Gluon polarization in the nucleon from quasi-real photoproduction of high-pT hadron pairs

We present a determination of the gluon polarization Delta G/G in the nucleon, based on the helicity asymmetry of quasi-real photoproduction events, Q^2<1(GeV/c)^2, with a pair of large transverse-momentum hadrons in the final state. The data were obtained by the COMPASS experiment at CERN using a 160 GeV polarized muon beam scattered on a polarized 6-LiD target. The helicity asymmetry for the selected events is= 0.002 +- 0.019(stat.) +- 0.003(syst.). From this value, we obtain in a leading-order QCD analysis Delta G/G=0.024 +- 0.089(stat.) +- 0.057(syst.) at x_g = 0.095 and mu^2 =~ 3 (GeV}/c)^2.


Introduction
The decomposition of the nucleon spin in terms of the contributions from its constituents has been a central topic in polarized deep-inelastic scattering (DIS) for the last twenty years. The European Muon Collaboration study of the proton spin structure [1] has shown that the spin of the quarks only contributes to a small fraction ∆Σ of the proton spin. This result has been confirmed by several experiments on the proton, the deuteron, and 3 He, establishing ∆Σ between 20% and 30% [2,3], in contrast to the 60% expected in the quark-parton model [4].
Another contribution to the nucleon spin, ∆G, originates from the spin of the gluons. In inclusive DIS, it can only be determined from the Q 2 dependence of the spin structure function g 1 . Next-to-Leading Order (NLO) QCD analyses provide estimates for ∆G below or around unity at a scale of 3 (GeV/c) 2 . The precision of these fits is however strongly limited by the small Q 2 range covered by the data.
In semi-inclusive DIS or in proton-proton scattering, the final state can be used to select hard processes involving gluons from the nucleon. In polarized semi-inclusive DIS, the polarization ∆G/G of gluons carrying a fraction x g of the nucleon momentum is obtained from the cross-section helicity asymmetry of the photon-gluon fusion (PGF), γ * g → qq.
Two procedures have been proposed to tag this process. The first one consists in selecting open-charm events, which provides the purest sample of PGF events [5,6], but at a low rate. Another possibility is to select events with two jets at high transverse momentum, p T , with respect to the virtual photon direction or, in fixed-target experiments, two high-p T hadrons [7]. The latter procedure provides much larger statistics but leaves a significant fraction of background events in the selected sample. As a result, the cross-section helicity asymmetry A contains in addition to the contribution from PGF a contribution A bgd from the background processes: Here, R PGF is the fraction of PGF events andâ PGF LL ≡ d∆σ µg PGF /dσ µg PGF is the analyzing power of PGF that is the helicity asymmetry of the hard lepton-gluon scattering crosssection. This quantity is calculated from the leading order expressions of the polarized and unpolarized partonic cross-sections. On the other hand, R PGF and A bgd must be estimated by a simulation, which introduces a model dependence in the evaluation of ∆G/G. This paper presents a measurement of the cross-section helicity asymmetry obtained for the large sample of muon-deuteron events collected by the COMPASS experiment at CERN in the low virtuality domain, Q 2 < 1 (GeV/c) 2 . We select interactions in which a pair of high-p T hadrons is produced. The gluon polarization ∆G/G is extracted from this asymmetry using the event generator PYTHIA 6.2 [8] and leading-order expressions for the analyzing powers of the PGF and of the background processes. Possible spin effects in the fragmentation are neglected.

