DVCS @ HERMES · 2011. 7. 7. · Deeply Virtual Compton Scattering ... H and E are quark helicity...

DVCS @ HERMESM. MURRAY, UNIVERSITY OF GLASGOW

PacSpin 2011

1Tuesday, 21 June 2011

Deeply Virtual Compton Scattering

• Physics - Interests & Constraints

• HERMES DVCS Measurements

• GPDs & Future Measurements


















e p ➝ e p γ




Generalised Parton Distributions

t - Mandelstam variable (squared momentum transfer to nucleon)

x - Fraction of nucleon’s longitudinal momentum carried by active quark

ξ - half the change in the longitudinal momentum of the active quark.

t






t






t


GPD PhysicsFour distributions of interest: H, E, H, E~ ~

H and E integrate over quark helicitiesH and E are quark helicity difference distributions~ ~


GPD PhysicsFour distributions of interest: H, E, H, E~ ~

H and E integrate over quark helicitiesH and E are quark helicity difference distributions~ ~

Nucleon helicity inversion

Nucleon helicity conservation

Phys. Rev. Lett. 78:610, 1997

“Ji’s Relation”


GPD Physics


GPD Physics

H - unpolarised nucleon H - polarised nucleon~


GPD Physics

GPDs describe only the soft part of the interaction

Accessed via cross-sections and asymmetries: requires convolution with a hard scattering kernel

Results in “Compton Form Factors” accessible through DVCS, which have real and imaginary parts

H➞H H➞H E➞E E➞E~~~ ~


GPD PhysicsGPDs describe only the soft part of the interaction



GPD PhysicsGPDs describe only the soft part of the interaction


Limited x access


DVCS @ HERMES

∝

∝

∝ Im(H)

Re(H)

Im(H)

∝ Re(H)

~

~

~

~

~

~


DVCS @ HERMES

x

y

z φ

"pγ

"k

"k′

"q

uli


• 1 GeV2 < Q2≣-q2 < 10 GeV2

• 0.03 < xB < 0.3

• 0 GeV2 < -t≣-(p-p’)2 < 0.7 GeV2

〈Q2〉≅ 2.4 GeV2

〈xB〉≅ 0.1

〈-t〉≅ 0.1 GeV2

DVCS @ HERMESForward

spectrometer ⇒

measure asymmetries

directly


DVCS @ HERMES

BH/DVCS

MC Sum

Resonance Production

SIDIS Production

Exclusive π0 Production

Data


DVCS @ HERMES

Wanted Signal

BH/DVCS from Δ, e.ge Δ → e Δ γ → e p π0 γ

e p → e X γ

e p → e p π0

BH/DVCS

MC Sum

Resonance Production

SIDIS Production

Exclusive π0 Production

Data


DVCS @

HERMES

Amplitude Value-0.3 -0.2 -0.1 0 0.1 0.2 0.3

)φcos(2LLA

φcos LLA

)φcos(0LLA

)φsin(2ULA

φsin ULA

φcos )sφ - φcos(LT,IA

φsin )sφ - φsin(LT,IA

)sφ - φcos(

LT,BH+DVCSA

)sφ - φcos(

LT,IA

φsin )sφ - φcos(UT,IA

φcos )sφ - φsin(UT,IA

)sφ - φsin(

UT,DVCSA

)sφ - φsin(

UT,IA

)φsin(2LU,IA

φsin LU,DVCSA

φsin LU,IA

)φcos(3CA

)φcos(2CA

φcos CA

)φcos(0CA

HERMES DVCS HydrogenDeuteriumHydrogen Preliminary


DVCS @

HERMES

Amplitude Value-0.3 -0.2 -0.1 0 0.1 0.2 0.3

)φcos(2LLA

φcos LLA

)φcos(0LLA

)φsin(2ULA

φsin ULA



)sφ - φcos(

LT,BH+DVCSA

)sφ - φcos(

LT,IA



)sφ - φsin(

UT,DVCSA

)sφ - φsin(

UT,IA

)φsin(2LU,IA

φsin LU,DVCSA

φsin LU,IA

)φcos(3CA

)φcos(2CA

φcos CA

)φcos(0CA



Beam Asymmetries

)φco

s (0

CA -0.1

0

0.1 HERMES

φco

s C

A

0

0.1

0.2

0.3

)φco

s (2

CA -0.1

0

0.1

)φco

s (3

CA -0.1

0

0.1

overall

frac

tion

Ass

oc.

