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Deeply virtual Compton scattering and hard exclusive pion production measured by HERMES
ELSEVIER
Nuclear Physics A721 (2003) 785c-788~ www.elsevier.com/locate/npe
Deeply Virtual Compton Scattering and Hard Exclusive Pion Production measured by HERMES B. Seitz’on
behalf of the HERMES
“II. Physikalisches
Institut,
University
Collaboration of Giegen, 35392 Giegen, Germany
Sizeable beam helicity and charge asymmetries arising from the Deeply Virtual Compton Scattering (DVCS) p recess in the hard electro-production of real photons have been measured for the first time by HERMES. A large asymmetry using an unpolarised beam and a longitudinal polarised target has been observed in the exclusive electro-production of ?y+. Measurement of these reactions provides access to the presently unknown Generalised Parton Distributions (GPD) of the nucleon. 1. Introduction The nature of the structure of polarised nucleons is one of the central questions of present hadronic physics. The nucleon is a composite fermion and its spin should be obtained from the spins and angular momenta of its constituents, the quarks and gluons. The HERMES experiment at DESY was designed to study the spin structure of the nucleon using the Deep Inelastic Scattering (DIS) process [l]. Recently theoretical interest has been growing about the nature of the unknown Generalised Parton Distribution (GPD) functions of the nucleon which appear in the factorisation scheme of hard exclusive processes [2]. Th ese GPDs are a natural generalisation of the well know Parton Density Functions (PDF) in inclusive deep inelastic scattering. Generalised Parton Distributions were introduced in a formalism which provides a unified theoretical description of exclusive reactions in the Bjorken regime. May be most of the recent interest and activity in this field has been triggered by the observation of Ji, who showed that the second moment of these GPDs provides an access to the contribution of the spin and orbital angular momentum of the quarks to the nucleon spin [3]. 2. Deeply
Virtual
Compton
Scattering
The cleanest process to measure Generalised Parton Distributions is DVCS, the electroproduction of a real photon [4]. This process, however, leads to the same final state as the BH process. Hence, these two processes interfere quantum-mechanically. At HERMES energies, the comparatively large BH amplitude serves as a lever arm to access the small DVCS amplitude. The leading-order and leading-twist interference term:
0375-9474/03/% -‘see front matter 0 2003 Elsevier Science B.V doi:10.1016&0375-9474(03)01181-3
All rights reserved
786~
B. Seitz/Nuclear Physics A721 (2003) 785c-788~
-0.4
~,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, -3
$ WI
-2
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2
3
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Figure 1. The left plot shows preliminary HERMES data for the beam charge asymmetry AC. The curve represents a fit to the data. The right plot shows preliminary HERMES data for the azimuthal dependence of the single spin asymmetry ALU together with the data published in Ref. [7]. The dashed line represents a fit to the new data.
depends on the charge and the helicity of the incident lepton, where +(-) denotes a negatively (positively) charged lepton with polarisation P, [5]. The quantity A @ is the linear combination of DVCS helicity amplitudes that contribute in the case of polarised beam and unpolarised target. Two observables making use of this interference were studied at HERMES so far: the beam helicity asymmetry and the beam charge asymmetry on an unpolarised target as a function of the azimuthal angle 4 between the lepton scattering plane and the hadronic plane. The real part of the interference term can be accessed via the beam charge asymmetry
N+(4) - N-(4) Ac(4) = N+(4) + N-(c/g’ where N+(N-) represent the luminosity-normalised yields for the corresponding beam charges. The beam charge asymmetry AC is expected to show a COST behaviour. The preliminary HERMES result is shown in the left plot of Fig. 1, where P2 = A?‘. A clear cos+ behaviour is observed. A value of A?’ = 0.11 f 0.04 f 0.03 is found. The total uncertainty is dominated by the low statistics electron data sample. Details of this analysis can be found in Ref. [S]. An improved measurement is expected from HERMES Run II, where extended periods with both beam charges are foreseen. The sin 4 moment of the asymmetry of this interference term with respect to the beam polarisation provides information on the imaginary part of the DVCS amplitude combi-
B. Seitz/Nuclear Physics A721 (2003) 785c-788~
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.
~~~~~~
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x
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-0.6 ’
’
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Figure 2. Cross section asymmetry AuL(4) averaged over z, Q2 and t for the reaction e++p’+ e++n+x+. The curve is the best fit to the data by A(+) = AUL. sin 4 where AuL = -0.18 f 0.05 and the reduced X2 of the fit is 0.8. The error band below represents the combined systematic uncertainty.
@WadI
nation A&l.
