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Recent experimental results on Deep Virtual Compton Scattering and Generalized Parton Distributions
Nuclear Physics B (Proc. Suppl.) 181–182 (2008) 62–65 www.elsevierphysics.com
Recent experimental results on Deep Virtual Compton Scattering and Generalized Parton Distributions M. Guidala a
Institut de Physique Nucl´eaire d’Orsay, 91406 Orsay, France We review and discuss briefly the recent experimental results on Deep Virtual Compton Scattering on the proton. With the variety of independent observables beginning to be available and, in some instances, some very high precision data, some first global analysis for this process can be started, based on dedicated fitter codes, aiming at revealing the Generalized Parton Distributions content of the nucleon.
Generalized Parton Distributions (GPDs) have emerged this past decade as a powerful concept and tool to study nucleon structure. They describe, among other aspects, the (correlated) spatial and momentum distributions of the quarks in the nucleon (including the polarization aspects), its quark-antiquark content, a way to access the orbital momentum of the quarks, etc... We refer the reader to refs [1–3] for example, for very detailed and quasi-exhaustive reviews on the GPD formalism and the definitions of some of the variables and notations that will be employed in the following. In short, the GPDs are the structure functions which parametrize the nucleon structure in the exclusive leptoproduction of a photon (Deep Virtual Compton Scattering -DVCS-) or of a meson on a nucleon, in the so-called Bjorken regime (i.e., in simplifying, large Q2 , where Q2 is the virtuality of the incoming photon). Using Ji’s notation [4], there are at leading twist and leading order QCD (Quantum Chromo-Dynamics), four helicity con˜ E, E, ˜ and serving GPDs which are called H, H, which depend upon three variables : x, ξ and xB /2 t, with ξ = 1−x where xB is the standard B /2 Bjorken variable of Deep Inelastic Scattering and t the squared 4-momentum transfer to the nucleon. These two latter variables, ξ and t, are accessed experimentally in a straightforward way by detecting, respectively, the scattered electron and the recoil proton or the outgoing photon in the case of DVCS. However x is a variable which is 0920-5632/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2008.09.005
in general integrated over in the aforementionned physical processes and thus not simply accessible. This means that, in general, the differential cross section of DVCS be proportional to terms of +1 willH(x,ξ,t) the type : | −1 dx x±ξ∓i |2 with similar terms ˜ E. ˜ However, it can be seen from this for E, H, formula that, decomposing it in a principal part and a δ function that, when one measures an observable sensitive to the imaginary part of the amplitude, such as many polarization observables, one actually can also access the GPDs directly at some specific point, x = ξ (i.e. H(ξ, ξ, t)). Therefore, one can in general, at the leading twist level, extract from experimental observables two kinds of GPD-related quantities which are, precisely, taking H as an example, Re(H) = 1 1 1 dx [H(x, ξ, t) − H(−x, ξ, t)] ( x−ξ + x+ξ ) and 0 Im(H) = H(ξ, ξ, t) − H(−ξ, ξ, t). There are sim˜ E, E, ˜ modulo some signs. This ilar terms for H, therefore defines 8 quantitites Re(H), Re(E), ˜ ˜ Im(H), Im(E), Im(H) ˜ and Re(H), Re(E), ˜ Im(E) which are usually called Compton Form Factors (CFFs) [5]. We now briefly review a few recent experimental results on DVCS focusing on the quark valence region due to space contraints and discuss their link and sensitivity to the CFFs. Jefferson Lab (JLab) Hall A experiment E-00110 [6] has measured for the first time ever the cross section of the DVCS process in the valence region. The 4-fold, beam-polarized and unpolardσ→ ±dσ← ized, differential cross sections dx , where 2 B dQ dtdΦ
63
M. Guidal / Nuclear Physics B (Proc. Suppl.) 181–182 (2008) 62–65
2
4
σ (nb/GeV )
Ee=5.75 GeV, xB=0.36, Q =2.3 GeV
2
Q2 = 2.8 xB = 0.45
a(t)
0.11
0.2
0.1
Q2 = 3.7 xB = 0.46
0.1
0.09
0
0.08 0.07
0.3 0.06
4
Q2 = 2.3 xB = 0.35
Q2 = 2.7 xB = 0.36
Q2 = 3.0 xB = 0.36
Q2 = 1.7 xB = 0.25
Q2 = 1.9 xB = 0.25
Q2 = 2.2 xB = 0.25
Q2 = 1.2 xB = 0.13
Q2 = 1.4 xB = 0.17
Q2 = 1.6 xB = 0.18
0.2
0.05
Δσz0 (nb/GeV )
Q2 = 3.3 xB = 0.46
0.04
0.1
0.03
0
0.02 0.02
0.3
0.015
0.2
0.01
0.1
0.005
0
0 -0.005
0.3
-0.01
0.2
-0.015
0.1
-0.02 0
φ (deg.)