00.10.20.3

-0.1

0

0.1 Preliminary 2006-07JHEP11 (2009) 083

0

0.1

0.2

0.3

-0.1

0

0.1

-0.1

0

0.1

]2-t [GeV

-210 -1100

0.1

0.2

0.3

0.4

-0.1

0

0.1

0

0.1

0.2

0.3

-0.1

0

0.1

-0.1

0

0.1

Bx-110

0

0.1

0.2

0.3

0.4

-0.1

0

0.1 γ p +/- e→ p +/-e

0

0.1

0.2

0.3

-0.1

0

0.1

-0.1

0

0.1

]2 [GeV2Q1 10

0

0.1

0.2

0.3

0.4

Beam Charge Asymmetries access Re(H)

Δ-resonance


Beam Asymmetriesφ

sin

LU,I

A

-0.6

-0.4

-0.2

0

0.2 HERMES

φsi

n LU

,DVC

SA

-0.4

-0.2

0

0.2

)φsi

n (2

LU,I

A

-0.4

-0.2

0

0.2

overall

frac

tion

Ass

oc.

00.20.4

-0.6

-0.4

-0.2

0

0.2 Preliminary 2006-07JHEP11 (2009) 083

-0.4

-0.2

0

0.2

-0.4

-0.2

0

0.2

]2-t [GeV

-210 -1100

0.1

0.2

0.3

0.4

-0.6

-0.4

-0.2

0

0.2

2.8%3.4% Scale Uncertainty

-0.4

-0.2

0

0.2

-0.4

-0.2

0

0.2

Bx

-1100

0.1

0.2

0.3

0.4

-0.6

-0.4

-0.2

0

0.2

γ p +/- e→ p +/-e

-0.4

-0.2

0

0.2

-0.4

-0.2

0

0.2

]2 [GeV2Q1 10

0

0.1

0.2

0.3

0.4

Beam Helicity Asymmetries access Im(H)

Larger values for the BHA than BCA -

correlated to the difference

in the CFF access?


DVCS @

HERMES

Amplitude Value-0.3 -0.2 -0.1 0 0.1 0.2 0.3

)φcos(2LLA

φcos LLA

)φcos(0LLA

)φsin(2ULA

φsin ULA



)sφ - φcos(

LT,BH+DVCSA

)sφ - φcos(

LT,IA



)sφ - φsin(

UT,DVCSA

)sφ - φsin(

UT,IA

)φsin(2LU,IA

φsin LU,DVCSA

φsin LU,IA

)φcos(3CA

)φcos(2CA

φcos CA

)φcos(0CA



~

Long. Pol. target asymmetries access Im(H)

A. Airapetian et al, JHEP 06 (2010) 019

http://arxiv.org/abs/1004.0177

Target Asymmetries φ

sin

UL

A

-0.2

0

)φsi

n (2

UL

A

-0.2

0

)φsi

n (3

UL

A

-0.2

0

0.2

integrated

Res

o. fr

ac.

0.10.20.3

0 0.2 0.4 0.6

0 0.2 0.4 0.6

0 0.2 0.4 0.6

] 2-t [GeV0 0.2 0.4 0.6

0 0.1 0.2 0.3

0 0.1 0.2 0.3

0 0.1 0.2 0.3

Bx0 0.1 0.2 0.3

0 5 10

VGG Regge

0 5 10

0 5 10

] 2 [GeV 2Q0 5 10

VGG Model:

Phys.Rev. D60 (1999) 094017

http://arxiv.org/abs/hep-ph/9905372






Double Spin Asymmetries )φ

cos

(0LL

A

-0.20

0.20.40.6

integrated

φ c

os

LLA

-0.4-0.2

00.20.4

)φ c

os (2

LLA

-0.4-0.2

00.20.4

integrated

Res

o. fr

ac.

