Nuclear Physics B (Proc. Suppl.) 164 (2007) 9–16 www.elsevierphysics.com
From Inclusive Scattering to Exclusive Reactions – recent results from HERMES B. Seitza a
(On behalf of the HERMES collaboration)
II. Physikalisches Institut, University of Giessen, 35392 Giessen, Germany
Single-spin asymmetries for semi-inclusive electroproduction of charged pions in deep-inelastic scattering of positrons are measured for the first time with transverse target polarization. They provide access to the transversity distribution via the Collins mechanism and the previously unmeasured Sivers function. The comparison of this data to similar data taken with longitudinally polarized protons provides insight into subleading-twist contributions. A second class of reaction promising new insights into the structure of the nucleon, hard exclusive electroproduction of real photons (named Deeply Virtual Compton Scattering) or mesons closely linked to the novel formalism of Generalized Parton Distributions is studied. The data were accumulated by the HERMES experiment at DESY scattering the HERA 27.6 GeV electron or positron beam off longitudinally or transversely polarized hydrogen targets.
The angular momentum structure of the nucleon is one of the central questions of present hadron physics. The spin of the nucleon is composed of the spin and orbital 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 inclusive and semi-inclusive processes[1]. Impressive results on the contribution of different quark flavours to the nucleon spin were obtained recently[2]. Deep Inelastic Scattering (DIS) probes the substructure of hadrons by the absorption of a spacelike virtual photon by a quark. Interpreting these results in terms of the Parton Model using the infinite momentum frame and averaging over intrinsic transverse momenta reveals that the structure of the nucleon at leading twist is described by three structure functions. Two of these have been experimentally explored in some detail – the unpolarized quark density q(x) and the helicity density Δq(x) reflecting the probability of finding the helicity of quark to be the same as that of the target nucleon. Interpreted in the same helicity basis the third structure functions known as transversity δq(x) is related to a forward scattering amplitude involving a helicity flip of quark and target nucleon. It has no probabilistic inter0920-5632/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2006.11.104
⊥ S
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Figure 1. The definition of the azimuthal angles of the hadron production plane and the relevant component of the target spin, relative to the plane containing the momenta of the incident and scattered lepton.
pretation in this basis[3–5]. However, interpreted in the so called transversity basis, it is a number density. Since transversity is chiral-odd and hard interactions conserve chirality, it can only be probed by a process involving some additional chiral-odd object, e.g. the chiral-odd Collins fragmentation function[6]. The transversity and helicity densities may dif-
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fer as relativisticly boosts and rotations do not commute. Transversity measurements will thus provide insights into the last remaining leading twist structure of the nucleon and probe its relativistic structure. A non-vanishing transversity distribution manifests itself in single spin asymmetries measured in semi-inclusive deep inelastic scattering as a function of the angle φ defined between the scattering and production planes. It has been noted, however, that another mechanism – the Sivers mechanism[7], involving unpolarized quarks in a transversely polarized nucleon– contributes or leads to SSA as well. Whereas these two reaction mechanism are inherently indistinguishable in semi-inclusive reaction on a longitudinally polarized target, measurements on a transversely polarized target allow to disentangle contributions from transversity and the Sivers mechanism. The Sivers mechanism –described by the naive time reversal odd Sivers function– is of great interest in its own right as several interpretations conclude that a non-vanishing Sivers asymmetry indicates a sizeable orbital angular momentum of the quarks inside the nucleon[8]. HERMES provides first measurements of semi-inclusive DIS on transversely polarized protons. These allow to disentangle the Sivers and Collins mechanism. Comparing to previous measurements longitudinally polarized protons yields information on the strength of sub-leading twist contributions to these measurements. A second class of reactions promising new insights into the structure of the nucleon, hard exclusive electroproduction of real photons (named Deeply Virtual Compton Scattering) or mesons is studied by HERMES in great detail. They will be the focus of the remaining running period using a detector upgrade dedicated to study these reactions. Interpreted within the framework of Generalized Parton Distributions (GPDs) these measurements provide the only viable access to orbital angular momentum. 1. Transversity Transversity and the Sivers effect can be observed in measuring single spin asymmetries in
III
Figure 2. Virtual photon asymmetries for pions as labelled as a function of x, z and Ph⊥ . The error bars represent the statistical uncertainties, while the lower band represents the maximal systematic uncertainty due to acceptance and detector smearing as well as possible contributions from cos φ-moments of the unpolarized cross section.