200
0
φ (deg.)
200
0
φ (deg.)
0
200
φ (deg.)
Figure 1. Top row : DVCS unolaroized cross section and bottom row : DVCS difference of beam polarized cross sections, as a function of φ, at xB =0.36 and Q2 =2.3 GeV2 for 4 different t values. The curves are the results of the fit from the leading twist DVCS fitter code of ref. [7]. Φ is the azimuthal angle between the leptonic and hadronic planes, have been extracted for 3 bins in Q2 . These results are shown in fig. 1 for < Q2 >=2.3 GeV2 , the highest Q2 reached in the experiment, where the precision of the data can be remarked (a few percent staistical uncertainties on the unpolarized cross sections). The solid curves show the result of the fit to these high precision data based on the leading twist handbag diagram DVCS amplitude, following the procedure developped in ref. [7]. From these fits, based therefore on the eight CFFs considerede as free parameters, first model independent contraints on the Im(H) and Re(H) CFFs could be extracted, the two observables measured by the Hall A collaboration showing, at this kinematics, a particularly high sensitivity to the H GPD [5,7]. Experiment E-00-113, using the JLab Hall B CLAS spectrometer, has measured the beam spin asymmetry, i.e. the ratio of the beam-polarized
0
0.5
1
1.5 0
0.5
1
1.5 0
0.5
-t (GeV2)
Figure 2. Black circles : beam spin asymmetry at Φ = 90o as a function of t for different (xB ,Q2 ) bins, as measured by the JLab CLAS collaboration [8]. Green triangles are the results extracted from the Hall A cross sections measurements [6]. The red square is an earlier result from the CLAS collaboration [9]. to the unpolarized cross sections, of the same DVCS process, over the largest-ever phase space for this reaction [8]. Fig. 2 shows these results along with some theoretical predictions. The blue solid curves are the result of a twist-2 DVCS GPD calculation based on the so-called VGG model [10,11]. The blue dashed curves are the result of the corresponding twist-3 calculation. It can be seen that although the most general trends of the data are reproduced, some modifications to this particular model are clearly needed, which is a conclusion which was also reached in ref. [7]. Beam spin asymmetries provide less constraints for a model independent fit than normalized cross sections and it is currently a subject of study to see to what extent the GPD information, dominantly H, can be extracted. The dashed black curve is the result of a Regge calculation [12] for the DVCS process, based on meson exchanges, i.e.