0.10.20.3

0 0.2 0.4 0.6

-0.2

0

0.2

0.4

0.6

0 0.2 0.4 0.6

-0.4

-0.2

0

0.2

0.4

0 0.2 0.4 0.6-0.4

-0.2

0

0.2

0.4

] 2-t [GeV0 0.2 0.4 0.6

0 0.1 0.2 0.3

-0.2

0

0.2

0.4

0.6

0 0.1 0.2 0.3

-0.4

-0.2

0

0.2

0.4

0 0.1 0.2 0.3-0.4

-0.2

0

0.2

0.4

Bx0 0.1 0.2 0.3

0 5 10

-0.2

0

0.2

0.4

0.6 VGG Regge

0 5 10

-0.4

-0.2

0

0.2

0.4

0 5 10-0.4

-0.2

0

0.2

0.4

] 2 [GeV 2Q0 5 10

Long. Pol. target / Long. Pol. Beam access Re(H)~

Caveat! Relatively large BH

contribution to these asymmetries!

A. Airapetian et al, JHEP 06 (2010) 019





Beam Asymmetries

Deuterium is governed by different GPDs - but the asymmetry data is not so

different!

http

://w

ww.

arxi

v.org

/abs

/091

1.00

95

A. Airapetian et al, Nucl. Phys. B 829 (2010) 1-27


http://www.arxiv.org/abs/0911.0095


Target Asymmetries


A. Airapetian et al, Nucl. Phys. B842 (2011) 265-298

No good idea how to model

long. pol. deuterium

GPDs. Currently use a proton/

neutron hybrid


http://www.arxiv.gorg/abs/1008.3996

http://www.arxiv.gorg/abs/1008.3996

Nuclear Mass Dependence

-0.05

0

0.05

0

0.05

0.1

0.15

1 10 102

ACco

s (

t <

t coh.

)A

Ccos

(t >

t in

coh.

)

nuclear mass number A

Nuclear-Binding models expected the DVCS

asymmetry for nuclear targets to be ~2x that

of the Hydrogen asymmetry.


Nuclear Mass Dependence

-0.4

-0.2

0

-0.4

-0.2

0

1 10 102

ALU

,(I,+

)si

n (

t <

t coh.

)A

LU,(I

,+)

sin

(t >

t in

coh.

)

nuclear mass number A

Baryons

Fermions

The data shows no significant difference between coherent and

incoherent DVCS processes


A. Airpetian et al. Phys. Rev. C 81, 035202 (2010)




• 1 GeV2 < Q2≣-q2 < 10 GeV2

• 0.03 < xB < 0.3

• 0 GeV2 < -t≣-(p-p’)2 < 0.7 GeV2

〈Q2〉≅ 2.4 GeV2

〈xB〉≅ 0.1

〈-t〉≅ 0.1 GeV2

DVCS @ HERMESForward

spectrometer ⇒

measure asymmetries

directly


DVCS @ HERMES

1

0

2

−1

−2

TARGETCELL

RecoilDetector

m

LUMINOSITY

CHAMBERSDRIFT

FC 1/2

DVC

MC 1−3MONITOR

BC 1/2

BC 3/4 TRD

PROP.CHAMBERS

FIELD CLAMPS

PRESHOWER (H2)