The associated asymmetry
ALU is defined as
N+(4)- N-(4) ALU(4) = (,A,I, N+(4)+ N-(4)’ where N* represent the luminosity normalised yields of events with corresponding beam helicity states and ( ]Pham]) th e average magnitude of the beam polarisation. Data on the beam helicity asymmetry were recently published by HERMES [7]. These data compare favourably with calculations within the GPD framework. Since then, new data have been analysed. The preliminary results are shown together with the published data in the right plot of Fig. 1. The two data sets are in agreement. 3. Exclusive
electroproduction
of rf
HERMES has furthermore measured the single spin asymmetry with unpolarised beam and longitudinally polarised target in the exclusive production of ?r+ on the proton [8]. Exclusive events were selected by requiring the missing mass of the reaction e+ + p’ -+ e+ + A+ +X to correspond to the nucleon mass. Background contributions were estimated and subtracted using the electroproduction of 7c-, which cannot occur exclusively on a proton target. The 4 dependence of the polarised cross section appears most clearly in the cross section asymmetry defined similar to eq. 3 where Phlr,,, gets replaced by the average longitudinal polarisation of the target Ptorget This cross section asymmetry integrated over z,Q2 and t is shown in Fig. 3. The data show a large asymmetry in the distribution of the azimuthal angle 4 and a clear sin4 dependence of the cross section is seen. A fit to this dependence yields AuL = 0.18 f 0.05 f 0.01 with a reduced X2 of 0.8. A remaining asymmetry from semi-inclusive events as well as the uncertainty in the background yield and target polarisation has been included in the systematic uncertainty. Theoretical estimates of the observed asymmetry are not yet available. The asymmetry is surprisingly large and its sign is opposite to what
788~
B. Seitz/Nuclear Physics A721 (2003) 785c-788~
can be expected from a transverse polarisation component of the target with respect to the virtual photon. This suggests, that the dominant contribution to the measured asymmetry is of twist-3 [9].
4. Conclusion The HERMES experiment has provided the first data for the beam charge and beam spin asymmetries in DVCS. The beam charge asymmetry exhibits a clear cos bbehaviour. The single spin asymmetry using a polarised positron beam and an unpolarised hydrogen target could be extracted as well. A clear sin& shape is visible and compares favourably with a twist-3 calculation. This reaction is ideally suited to be analysed in the novel framework of GPDs and shows satisfactory agreement with present calculations. Furthermore, a sin d, asymmetry in the hard exclusive electro-production of w+ using a polarised target and an unpolarised beam was observed. Its sign is opposite of what is expected from the transverse polarisation component of the target nucleon with respect to the virtual photon direction. Although no quantitative prediction is available, this suggests that a dominant twist-3 contribution is necessary to explain the data. HERMES will continue to study hard exclusive reactions in the near future. The first measurements expected will be of hard exclusive meson production on the transversely polarised target. In the year 2004 HERMES will install a recoil detector around the target cell with special emphasis to improve kinematical resolution as well as the exclusivity and thus the systematical accuracy of the present DVCS measurement [lo]. The planned running period using this detector will also enhance the statistical precision significantly. Measurements with these detector will allow a fine binning in all relevant kinematical variables and a large sensitivity to model calculations [ll]. The present data, in combination with the new data expected from future HERMES measurements will provide one of the first tests of QCD factorisation theorems for exclusive processes and give access to GPDs.
REFERENCES 1. 2.
cf. contributions by H. Jackson and E.C. Aschenauer, these proceedings. D. Miiller et al., Fortschr. Phys. 42 (1994) 101; A.V. Radyushkin, Phys. Rev. D 56 (1997) 5524; X. Ji Phys. R ev. D 55 (1997) 7114; J. Collins et al. Phys. Rev. D 56 (1997) 2983. 3. X. Ji Phys. Rev. Lett 78 (1997) 610. 4. K. Goecke et al. Prog. Part. Nucl. Phys. 47 (2001) 401. 5. M. Diehl et al., Phys. Lett. B 411 (1997) 193. 6. F. Ellmghaus [HERMES Co11a b oration], arXiv:hep-ex/0207029. 7. A. Airapetian et al. [HERMES Collaboration], Phys. Rev. Lett. 87 (2001) 182001. 8. A. Airapetian et al. [HERMES Collaboration], Phys. Lett. B 535 (2002) 85. 9. A. V. Belitsky, D. Miiller, Phys. Lett. B 513 (2001) 349. 10. HERMES Recoil group, Technical Design Report,DESY PRC 01-01, 2002. 11. V. A. Korotkov and W. D. Nowak, Eur. Phys. J. C 23 (2002) 455; V. A. Korotkov and W. D. Nowak, arXiv: hep-ph/0207103.