M. Guidal / Nuclear Physics B (Proc. Suppl.) 181–182 (2008) 62–65
not based on GPDs. It gives a fair description of the data up to Q2 =2.3 GeV2 . The question can be raised whether, up to this Q2 , the two approaches, GPDs and Regge, are orthogonal and incompatible or parallel and dual. As just discussed, the beam polarisation observables are particularly sensitive to the H GPD. In order to access the other CFFs, other experimental observables are needed. In particular, it is shown in ref. [7] that by measuring all unpolarized, beam and target single polarized observables and associated doubly polarized observables, all eight CFFs can be extracted. Such an experimental program has already started with the measurement of various observables. The precision of these measurements is still limited mainly due to the fact that they are integrated over relatively large (xB , Q2 , t) phase space domains, much larger than the ones of the JLab Hall A and Hall B beam polarized data just presented. It might therefore be still a bit preliminary to include them in a global fit procedure, although this is work in progress in the framework of ref. [7]. The HERMES collaboration [13,14] has for instance measured the proton DVCS beam charge asymmetry (see fig. 3) which is sensitive uniquely ˜ to the real part CFFs (except for Re(E)). Also, the proton longitudinally polarized target asymmetry (see fig. 4) has been measured by the CLAS collaboration [15], which is particularly sensitive ˜ [5,7]. These data allow for instance to to Im(H) clearly determine the sign of this latter CFF. Very recently, first transversally polarized target asymmetries have also been measured by the HERMES collaboration [14] which carry a strong sensitivity to Im(E). Let us also mention that a first measurement of the beam spin asymmetry for DVCS on the neutron has been published [16] by the JLab Hall A collaboration. In the long term, with higher precision, this kind of data will allow a quark flavor decomposition of the GPDs, adding therefore “flavor” to our “vision” of the nucleon. All these present data are very encouraging, give first insights on the nucleon GPDs and allow to test the CFFs fitting and extraction procedures. The experimental program must however clearly be continued so as to provide a wide and
AC
64
0.2 0.1 0 -0.1 -0.2 0
0.5
1
1.5
2
2.5
3
|φ| (rad) Figure 3. The proton DVCS beam charge asymmetry as a function of Φ, measured by the HERMES collaboration. The solid curve shows a fit to the data : A+Bcos Φ+Ccos 2Φ+Dcos 3Φ. The “pure” cos Φ component is shown by the dotted curve.
precise enough set of DVCS data and observables and allow to uniquely, unambiguously and modelindependently determine the eight leading-twist CFFs. At short term, numerous quality data are expected from JLab, with the 6 GeV beam for many channels and observables : for DVCS in particular, several experiment are planned for the next few years in Hall A [17] and B [18,19]. They aim at increasing (at least doubling) the statistics (and therefore, in particular, refining the binning), explore new kinematical domains for the (polarized and unpolarized) cross sections (and beam spin asymmetries) and also measure new observables such as the (longitudinal) target spin cross sections and asymmetries and the double target-beam spin asymetries. HERMES, with a 27 GeV beam, has recently finished taking data with a dedicated recoil detector which will ensure the exclusivity of the reaction. New beam charge asymetries and beam spin asymetries should be available in the next couple of years in a lower xB domain than at JLab [20]. After 2010, the COMPASS experiment at CERN also intends to study GPDs with a 200 GeV muon beam. Similarly to HERMES, a dedicated recoil detector will have to be installed in
M. Guidal / Nuclear Physics B (Proc. Suppl.) 181–182 (2008) 62–65
0.4
AUL
0.2 0 -0.2 -0.4 -0.6 0
50
100
150
φ
200
250 300 Degree
350
Figure 4. The proton DVCS longitudinally polarized target spin asymmetry as a function of Φ, measured by the CLAS collaboration. The solid curve shows a fit to the data : Asin Φ+Bsin 2Φ. The sin 2Φ term is compatible with zero. The dashed curve is the VGG model prediction, based ˜ with twist-3 on the contributions of H and H, contribution included. The dotted curve shows ˜ the asymmetry when H=0 and therefore shows ˜ the sensitivity of this observable to H.
order to detect all the particles of the final state DVCS and ensure the exclusivity of the process. It will have the unique feature of accessing very small xB at sufficiently large Q2 . In the longer term (> 2013), the upgraded JLab, with a 12 GeV beam promises to yield a wealth of new experimental data, allowing to reach new kinematical domains, in particular, the higher Q2 regime, which is crucial for the understanding of preasymptotic effects and higher twists. Two experiments for DVCS [21,22] with the 12 GeV beam have already been approved by the JLab PAC. A ruch harvest of data related to DVCS and GPDs lies therefore in front of us and with the development of dedicated fitter codes and advances in theory, all hopes are permitted for a complete extraction of the nucleon GPD information. REFERENCES 1. K. Goeke, M. V. Polyakov and M. Vanderhaeghen, Prog. Part. Nucl. Phys. 47, 401 (2001).