semi-inclusive electroproduction of hadrons on a transversely polarized target. While on a longitudinally polarized target a distinction between the Collins mechanism related to transversity and the Sivers mechanism is not possible, the additional degree of freedom provided by the targets azimuthal angle φs provide distinctive signature: sin (φ − φS ) for the Sivers mechanism, sin (φ + φS ) for the Collins mechanism. HERMES studied these asymmetries for pions running a transversely polarized hydrogen target[11]. This measurement has for the first time clearly disentangled two very different physical effect that were indistinguishable in previous data[9,10]. Their signals were extracted as distinctive Fourier component of the dependence of
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of a correlation between the transverse polarization of the target nucleon and the intrinsic transverse momentum of the quarks. Data on the so called Sivers asymmetry as a function of x,z and Ph⊥ for π + and π − are shown in Fig 3. The averaged Sivers asymmetry is significantly positive at 0.017 ± 0.004 for π + , providing the first evidence for a T-odd parton distribution function appearing in leptoproduction. The π − asymmetry is consistent with zero: 0.004 ± 0.005. Since the π + asymmetry is dominated by u quarks, its positive value with the definition of azimuthal angels used in this analysis implies a negative value for the Sivers function of this flavour. The apparently negative value of the naively T-odd Sivers distribution function describing this correlation can be later compared to its appearance in polarized Drell Yan processes, where it is predicted to have the opposite signs due to fundamental time reversal invariance in QCD. Figure 3. Sivers asymmetries for the pions as labelled as a function of x,z and Ph⊥ . The uncertainties are shown as in Fig.2
the target-spin asymmetry on the azimuthal angles of both the pion and the target spin axis about the virtual photon direction and relative to the lepton plane. One signal is interpreted to arise from the the transverse polarization of quarks in the target as revealed by the influence on the fragmentation of the struck quark. New preliminary data on the extracted so called Collins asymmetries as a function of x, t and Ph⊥ are shown in Fig. 2 [12]. The averaged Collins asymmetry for π + is positive at 0.020±0.007, while is is negative at −0.032±0.008 for π − . These opposite signs can be expected if the transversity densities resemble the helicity densities, although the absolute magnitude of the π − asymmetry is surprising. It appears that fragmentation that is disfavoured in terms of quark flavour has a surprising importance, and enters with a sign opposite to the that of the favoured case. The other signal can be interpreted in terms
1.1. Subleading-twist effects These data can also be used to eliminate the contribution due to the transverse spin component from the measured asymmetries on a longitudinally polarized hydrogen target, thereby allowing for the first time the pure extraction of the subleading twist contribution [13]. Knowledge of this subleading contribution is essential to any extraction of information on the transversity distribution or Collins fragmentation function for data with longitudinal target polarization. For the extraction of the subleading-twist contribution the lepton axis asymmetry on a longitudinally polarized hydrogen target[10] were reanalysed to have the same binning in x and z as in the measurement on a transversely polarized target[11]. The moments for charged pions are shown as functions of x and z in Fig.4. The resulting longitudinal photon-axis moments are significantly positive for π + and consistent with zero for π − . Hence in the case of the π + this subleading twist contribution dominates the measurement on a target that is longitudinally polarized with respect to the beam direction. It becomes clear that those asymmetries cannot be interpreted in terms of only the Collins fragmentation function or the Sivers function.
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real photons (Deeply Virtual Compton Scattering (DVCS)), electroproduction of pseudo scalar and vector mesons, namely the π + and the ρ◦ . Accessing these GPDs poses a unique experimental challenge due to small cross sections and high resolution requirements. Several key experiments paving the road towards GPDs were defined[15] placing HERMES in an ideal position to pioneer these measurements:
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Figure 4. The various azimuthal moments appearing in the measurement of single-spin asymmetries on a longitudinally polarized target for charged pions as a function of x and z. The open symbols are the measured lepton axis moments. The closed symbol is the subleading twist contribution to the measured lepton-axis asymmetries on a longitudinally polarized target.