Nuclear Physics A721 (2003) 785c-788~ www.elsevier.com/locate/npe
Deeply Virtual Compton Scattering and Hard Exclusive Pion Production measured by HERMES B. Seitz’on
behalf of the HERMES
“II. Physikalisches
Institut,
University
Collaboration of Giegen, 35392 Giegen, Germany
Sizeable beam helicity and charge asymmetries arising from the Deeply Virtual Compton Scattering (DVCS) p recess in the hard electro-production of real photons have been measured for the first time by HERMES. A large asymmetry using an unpolarised beam and a longitudinal polarised target has been observed in the exclusive electro-production of ?y+. Measurement of these reactions provides access to the presently unknown Generalised Parton Distributions (GPD) of the nucleon. 1. Introduction The nature of the structure of polarised nucleons is one of the central questions of present hadronic physics. The nucleon is a composite fermion and its spin should be obtained from the spins and angular momenta of its constituents, the quarks and gluons. The HERMES experiment at DESY was designed to study the spin structure of the nucleon using the Deep Inelastic Scattering (DIS) process [l]. Recently theoretical interest has been growing about the nature of the unknown Generalised Parton Distribution (GPD) functions of the nucleon which appear in the factorisation scheme of hard exclusive processes [2]. Th ese GPDs are a natural generalisation of the well know Parton Density Functions (PDF) in inclusive deep inelastic scattering. Generalised Parton Distributions were introduced in a formalism which provides a unified theoretical description of exclusive reactions in the Bjorken regime. May be most of the recent interest and activity in this field has been triggered by the observation of Ji, who showed that the second moment of these GPDs provides an access to the contribution of the spin and orbital angular momentum of the quarks to the nucleon spin [3]. 2. Deeply
Virtual
Compton
Scattering
The cleanest process to measure Generalised Parton Distributions is DVCS, the electroproduction of a real photon [4]. This process, however, leads to the same final state as the BH process. Hence, these two processes interfere quantum-mechanically. At HERMES energies, the comparatively large BH amplitude serves as a lever arm to access the small DVCS amplitude. The leading-order and leading-twist interference term:
0375-9474/03/% -‘see front matter 0 2003 Elsevier Science B.V doi:10.1016&0375-9474(03)01181-3
All rights reserved
786~
B. Seitz/Nuclear Physics A721 (2003) 785c-788~
-0.4
~,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, -3
$ WI
-2
-1
0
1
2
3
9 PadI
Figure 1. The left plot shows preliminary HERMES data for the beam charge asymmetry AC. The curve represents a fit to the data. The right plot shows preliminary HERMES data for the azimuthal dependence of the single spin asymmetry ALU together with the data published in Ref. [7]. The dashed line represents a fit to the new data.
depends on the charge and the helicity of the incident lepton, where +(-) denotes a negatively (positively) charged lepton with polarisation P, [5]. The quantity A @ is the linear combination of DVCS helicity amplitudes that contribute in the case of polarised beam and unpolarised target. Two observables making use of this interference were studied at HERMES so far: the beam helicity asymmetry and the beam charge asymmetry on an unpolarised target as a function of the azimuthal angle 4 between the lepton scattering plane and the hadronic plane. The real part of the interference term can be accessed via the beam charge asymmetry
N+(4) - N-(4) Ac(4) = N+(4) + N-(c/g’ where N+(N-) represent the luminosity-normalised yields for the corresponding beam charges. The beam charge asymmetry AC is expected to show a COST behaviour. The preliminary HERMES result is shown in the left plot of Fig. 1, where P2 = A?‘. A clear cos+ behaviour is observed. A value of A?’ = 0.11 f 0.04 f 0.03 is found. The total uncertainty is dominated by the low statistics electron data sample. Details of this analysis can be found in Ref. [S]. An improved measurement is expected from HERMES Run II, where extended periods with both beam charges are foreseen. The sin 4 moment of the asymmetry of this interference term with respect to the beam polarisation provides information on the imaginary part of the DVCS amplitude combi-
B. Seitz/Nuclear Physics A721 (2003) 785c-788~
787c
0.6 0.4 n 0.2 -
‘>
0 -
.
~~~~~~
If..
-0.2 -0.4 !I
x
1’
-0.6 ’
’
’
’
-3
-2
-1
0
1
’
’
2
3
Figure 2. Cross section asymmetry AuL(4) averaged over z, Q2 and t for the reaction e++p’+ e++n+x+. The curve is the best fit to the data by A(+) = AUL. sin 4 where AuL = -0.18 f 0.05 and the reduced X2 of the fit is 0.8. The error band below represents the combined systematic uncertainty.
@WadI
nation A&l.