65
2. M. Diehl, Phys. Rept. 388, 41 (2003). 3. A.V. Belitsky, A.V. Radyushkin, Phys. Rept. 418, 1 (2005). 4. X. Ji, Phys.Rev.Lett. 78, 610 (1997); Phys.Rev. D55, 7114 (1997). 5. A. Belitsky, D. Muller and A. Kirchner, Nucl. Phys. B 629, 323 (2002) 6. C. Mu˜ noz Camacho et al., Phys. Rev. Lett. 97, 262002 (2006). 7. M. Guidal, to be published by Eur. Phys. J. A, arXiv:0807.2355 [hep-ph] 8. F.-X. Girod et al., Phys. Rev. Lett. 100, 162002 (2008). 9. S. Stepanyan et al., Phys. Rev. Lett. 87, 182002 (2001). 10. M. Vanderhaeghen, P.A.M. Guichon, M. Guidal, Phys. Rev. D 60, 094017 (1999). 11. M. Guidal, M. V. Polyakov, A. V. Radyushkin and M. Vanderhaeghen, Phys. Rev. D 72, 054013 (2005). 12. J.-M. Laget, Phys. Rev. C 76, 052201 (2007). 13. A. Airapetian et al., submitted to publication, hep-ex/0605108 14. A. Airapetian et al., JHEP 0806, 066 (2008). 15. S. Chen et al., Phys. Rev. Lett. 97, 072002 (2006). 16. M. Mazouz et al., Phys. Rev. Lett. 99, 242501 (2007). 17. JLab approved experiment E-07-007; spokespersons : C. Munoz Camacho, J. Roche, C. Hyde-Wright and P.-Y. Bertin. 18. JLab approved experiment E-06-003; spokespersons : V. Burkert, L. Elhouadrhiri, M. Gar¸con, R. Niyazov and S. Stepanyan. 19. JLab approved experiment E-05-114; spokespersons : A. Biselli, L. Elhouadrhiri, K. Joo and S. Niccolai. 20. R. Kaiser et al., “A large acceptance recoil detector for HERMES”, Addendum to the Proposal DESY PRC 97-07, HERMES 97-032. 21. JLab approved experiment E-12-06-114; spokespersons : C. Hyde-Wright, B. Michel, C. Munoz Camacho and J. Roche. 22. JLab approved experiment E-12-06-119; spokespersons : V. Burkert, L. Elouadrhiri, M. Gar¸con, M. Holtrop, D. Ireland, K. Joo, W. Kim, F. Sabatie.
Recent experimental results on Deep Virtual Compton Scattering and Generalized Parton Distributions M. Guidala a
Institut de Physique Nucl´eaire d’Orsay, 91406 Orsay, France We review and discuss briefly the recent experimental results on Deep Virtual Compton Scattering on the proton. With the variety of independent observables beginning to be available and, in some instances, some very high precision data, some first global analysis for this process can be started, based on dedicated fitter codes, aiming at revealing the Generalized Parton Distributions content of the nucleon.
Generalized Parton Distributions (GPDs) have emerged this past decade as a powerful concept and tool to study nucleon structure. They describe, among other aspects, the (correlated) spatial and momentum distributions of the quarks in the nucleon (including the polarization aspects), its quark-antiquark content, a way to access the orbital momentum of the quarks, etc... We refer the reader to refs [1–3] for example, for very detailed and quasi-exhaustive reviews on the GPD formalism and the definitions of some of the variables and notations that will be employed in the following. In short, the GPDs are the structure functions which parametrize the nucleon structure in the exclusive leptoproduction of a photon (Deep Virtual Compton Scattering -DVCS-) or of a meson on a nucleon, in the so-called Bjorken regime (i.e., in simplifying, large Q2 , where Q2 is the virtuality of the incoming photon). Using Ji’s notation [4], there are at leading twist and leading order QCD (Quantum Chromo-Dynamics), four helicity con˜ E, E, ˜ and serving GPDs which are called H, H, which depend upon three variables : x, ξ and xB /2 t, with ξ = 1−x where xB is the standard B /2 Bjorken variable of Deep Inelastic Scattering and t the squared 4-momentum transfer to the nucleon. These two latter variables, ξ and t, are accessed experimentally in a straightforward way by detecting, respectively, the scattered electron and the recoil proton or the outgoing photon in the case of DVCS. However x is a variable which is 0920-5632/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2008.09.005