2. Hard Exclusive Reactions Measuring hard exclusive reactions provides a new tool in understanding the structure of nucleons in terms of so called generalized parton distributions. This new class of functions combines aspects from diverse approaches in understanding the nucleon like form factor measurements, ordinary parton distribution functions or even inverse reactions. At leading order, four of these functions are needed to completely describe the nucleon, the unpolarized GPDs H and E and the ˜ and E, ˜ each of them dependpolarized GPDs H ing on x, the momentum transfer t and the so called skewness ξ. The Q2 -evolution is governed by the conventional DGLAP evolution. Hard exclusive reaction in the context of the present article comprise the electroproduction of
• Transverse Target Spin asymmetry for Deeply Virtual Compton Scattering, Vector meson production and the production of pseudo scalar mesons • cross section measurements for all classes of hard exclusive reactions The present HERMES set-up allows only the detection of the scattered lepton and the produced photon or meson. DVCS events are then identified by requiring the missing mass MX to be close to the mass of the proton. A similar technique can be applied by requiring the missing energy ΔE to be small for the hard exclusive production of vector mesons. Accessing hard exclusive pion production on the proton is feasible by subtracting the normalized yield of π − from the π + –yield for low missing masses. These methods were carefully cross checked by a complete Monte Carlo simulation of the set-up. 2.1. Deeply Virtual Compton Scattering The cleanest process to measure GPDs is Deeply Virtual Compton Scattering, the hard electroproduction of a real photon [17]. This process leads to the same final state as the BetheHeitler 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 inter-
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ference term [18] √ 1 1 4 2 m e6 ˜ 1,1 ) √ (M cos φ I = ± t Q xB 1 − xB ( − 1) 1+ ˜ 1,1 ) (M − Pl sin φ depends on the charge and the helicity of the incident lepton, where +(−) denotes a negatively (positively) charged lepton with polarization Pl . ˜ 1,1 is the linear combination of The quantity M DVCS helicity amplitudes that contribute in the case of polarized beam and unpolarized target. The DVCS helicity amplitudes depend on the nucleon form factors and certain combinations of GDPs. Four observables making use of this interference were studied at HERMES so far: the beam helicity asymmetry ALU , target spin asymmetries on a longitudinally and transversely polarized target as well as the beam charge asymmetry AC on a variety of unpolarized targets as a function of the azimuthal angle φ between the lepton scattering plane and the production plane. Recently a third observable, the target-spin asymmetry on a longitudinally polarized hydrogen target was added. The beam charge asymmetry AC provides access to the real part of the interference term. It is expected to show a cos φ behaviour [19]. Preliminary HERMES data on the proton are shown in Fig.5. The remaining sin φ term is attributed to a beam helictiy asymmetry stemming from a non-balance of the beam helicity in the data sample Access to the imaginary part of the interference term is provided by measuring the beam helicity asymmetry ALU . Measurements of ALU on the proton were carried out by HERMES [20] and CLAS [21]. New preliminary HERMES results on the proton based on HERMES data collected in 2000 are shown in Fig.6. The asymmetry indeed shows the expected sin φ modulation. The amplitude measured is consistent with the already published results. A third asymmetry in DVCS was extracted using a longitudinally polarized target and a beam helictiy balanced data sample rendering the beam
Figure 5. Beam-charge asymmetry AC measured on the proton showing the expected cos φ behaviour. The remaining sin φ contribution is attributed to a non-zero beam-spin asymmetry stemming from analysing a non-balance in the beam-helicity in the data sample. Exclusive events are defined through a missing mass constrained Mx < 1.7 GeV.
factually unpolarized. This asymmetry is expected to be dominated by sin φ with and admixture of sin 2φ components stemming from higher twist. The sin φ term is proportional to the GPDs ˜ and E. ˜ Since H can be measured by the H,H ˜ will dominate the beam-spin asymmetry and E hard exclusive production of π + , measuring the longitudinal target-spin asymmetry will provide ˜ The preliminary results of this meaaccess to H. surement is depicted in figure 7. Significant contributions from sin φ and sin 2φ components could be extracted. 2.2. Hard Exclusive Meson Production Generalized Parton Distributions can also be accessed in the hard electroproduction of mesons.
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Figure 6. Beam-spin asymmetry ALU as a function of the azimuthal angle φ for the hard exclusive electroproduction of photons off the proton. Exclusive events are defined through a missing mass constrained Mx < 1.7 GeV.
The meson wave function will act as a spin and flavour filter in hard exclusive electroproduction of pseudo-scalar and vector-mesons. Hence measurements of this processes are extremely valuable in accessing GPDs. While exclusive vector meson production is only sensitive to unpolarized GPDs, pseudo-scalar meson production is sensitive to polarized GPDs without the need for a polarized target or beam. Different observables like cross sections or single spin asymmetries are able to select different combinations of GPDs. Single Spin asymmetries were already presented by HERMES [22]. A more refined analysis also allows the extraction of the cross section [23]. The data –still uncorrected for radiative effects– are presented in Fig.8. They are compared to calculations of the longitudinal part of the cross section computed by a GPD model[24]. At HERMES the separation of the transverse and longitudinal components of the
Figure 7. Target-spin asymmetry AU L as a function of the azimuthal angle φ for the hard exclusive electroproduction of photons off the proton. Exclusive events are defined through a missing mass constrained Mx < 1.7 GeV. The data show significant contributions from sin φ and sin 2φ components.