DRIFT CHAMBERS

TRIGGER HODOSCOPE H1

0 1 2 3 4 5 6 7 8 9 10

RICH270 mrad

270 mrad

MAGNET

m

140 mrad

140 mradCALORIMETER

e+27.5 GeV

STEEL PLATE

HODOSCOPE H0SILICON


Current DVCS Data

]4/c2 [GeVX2M

-4 -2 0 2 4 6 8 10 12 140

500

1000

1500

2000

2500

3000

Significant improvement in the purity of the signal

SumTrack in the Recoil Detector

Kin. Fit says probably not DVCSKin. Fit says probably DVCS


Current DVCS Dataφ

sin

LUA

-0.4

-0.2

0

HERMESPRELIMINARY2006/07 data

OverallOverall)φ

sin

(2LU

A

-0.2

-0.1

0

0.1

-0.4

-0.2

0

3.4% scale uncertainty

]2-t [GeV-110

-0.2

-0.1

0

0.1

-0.4

-0.2

0

without Recoil Det.with Recoil Det.in Recoil Det. accept.

Bx-110

-0.2

-0.1

0

0.1

-0.4

-0.2

0

γ p + e→ p +e

]2 [GeV2Q1 10

-0.2

-0.1

0

0.1


Current DVCS Data

φsi

n LU

A-0.4

-0.2

0

HERMESPRELIMINARY2006/07 data

OverallOverall)φ

sin

(2LU

A

-0.2

-0.1

0

0.1

-0.4

-0.2

0

3.4% scale uncertainty

]2-t [GeV-110

-0.2

-0.1

0

0.1

-0.4

-0.2

0

without Recoil Det.with Recoil Det.in Recoil Det. accept.

Bx-110

-0.2

-0.1

0

0.1

-0.4

-0.2

0

γ p + e→ p +e

]2 [GeV2Q1 10

-0.2

-0.1

0

0.1

overall

Proc

ess

frac

tions

0

0.5

1

]2-t [GeV

-210 -110

0

0.5

1

Bx

-110

0

0.5

1

]2 [GeV2Q1 10

0

0.5

1

Elastic Assoc.with Recoil Det. in Recoil Det. accept.without Recoil Det.


GPD Discovery

H1�ZEU

S

COMPASS

HERMES

JLAB

1.0000.5000.1000.0500.0100.0050.0010.0

0.1

0.2

0.3

0.4

0.5

x

xH�x,x,

t�

0 50 100 150

�0.2

�0.1

0.0

0.1

0.2

�

ABCSA�� H1�ZEUS

HERMESCLASHall A

H1�ZEUSHERMESCLAS

predictions from fits to


To appear in Nucl. Phys. B (2010)

Postulate GPDs fromfirst principle models

New CFF Fit Result incorporating AUL moments

Kumerički and Müller

http://arxiv.org/abs/1005.4922M. Guidal






Future DataCOMPASS-II SPSC-I-238

Jefferson Lab PR-10-006

Measurements of the dvcs cross-section can help determine x and t

entanglement

All four GPDs will be accessed in proposed measurements at JLab

and COMPASS


Meson DataMeson data can also play a

vital role in accessing GPDs - especially the

“polarised” GPDs H and E!~~

Extraction of SDMES and Helicity Amplitude Ratios at HERMES for ρ mesons have

shown that the handbag approximation is insufficient!

17

Q2 [GeV2]

! 11 [

deg]

Deuteron

Proton

0

25

50

1 2 3Q2 [GeV2]

! 01 [

deg]

DeuteronProton

-90

0

90

1 2 3

Fig. 6. The Q2 dependence of the phase difference δ11 (left panel) and δ01 (right panel, see Sec. 7.4) between the amplitudes T11

and T01, respectively, and T00 obtained for proton and deuteron data. Points show the phase differences δ11 and δ01 calculatedfrom ratios of amplitudes given in Tabs. 2 and 3 after averaging over −t′ bins. Inner error bars show the statistical uncertaintyand the outer ones show the statistical and systematic uncertainties added in quadrature. The fitted parameterization is givenby Eqs. (70) and (78) respectively for δ11 and δ01. The parameters of the curves are given in Tabs. 4 and 6 for combined protonand deuteron data. The central lines are calculated with the fitted values of the parameters, while the dashed lines correspondto one standard deviation in the uncertainty of the curve parameter.