in general integrated over in the aforementionned physical processes and thus not simply accessible. This means that, in general, the differential cross section of DVCS be proportional to terms of +1 willH(x,ξ,t) the type : | −1 dx x±ξ∓i |2 with similar terms ˜ E. ˜ However, it can be seen from this for E, H, formula that, decomposing it in a principal part and a δ function that, when one measures an observable sensitive to the imaginary part of the amplitude, such as many polarization observables, one actually can also access the GPDs directly at some specific point, x = ξ (i.e. H(ξ, ξ, t)). Therefore, one can in general, at the leading twist level, extract from experimental observables two kinds of GPD-related quantities which are, precisely, taking H as an example, Re(H) = 1 1 1 dx [H(x, ξ, t) − H(−x, ξ, t)] ( x−ξ + x+ξ ) and 0 Im(H) = H(ξ, ξ, t) − H(−ξ, ξ, t). There are sim˜ E, E, ˜ modulo some signs. This ilar terms for H, therefore defines 8 quantitites Re(H), Re(E), ˜ ˜ Im(H), Im(E), Im(H) ˜ and Re(H), Re(E), ˜ Im(E) which are usually called Compton Form Factors (CFFs) [5]. We now briefly review a few recent experimental results on DVCS focusing on the quark valence region due to space contraints and discuss their link and sensitivity to the CFFs. Jefferson Lab (JLab) Hall A experiment E-00110 [6] has measured for the first time ever the cross section of the DVCS process in the valence region. The 4-fold, beam-polarized and unpolardσ→ ±dσ← ized, differential cross sections dx , where 2 B dQ dtdΦ
63
M. Guidal / Nuclear Physics B (Proc. Suppl.) 181–182 (2008) 62–65
2
4
σ (nb/GeV )
Ee=5.75 GeV, xB=0.36, Q =2.3 GeV
2
Q2 = 2.8 xB = 0.45
a(t)
0.11
0.2
0.1
Q2 = 3.7 xB = 0.46
0.1
0.09
0
0.08 0.07
0.3 0.06
4
Q2 = 2.3 xB = 0.35
Q2 = 2.7 xB = 0.36
Q2 = 3.0 xB = 0.36
Q2 = 1.7 xB = 0.25
Q2 = 1.9 xB = 0.25
Q2 = 2.2 xB = 0.25
Q2 = 1.2 xB = 0.13
Q2 = 1.4 xB = 0.17
Q2 = 1.6 xB = 0.18
0.2
0.05
Δσz0 (nb/GeV )
Q2 = 3.3 xB = 0.46
0.04
0.1
0.03
0
0.02 0.02
0.3
0.015
0.2
0.01
0.1
0.005
0
0 -0.005
0.3
-0.01
0.2
-0.015
0.1
-0.02 0
φ (deg.)
200
0
φ (deg.)
200
0
φ (deg.)
0
200
φ (deg.)
Figure 1. Top row : DVCS unolaroized cross section and bottom row : DVCS difference of beam polarized cross sections, as a function of φ, at xB =0.36 and Q2 =2.3 GeV2 for 4 different t values. The curves are the results of the fit from the leading twist DVCS fitter code of ref. [7]. Φ is the azimuthal angle between the leptonic and hadronic planes, have been extracted for 3 bins in Q2 . These results are shown in fig. 1 for < Q2 >=2.3 GeV2 , the highest Q2 reached in the experiment, where the precision of the data can be remarked (a few percent staistical uncertainties on the unpolarized cross sections). The solid curves show the result of the fit to these high precision data based on the leading twist handbag diagram DVCS amplitude, following the procedure developped in ref. [7]. From these fits, based therefore on the eight CFFs considerede as free parameters, first model independent contraints on the Im(H) and Re(H) CFFs could be extracted, the two observables measured by the Hall A collaboration showing, at this kinematics, a particularly high sensitivity to the H GPD [5,7]. Experiment E-00-113, using the JLab Hall B CLAS spectrometer, has measured the beam spin asymmetry, i.e. the ratio of the beam-polarized
0
0.5
1
1.5 0
0.5
1
1.5 0
0.5
-t (GeV2)
Figure 2. Black circles : beam spin asymmetry at Φ = 90o as a function of t for different (xB ,Q2 ) bins, as measured by the JLab CLAS collaboration [8]. Green triangles are the results extracted from the Hall A cross sections measurements [6]. The red square is an earlier result from the CLAS collaboration [9]. to the unpolarized cross sections, of the same DVCS process, over the largest-ever phase space for this reaction [8]. Fig. 2 shows these results along with some theoretical predictions. The blue solid curves are the result of a twist-2 DVCS GPD calculation based on the so-called VGG model [10,11]. The blue dashed curves are the result of the corresponding twist-3 calculation. It can be seen that although the most general trends of the data are reproduced, some modifications to this particular model are clearly needed, which is a conclusion which was also reached in ref. [7]. Beam spin asymmetries provide less constraints for a model independent fit than normalized cross sections and it is currently a subject of study to see to what extent the GPD information, dominantly H, can be extracted. The dashed black curve is the result of a Regge calculation [12] for the DVCS process, based on meson exchanges, i.e.