2
Experimental set-up The experiment [9] is located at the M2 beam line of the CERN SPS, which provides a 160 GeV µ + beam at a rate of 2 × 10 8 muons per spill of 4.8 s with a cycle time of 16.8 s. The muons are produced in the decay of pions and kaons, and the beam has a natural polarization of P b = −0.76, with a relative accuracy of 5% [10]. The incident muon momentum is measured upstream of the experimental area in a beam spectrometer, while its direction and position at the entrance of the target are determined in a telescope of scintillating fiber hodoscopes and silicon microstrip detectors. The polarized target system [11] consists of an upstream cell (u) and a downstream cell (d), each 60 cm long and 3 cm in diameter, separated by 10 cm. The cells are located on the axis of a superconducting solenoid magnet providing a field of 2.5 T along the beam direction, and are filled with 6 LiD. This material is used as a deuteron target and was selected for its high dilution factor f of about 40%, which accounts for the fact that only a fraction of the target nucleons are polarizable. Typical polarization values of 50% are obtained by dynamic nuclear polarization, and measured with a relative accuracy of 5%. The two cells are polarized in opposite directions by using different microwave frequencies so that data with both spin orientations are recorded simultaneously. The muon flux then cancels out in the counting rate asymmetry. However, the acceptance of the spectrometer is not identical for the two cells, which gives rise to an acceptance asymmetry. To account for this, a rotation of the magnetic field is performed in order to reverse the orientation of the spins in each cell. The acceptance asymmetry then disappears in the sum between the counting rate asymmetries before and after rotation (for details, see Eq. 2). A perfect cancellation requires the ratio L u a u /L d a d to be the same before and after rotation, where L u , L d are the luminosities and a u , a d the acceptances for the upstream and downstream target cells. False asymmetries due to the variations of this ratio with time are minimized by performing the rotation frequently, i.e. every 8 hours. However, because of the change in the orientation of the target field, the set-up is slightly different before and after rotation, which affects the L u a u /L d a d ratio. To cancel this effect the orientation of the spins for a given field orientation is reversed by repolarization a few times during the running period.
The COMPASS spectrometer has a large angle and a small angle spectrometer built around two dipole magnets, in order to allow the reconstruction of the scattered muon and of the produced hadrons in broad momentum and angular ranges. Different types of tracking detectors are used to deal with the rapid variation of the particle flux density with the distance from the beam. Tracking in the beam region is performed by scintillating fibers. Up to 20 cm from the beam we use Micromegas and GEMs. Further away, tracking is carried out in multiwire proportional chambers and drift chambers. Large-area trackers, based on straw detectors and large drift chambers extend the tracking over a surface of up to several square meters. Muons are identified by dedicated trackers placed downstream of hadron absorbers. Hadron/muon separation is strengthened by two large iron-scintillator sampling calorimeters, installed upstream of the hadron absorbers and shielded to avoid electromagnetic contamination. The particle identification provided by the ring imaging Cherenkov detector is not used in the present analysis.
The trigger system [12] provides efficient tagging down to Q 2 = 0.002 (GeV/c) 2 , by detecting the scattered muon in a set of hodoscopes placed behind the two dipole magnets. A large enough energy deposit in the hadronic calorimeters is required in order to suppress unwanted triggers generated by halo muons, elastic muon-electron scattering events, and radiative events.

3
Asymmetry measurement The present analysis deals with data collected in 2002 and 2003. The selected events are required to contain at least two charged hadrons associated to the primary vertex, in addition to the incident and scattered muons. We consider events with 0.35 < y < 0.9, where y is the fraction of energy lost by the incident muon. The lower y cut removes events with a low sensitivity to the gluon polarization, while the upper one rejects events which could be affected by large radiative effects. Since PYTHIA provides a reliable model for interactions of virtual photons with nucleons at low virtuality [13], we select events with Q 2 < 1 (GeV/c) 2 , which corresponds to about 90% of the total data set. The DIS sample, Q 2 > 1 (GeV/c) 2 , is being analyzed separately using LEPTO which is better adapted to this domain.
Furthermore, cuts are applied on the two hadrons with highest transverse momentum. The muon contamination of the hadron sample is eliminated by requiring the energy deposit in the calorimeters to be large enough with respect to the reconstructed momentum, E/p > 0.3. In addition, hadron candidates detected also downstream of the hadron absorbers are discarded. The invariant mass of the two-hadron system is required to be larger than 1.5 GeV/c 2 , and x F to be larger than 0.1, where x F = 2p * L /W . Here, p * L is the longitudinal momentum of the hadron in the photon-nucleon center of mass frame and W is the invariant mass of the hadronic final state. Finally, the fraction of PGF events in the sample is enhanced by requiring the transverse momentum of the two hadrons to be large: p h1 as in the SMC high-p T analysis [14]. In total, around 250 000 events remain after these cuts, defining the high-p T sample.
The asymmetry A can be obtained from the number of events in the upstream and downstream cells, before and after field rotation: The two terms in this expression correspond to opposite orientations of the target magnetic field, with for example N ↑⇓ u the number of events in the upstream cell when the cell polarization is anti-parallel to the beam polarization.
The statistical error on the asymmetry is minimized by weighting each event with its overall sensitivity to the gluon polarization [15]. The event weight is taken to be w = f DP b , where D is a kinematic factor which approximates the amount of polarization transferred from the incident muon to the virtual photon: Here, all terms containing the muon mass m were taken into account since the sample of events is at low Q 2 . The factor D is proportional to the analyzing power of PGF apart from a weak dependence on the event kinematics, and was therefore used in the weight instead ofâ PGF LL which is unknown on an event-by-event basis. The average value of D is around 0.6. In the weighting method, the expression for the asymmetry becomes With the high-p T sample defined above, we obtain A D = 0.002 ± 0.019(stat) ± 0.003(syst).
The systematic error accounts for the false asymmetries, which were estimated using a sample of low p T events with much larger statistics. Other sources of systematic errors, including the error on the beam and target polarizations, are proportional to the (small) measured asymmetry, and have been neglected.