-t/ [GeV2]

Q*R

e(T 11

/T00

) [GeV]

DeuteronProton

1

1.5

0.1 0.2 0.3-t/ [GeV2]

Im(T

11/T

00)/Q

[GeV

-1 ]

DeuteronProton

0.2

0.4

0.1 0.2 0.3

Fig. 7. The t′ dependence of Q ·Re(T11/T00) (left panel) and Im(T11/T00)/Q (right panel) for proton and deuteron data. Pointsshow the amplitude ratios from Tabs. 2 and 3 after averaging over four Q2 bins using Eqs. (67) and (68). The straight lines inthe left and right panel show the value of a and b, respectively, from Eqs. (66) and (69) while the parameters a and b are givenin Tab. 4. The meaning of the error bars and the explanation of the curves are the same as for Fig. 4.

-1

-0.5

0

0.5

0 0.2 0.4 0.6-t´ [GeV2]

AU

T, l

sin(!"! s

)

Figure 3: Model predictions for the sin(φ − φS) Fourier amplitudeas a function of −t′. The curves represents predictions of GPD-

model calculations. The full circles show the values of Asin(φ−φS)UT,"

taken from Fig. 2. The error bars (bands) represent the statistical(systematic) uncertainties. See text for details.

larger values of −t′, caused by a negative real part in E .The dash-dotted curve arises from an alternative GPD ap-proach [34], in which the imaginary part of H becomesnegative while the real part of E remains positive at largervalues of −t′.

An attempt to evaluate the complete set of Fourier am-

plitudes (7), and in particular the value of Asin(φ−φS)UT," , is

presented in [17]. In this model, the GPDs are calculatedin a similar way as in the models [15, 35], except that theexperimental value of the pion form factor Fπ is used. Herea large non-pole contribution from E over-compensates thepion-pole contribution leading to the zero-crossing behav-ior of the amplitude as a function of −t′ (see dashed curvein Fig. 3). This model appears to be qualitatively in agree-ment with the data. However, within the large experimen-

tal uncertainty Asin(φ−φS)UT," is also consistent with zero. A

vanishing Fourier amplitude in this model implies the dom-inance (due to the pion pole) of E over H at low −t′. Thisis in agreement with the recent Hermes measurement ofthe exclusive π+ cross section [22], which is well describedat −t′ = 0.1 GeV2 by a GPD model [35] based only on Ewhile neglecting the contribution of H .

In summary, the Fourier amplitudes of the single-spinazimuthal asymmetry are measured in exclusive electro-production of π+ mesons on transversely polarized pro-tons, for the first time. Within the experimental uncer-tainties the amplitude of the sin(φ − φS) modulation isfound to be consistent with zero, thus excluding a purepion-pole contribution to the GPD E in leading-twist cal-culations. This could also be an indication for the dom-inance of E over the GPD H at low −t′. The observedamplitude of the sinφS modulation is large and positivewhich implies the presence of a sizeable interference be-tween contributions from longitudinal and transverse vir-tual photons. A next-to-leading twist calculation as wellas knowledge of the contributions from transverse pho-

tons and their interference with longitudinal photons arerequired for a description of the measurements.

We gratefully acknowledge the Desy management forits support and the staff at Desy and the collaboratinginstitutions for their significant effort. This work was sup-ported by the FWO-Flanders and IWT, Belgium; the Nat-ural Sciences and Engineering Research Council of Canada;the National Natural Science Foundation of China; theAlexander von Humboldt Stiftung; the German Bundesmin-isterium fur Bildung und Forschung (BMBF); the DeutscheForschungsgemeinschaft (DFG); the Italian Istituto Nazionaledi Fisica Nucleare (INFN); the MEXT, JSPS, and G-COEof Japan; the Dutch Foundation for Fundamenteel Onder-zoek der Materie (FOM); the U.K. Engineering and Physi-cal Sciences Research Council, the Science and TechnologyFacilities Council, and the Scottish Universities PhysicsAlliance; the U.S. Department of Energy (DOE) and theNational Science Foundation (NSF); the Russian Academyof Science and the Russian Federal Agency for Scienceand Innovations; the Ministry of Economy and the Min-istry of Education and Science of Armenia; and the Eu-ropean Community-Research Infrastructure Activity un-der the FP6 ”Structuring the European Research Area”program (HadronPhysics, contract number RII3-CT-2004-506078).