M. Guidal / Nuclear Physics B (Proc. Suppl.) 181–182 (2008) 62–65
not based on GPDs. It gives a fair description of the data up to Q2 =2.3 GeV2 . The question can be raised whether, up to this Q2 , the two approaches, GPDs and Regge, are orthogonal and incompatible or parallel and dual. As just discussed, the beam polarisation observables are particularly sensitive to the H GPD. In order to access the other CFFs, other experimental observables are needed. In particular, it is shown in ref. [7] that by measuring all unpolarized, beam and target single polarized observables and associated doubly polarized observables, all eight CFFs can be extracted. Such an experimental program has already started with the measurement of various observables. The precision of these measurements is still limited mainly due to the fact that they are integrated over relatively large (xB , Q2 , t) phase space domains, much larger than the ones of the JLab Hall A and Hall B beam polarized data just presented. It might therefore be still a bit preliminary to include them in a global fit procedure, although this is work in progress in the framework of ref. [7]. The HERMES collaboration [13,14] has for instance measured the proton DVCS beam charge asymmetry (see fig. 3) which is sensitive uniquely ˜ to the real part CFFs (except for Re(E)). Also, the proton longitudinally polarized target asymmetry (see fig. 4) has been measured by the CLAS collaboration [15], which is particularly sensitive ˜ [5,7]. These data allow for instance to to Im(H) clearly determine the sign of this latter CFF. Very recently, first transversally polarized target asymmetries have also been measured by the HERMES collaboration [14] which carry a strong sensitivity to Im(E). Let us also mention that a first measurement of the beam spin asymmetry for DVCS on the neutron has been published [16] by the JLab Hall A collaboration. In the long term, with higher precision, this kind of data will allow a quark flavor decomposition of the GPDs, adding therefore “flavor” to our “vision” of the nucleon. All these present data are very encouraging, give first insights on the nucleon GPDs and allow to test the CFFs fitting and extraction procedures. The experimental program must however clearly be continued so as to provide a wide and
AC
64
0.2 0.1 0 -0.1 -0.2 0
0.5
1
1.5
2
2.5
3
|φ| (rad) Figure 3. The proton DVCS beam charge asymmetry as a function of Φ, measured by the HERMES collaboration. The solid curve shows a fit to the data : A+Bcos Φ+Ccos 2Φ+Dcos 3Φ. The “pure” cos Φ component is shown by the dotted curve.
precise enough set of DVCS data and observables and allow to uniquely, unambiguously and modelindependently determine the eight leading-twist CFFs. At short term, numerous quality data are expected from JLab, with the 6 GeV beam for many channels and observables : for DVCS in particular, several experiment are planned for the next few years in Hall A [17] and B [18,19]. They aim at increasing (at least doubling) the statistics (and therefore, in particular, refining the binning), explore new kinematical domains for the (polarized and unpolarized) cross sections (and beam spin asymmetries) and also measure new observables such as the (longitudinal) target spin cross sections and asymmetries and the double target-beam spin asymetries. HERMES, with a 27 GeV beam, has recently finished taking data with a dedicated recoil detector which will ensure the exclusivity of the reaction. New beam charge asymetries and beam spin asymetries should be available in the next couple of years in a lower xB domain than at JLab [20]. After 2010, the COMPASS experiment at CERN also intends to study GPDs with a 200 GeV muon beam. Similarly to HERMES, a dedicated recoil detector will have to be installed in
M. Guidal / Nuclear Physics B (Proc. Suppl.) 181–182 (2008) 62–65
0.4
AUL
0.2 0 -0.2 -0.4 -0.6 0
50
100
150
φ
200
250 300 Degree
350
Figure 4. The proton DVCS longitudinally polarized target spin asymmetry as a function of Φ, measured by the CLAS collaboration. The solid curve shows a fit to the data : Asin Φ+Bsin 2Φ. The sin 2Φ term is compatible with zero. The dashed curve is the VGG model prediction, based ˜ with twist-3 on the contributions of H and H, contribution included. The dotted curve shows ˜ the asymmetry when H=0 and therefore shows ˜ the sensitivity of this observable to H.