cross section is not feasible. Since the transverse part of the cross section, however, is predicted to be power suppressed with respect to the longitudinal one, the data are larger Q2 are expected to be dominated by the longitudinal part. The full lines in Fig. refpi show the leading order calculation, the dashed lines include power corrections due to the intrinsic transverse momenta of the partons and due to soft overlap type contributions. All calculation were performed at mean x and Q2 and integrated over t. The Q2 dependence is in general agreement with the data. While the leading order calculations underestimate the data, the evaluation of power corrections appears to be overestimated. Access to the GPD E can be gained through measuring the transverse target-spin asymme-
B. Seitz / Nuclear Physics B (Proc. Suppl.) 164 (2007) 9–16
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try in hard exclusive electroproducion of vector mesons where the asymmetry depends linearly on E [15]. This observable also provides sensitivity to the total angular momentum carried by the u-quarks[25]. Preliminary HERMES data are shown in Fig.9 as a function of x. The observed behaviour is in accordance with theoretical expectations. Further measurement will allow to separate the asymmetry into its longitudinal and transverse photon components.
L VGG: LO L VGG: LO+power corrections 0
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Q ( GeV )
Figure 8. Total cross section for the exclusive π + production as a function of Q2 for three different x ranges and integrated over t. The inner error bars represent the statistical uncertainty and the outer error bars the quadratic sum of statistical and systematic uncertainty. The curves present calculations based on a GPD model[24].
Figure 9. Transverse target-spin asymmetry for hard exclusive electroproduction of the ρ◦ as a function of x. The x-behaviour of the data is according to theoretical expectations.
Single spin asymmetries for semi-inclusive electroproduction of charged pions in deep inelastic scattering of positrons are measured for the first time with transverse target polarization. The extracted Fourier components as a function of the azimuthal angle of the pion φ and the target spin axis φs about the virtual photon direction and relative to the lepton scattering plane are interpreted as a signal of the previously unmeasured quark transversity distribution in conjunction with the Collins fragmentation function and an asymmetry arising from a correlation between the transverse polarization of the target nucleon and the intrinsic transverse momentum of the quark, are represented by the previously unmeasured Sivers distribution function. Evidence for both signals is observed. The extraction of subleading-twist contributions was done by comparing these results on a transversely polarized target with data taken previously on a longitudinally polarized target. While the extracted subleading-twist contribution for π − is consistent with zero, large effects were observed in case of the π + showing that these effects are large and can –at HERMES kinematics– be comparable to leading-twist effects. In addition, HERMES provided data on key reactions to access Generalized Parton Distributions. Beam charge asymmetries were measured in DVCS off hydrogen. The observed asymmetries show the cos φ-behaviour expected from interference between Deeply Virtual Compton Scattering and the Bethe-Heitler process. They provide access to DVCS at the amplitude level.
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HERMES measured asymmetries in beam spin for hard electroproduction of photons in deep inelastic scattering off hydrogen. These data exhibit the predicted sin φ-behaviour. Also, single spin asymmetries in DVCS off a longitudinally polarized hydrogen target were extracted. They show a significant sin φ and sin 2φ component. Data analysis for single spin asymmetries in DVCS off a transversely polarized target is ongoing and promises to be particularly sensitive to the total angular momentum carried by u-quarks. Results were presented for hard exclusive π + production on the proton. The preliminary total cross section has been measured as a function of Q2 for different values of x and has been compared to calculations based on GPD models. Data from the transverse target running are under analysis which will allow a direct comparison to GPD models. HERMES presents the first measurements of the transverse target-spin asymmetry in hard exclusive vector mesons providing a direct handle on the GPD E and the total angular momentum of the u quark. Further analysis of these data providing a LT-separation allowing direct model comparisons is underway. A dedicated recoil detector to be installed in 2005 will provide new precision data on hard exclusive reactions extending the studies presented here [26]. REFERENCES 1. K. Rith, Prog. Part. Nucl. Phys. 49(2002) 245. 2. A. Airapetian et al.[HERMES Collaboration], Phys. Rev. D 71 (2005) 012003 3. J. P. Ralston, D. E. Soper, Nucl. Phys. B 152 (179) 109 4. X. Artru, M. Mekfhi, Z. Phs. C 45 (1990) 669 5. R. L. Jaffe, X. Ji, Nucl. Phys. B 375 (1992) 527 6. J. C. Collins, Nucl. Phys. B 396 (1993) 161 7. D. W. Sivers, Phys. Rev. D 41 (1990) 83 8. M. Burkhardt hep-ph/0505189 9. A. Airapetian et al.[HERMES Collaboration], Phys. Rev. D 64 (2001) 097101 10. A. Airapetian et al.[HERMES Collaboration],
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