References

[1] D. Muller, D. Robaschik, B. Geyer, F.M. Dittes, and J. Horejsi,Fortschr. Phys. 42 (1994) 101.

[2] A.V. Radyushkin, Phys. Lett. B 380 (1996) 417.[3] X. Ji, Phys. Rev. Lett. 78 (1997) 610.[4] M. Burkardt, Phys. Rev. D 62 (2000) 071503; Erratum–ibid. D

66 (2002) 119903.[5] M. Diehl, Eur. Phys. J. C 25 (2002) 223; Erratum-ibid. C31

(2003) 277.[6] J.P. Ralston and B. Pire, Phys. Rev. D 66 (2002) 111501.[7] A.V. Belitsky and D. Muller, Nucl. Phys. A 711 (2002) 118.[8] M. Burkardt, Int. J. Mod. Phys. A 18 (2003) 173.[9] J.C. Collins, L.L. Frankfurt, and M. Strikman, Phys. Rev. D 56

(1997) 2982.[10] K. Goeke, M.V. Polyakov, and M. Vanderhaeghen, Prog. Part.

Nucl. Phys. 47 (2001) 401.[11] M. Diehl, Phys. Rept. 388 (2003) 41.[12] A.V. Belitsky and A.V. Radyushkin, Phys. Rept. 418 (2005) 1.[13] L.L. Frankfurt, P.V. Pobylitsa, M.V. Polyakov, and M. Strik-

man, Phys. Rev. D 60 (1999) 014010.[14] L.L. Frankfurt, M.V. Polyakov, M. Strikman, and M. Vander-

haeghen, Phys. Rev. Lett. 84 (2000) 2589.[15] A.V. Belitsky and D. Muller, Phys. Lett. B 513 (2001) 349.[16] M. Diehl and W. Kugler, Eur. Phys. J. C 52 (2007) 933.[17] S. Goloskokov and P. Kroll, arXiv:0906.0460 [hep-ph].[18] M. Diehl and S. Sapeta, Eur. Phys. J. C 41 (2005) 515.[19] A. Bacchetta, U. D’Alesio, M. Diehl, and C.A. Miller, Phys.

Rev. D 70 (2004) 117504.[20] Ch. Bechler and D. Muller, arXiv:0906.2571 [hep-ph].[21] M.M. Kraskulov and U. Mosel, arXiv:0904.4442 [hep-ph].[22] A. Airapetian et al., Phys. Lett. B 659 (2008) 486.[23] A. Airapetian et al., Phys. Lett. B 535 (2002) 85.[24] K. Ackerstaff et al., Nucl. Instrum. Methods A417 (1998) 230.[25] A. Nass et al., Nucl. Instrum. Methods A505 (2003) 633.[26] A. Airapetian et al., Nucl. Instrum. Methods A540 (2005) 68.[27] N. Akopov et al., Nucl. Instrum. Methods A479 (2002) 511.[28] R. Barlow, Nucl. Instrum. Methods A297 (1990) 496.

6


Meson Data

Throughout the majority of exclusive physics data from HERMES we see that there is very little difference between protons and deuterons!!!


Conclusions

• DVCS can be used to access information on Generalised Parton Distributions

• That information can tell us unique things about nucleon structure

• HERMES has the most diverse DVCS measurements of any experiment.


Conclusions

• There is still no clear idea about how the nuclear medium modifies GPD-dependent behaviour.

• Already, GPDs can be constrained - but there is much left to do!

• DVCS and DVMP both seem to show that there is little difference between proton and deuteron data!!!


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DVCS @ HERMES · 2011. 7. 7. · Deeply Virtual Compton Scattering ... H and E are quark helicity...

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