order to detect all the particles of the final state DVCS and ensure the exclusivity of the process. It will have the unique feature of accessing very small xB at sufficiently large Q2 . In the longer term (> 2013), the upgraded JLab, with a 12 GeV beam promises to yield a wealth of new experimental data, allowing to reach new kinematical domains, in particular, the higher Q2 regime, which is crucial for the understanding of preasymptotic effects and higher twists. Two experiments for DVCS [21,22] with the 12 GeV beam have already been approved by the JLab PAC. A ruch harvest of data related to DVCS and GPDs lies therefore in front of us and with the development of dedicated fitter codes and advances in theory, all hopes are permitted for a complete extraction of the nucleon GPD information. REFERENCES 1. K. Goeke, M. V. Polyakov and M. Vanderhaeghen, Prog. Part. Nucl. Phys. 47, 401 (2001).
65
2. M. Diehl, Phys. Rept. 388, 41 (2003). 3. A.V. Belitsky, A.V. Radyushkin, Phys. Rept. 418, 1 (2005). 4. X. Ji, Phys.Rev.Lett. 78, 610 (1997); Phys.Rev. D55, 7114 (1997). 5. A. Belitsky, D. Muller and A. Kirchner, Nucl. Phys. B 629, 323 (2002) 6. C. Mu˜ noz Camacho et al., Phys. Rev. Lett. 97, 262002 (2006). 7. M. Guidal, to be published by Eur. Phys. J. A, arXiv:0807.2355 [hep-ph] 8. F.-X. Girod et al., Phys. Rev. Lett. 100, 162002 (2008). 9. S. Stepanyan et al., Phys. Rev. Lett. 87, 182002 (2001). 10. M. Vanderhaeghen, P.A.M. Guichon, M. Guidal, Phys. Rev. D 60, 094017 (1999). 11. M. Guidal, M. V. Polyakov, A. V. Radyushkin and M. Vanderhaeghen, Phys. Rev. D 72, 054013 (2005). 12. J.-M. Laget, Phys. Rev. C 76, 052201 (2007). 13. A. Airapetian et al., submitted to publication, hep-ex/0605108 14. A. Airapetian et al., JHEP 0806, 066 (2008). 15. S. Chen et al., Phys. Rev. Lett. 97, 072002 (2006). 16. M. Mazouz et al., Phys. Rev. Lett. 99, 242501 (2007). 17. JLab approved experiment E-07-007; spokespersons : C. Munoz Camacho, J. Roche, C. Hyde-Wright and P.-Y. Bertin. 18. JLab approved experiment E-06-003; spokespersons : V. Burkert, L. Elhouadrhiri, M. Gar¸con, R. Niyazov and S. Stepanyan. 19. JLab approved experiment E-05-114; spokespersons : A. Biselli, L. Elhouadrhiri, K. Joo and S. Niccolai. 20. R. Kaiser et al., “A large acceptance recoil detector for HERMES”, Addendum to the Proposal DESY PRC 97-07, HERMES 97-032. 21. JLab approved experiment E-12-06-114; spokespersons : C. Hyde-Wright, B. Michel, C. Munoz Camacho and J. Roche. 22. JLab approved experiment E-12-06-119; spokespersons : V. Burkert, L. Elouadrhiri, M. Gar¸con, M. Holtrop, D. Ireland, K. Joo, W. Kim, F. Sabatie.