1 99-00

fit to H1 99-00 & Prel.-b|t|e-2 0.50 GeV± 0.27 ±b = 5.83

H1


22

DVCS: Q2 and W dependencies

• Fit in Q2: (1/Q2)n

n = 1.52 ± 0.07 ± 0.04 ZEUS: n = 1.54 ± 0.07 ± 0.06

]2 [GeV2Q10 20 30 40 50 60 70 80 90

p)

[nb]

γ →

p

* γ (σ

-110

1

10 H1 04 Prel.

H1 96-00 Zeus

fit to H1 96-00 & Prel.n)2(1/Q 0.04± 0.07 ±n = 1.52

H1

W = 82 GeV2|t| < 1 GeV

W [GeV]40 50 60 70 80 90 100 110 120 130 140

p)

[nb]

γ →

p

* γ (σ

0

2

4

6

8

10

12

H1 04 Prel.

H1 99-00

Zeus

fit to H1 99-00 & Prel.δW 0.22± 0.16 ± = 1.00 δ

H1

2 = 8 GeV2Q2|t| < 1 GeV

• W dependence Fit Wδ δ = 1.00 ± 0.16 ± 0.22ZEUS: δ = 0.75 ± 0.15 + 0.08

Indicates hard regime (cf. J/ψ Production)

− 0.06


23

DVCS: Q2 and W dependencies

10-1

1

10

0 10 20 30 40 50 60 70 80 90

ZEUS HERA-IH1 HERA-IH1 HERA-II e-p (prelim.)

W = 82 GeV

H1 DVCS (Preliminary, 145 pb-1)

Q2 [GeV2]

σD

VC

S [nb

]

0

2

4

6

8

10

12

0 20 40 60 80 100 120 140

ZEUS HERA-IH1 HERA-IH1 HERA-II e-p (prelim.)

Q2 = 8 GeV2

H1 DVCS (Preliminary, 145 pb-1)

W [GeV]

σD

VC

S [nb

]New: Complete HERA II e-p data set analysed (145 pb-1)

Comparisons to models and more differential cross sections on the way


24

DVCS: Comparison with QCD Predictions

Comparison to NLO QCD:

• Band width reduced by t slope measurement• Good description of the data (CTEQ6)• Sensitive to PDF parametrisations?

W [GeV]40 50 60 70 80 90 100 110 120 130 140

p)

[nb]

γ →

p

* γ (σ

0

2

4

6

8

10

12 H1 04 Prel. H1 99-00 Zeus

NLO-QCD (Freund et al.)MRST 2001CTEQ6

H1

2 = 8 GeV2Q2|t| < 1 GeV

]2 [GeV2Q10 20 30 40 50 60 70 80 90

p)

[nb]

γ →

p

* γ (σ

-110

1

10 H1 04 Prel. H1 96-00 Zeus

NLO-QCD (Freund et al.)

MRST 2001

CTEQ6

H1

W = 82 GeV2|t| < 1 GeV


25

Conclusion• Trajectory intercepts rise with scale, slope universal?

• Experimental data from vector mesons and DVCS are beginning to constrain the proton structure

• Complimentary to inclusive analyses: Gluons at low x and transverse degrees of freedom become accessible

• There is still a lot to be measured and to be calculated

W [GeV]40 50 60 70 80 90 100 110 120 130 140

p)

[nb]

γ →

p

* γ (σ

0

2

4

6

8

10

12 H1 04 Prel. H1 99-00 Zeus

NLO-QCD (Freund et al.)MRST 2001CTEQ6

H1

2 = 8 GeV2Q2|t| < 1 GeV


26

Outlook• HERA II is coming to a close: ~ 400 pb-1 per experiment

• Running with half the proton energy until July (FL, B. Loehr after lunch): Lower W becomes accesible

In the H1 pipeline: • DVCS beam charge asymmetries • Large φ meson photoproduction sample

Days of running

H1

Inte

grat

ed L

umin

osity

/ p

b-1

Status: 15-Mar-2007 1/07/07

0 500 1000 15000

100

200

300

400electronspositrons

HERA-1

HERA-2

[GeV]-K+KM1 1.02 1.04 1.06 1.08 1.1

Eve

nts

/ 2 M

eV

0

5000

10000

15000

20000

25000

30000

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