The associated asymmetry
ALU is defined as
N+(4)- N-(4) ALU(4) = (,A,I, N+(4)+ N-(4)’ where N* represent the luminosity normalised yields of events with corresponding beam helicity states and ( ]Pham]) th e average magnitude of the beam polarisation. Data on the beam helicity asymmetry were recently published by HERMES [7]. These data compare favourably with calculations within the GPD framework. Since then, new data have been analysed. The preliminary results are shown together with the published data in the right plot of Fig. 1. The two data sets are in agreement. 3. Exclusive
electroproduction
of rf
HERMES has furthermore measured the single spin asymmetry with unpolarised beam and longitudinally polarised target in the exclusive production of ?r+ on the proton [8]. Exclusive events were selected by requiring the missing mass of the reaction e+ + p’ -+ e+ + A+ +X to correspond to the nucleon mass. Background contributions were estimated and subtracted using the electroproduction of 7c-, which cannot occur exclusively on a proton target. The 4 dependence of the polarised cross section appears most clearly in the cross section asymmetry defined similar to eq. 3 where Phlr,,, gets replaced by the average longitudinal polarisation of the target Ptorget This cross section asymmetry integrated over z,Q2 and t is shown in Fig. 3. The data show a large asymmetry in the distribution of the azimuthal angle 4 and a clear sin4 dependence of the cross section is seen. A fit to this dependence yields AuL = 0.18 f 0.05 f 0.01 with a reduced X2 of 0.8. A remaining asymmetry from semi-inclusive events as well as the uncertainty in the background yield and target polarisation has been included in the systematic uncertainty. Theoretical estimates of the observed asymmetry are not yet available. The asymmetry is surprisingly large and its sign is opposite to what
788~
B. Seitz/Nuclear Physics A721 (2003) 785c-788~
can be expected from a transverse polarisation component of the target with respect to the virtual photon. This suggests, that the dominant contribution to the measured asymmetry is of twist-3 [9].
4. Conclusion The HERMES experiment has provided the first data for the beam charge and beam spin asymmetries in DVCS. The beam charge asymmetry exhibits a clear cos bbehaviour. The single spin asymmetry using a polarised positron beam and an unpolarised hydrogen target could be extracted as well. A clear sin& shape is visible and compares favourably with a twist-3 calculation. This reaction is ideally suited to be analysed in the novel framework of GPDs and shows satisfactory agreement with present calculations. Furthermore, a sin d, asymmetry in the hard exclusive electro-production of w+ using a polarised target and an unpolarised beam was observed. Its sign is opposite of what is expected from the transverse polarisation component of the target nucleon with respect to the virtual photon direction. Although no quantitative prediction is available, this suggests that a dominant twist-3 contribution is necessary to explain the data. HERMES will continue to study hard exclusive reactions in the near future. The first measurements expected will be of hard exclusive meson production on the transversely polarised target. In the year 2004 HERMES will install a recoil detector around the target cell with special emphasis to improve kinematical resolution as well as the exclusivity and thus the systematical accuracy of the present DVCS measurement [lo]. The planned running period using this detector will also enhance the statistical precision significantly. Measurements with these detector will allow a fine binning in all relevant kinematical variables and a large sensitivity to model calculations [ll]. The present data, in combination with the new data expected from future HERMES measurements will provide one of the first tests of QCD factorisation theorems for exclusive processes and give access to GPDs.
REFERENCES 1. 2.
cf. contributions by H. Jackson and E.C. Aschenauer, these proceedings. D. Miiller et al., Fortschr. Phys. 42 (1994) 101; A.V. Radyushkin, Phys. Rev. D 56 (1997) 5524; X. Ji Phys. R ev. D 55 (1997) 7114; J. Collins et al. Phys. Rev. D 56 (1997) 2983. 3. X. Ji Phys. Rev. Lett 78 (1997) 610. 4. K. Goecke et al. Prog. Part. Nucl. Phys. 47 (2001) 401. 5. M. Diehl et al., Phys. Lett. B 411 (1997) 193. 6. F. Ellmghaus [HERMES Co11a b oration], arXiv:hep-ex/0207029. 7. A. Airapetian et al. [HERMES Collaboration], Phys. Rev. Lett. 87 (2001) 182001. 8. A. Airapetian et al. [HERMES Collaboration], Phys. Lett. B 535 (2002) 85. 9. A. V. Belitsky, D. Miiller, Phys. Lett. B 513 (2001) 349. 10. HERMES Recoil group, Technical Design Report,DESY PRC 01-01, 2002. 11. V. A. Korotkov and W. D. Nowak, Eur. Phys. J. C 23 (2002) 455; V. A. Korotkov and W. D. Nowak, arXiv: hep-ph/0207103.