Gluon polarization
As stated before, the determination of the gluon polarization from the high-p T asymmetry involves a Monte Carlo simulation. The generated events are propagated through a GEANT [16] model of the COMPASS spectrometer, and reconstructed using the same program as for real data. Finally, the same cuts as for real data are applied to obtain the Monte Carlo sample of high-p T events.
We use PYTHIA to generate two different kinds of processes. In direct processes, for example the PGF, the virtual photon takes part directly in the hard partonic interaction. In resolved-photon processes, it fluctuates into a hadronic state from which a parton is extracted (the partonic structure of the virtual photon is resolved). This parton then interacts with a parton from the nucleon. At Q 2 < 1 (GeV/c) 2 , the resolved-photon processes constitute about half of the high-p T sample. For Q 2 > 1 (GeV/c) 2 , their contribution drops to about 10%, and it becomes negligible for Q 2 > 2 (GeV/c) 2 . To compute the asymmetry of a given process, it is mandatory to find a hard scale µ 2 allowing the factorization of the cross-sections into a hard partonic cross-section calculable perturbatively, and a soft parton distribution function which needs to be measured. In Eq. (1) for instance, the asymmetry of the PGF factorizes into a hard asymmetry (the analyzing power) and a soft asymmetry (the gluon polarization). In our case, Q 2 is too small to be used as a scale. However, the scale provided by PYTHIA 1) is very close to the p 2 T of one of the partons produced in the hard reaction. Since the p T cut applied to the two highest-p T hadrons implies, for most of the events, large transverse momentum partons in the final state of the hard reaction, this quantity turns out to be large enough. Events for which no hard scale can be found are classified in PYTHIA as "low-p T processes." After varying many parameters of PYTHIA, the best agreement with our data was obtained by modifying only the width of the intrinsic transverse momentum distribution of partons within the resolved virtual photon 2) , which was decreased from 1 GeV/c to 0.5 GeV/c. The lower p T cut-off 3) is set by default to 1 GeV/c to prevent the cross-section for 2 → 2 processes such as PGF from diverging when the partonic transverse momentum vanishes. However, this does not occur in our high-p T sample, as the transverse-momentum distribution of the outgoing partons starts just below 1 GeV/c. To avoid cutting into this distribution, we have decreased the lower p T cut-off to 0.9 GeV/c and did not observe any effect on the agreement with the data. The simulated and real data samples of high-p T events are compared in Fig. 1 for Q 2 , y, and for the total and transverse momenta of the hadron with highest p T . An equally good agreement is obtained for the second hadron.
Various processes contribute to the Monte Carlo sample of high-p T events, as shown in Fig. 2. The direct processes are the PGF, the QCD Compton (QCDC, γ * q → qg), and the leading process (γ * q → q). For the resolved-photon processes, a parton f from the nucleon interacts with a parton f γ from the virtual photon, where f and f γ can be a quark or a gluon. We have neglected the resolved-photon processes qq → q ′q′ , qq → gg and gg → qq, which altogether represent only 0.6% of the sample. The low-p T processes contain all events for which no hard scale can be found. Each of these processes contributes 1) Parameter MSTP(32). 2) Parameter PARP(99) in Ref. [8].  to the cross-section helicity asymmetry, provided that a transverse photon is exchanged. The asymmetry can then be approximately expressed as Here, R QCDC is the fraction of QCD Compton events, and R f f γ is the fraction of events in the whole high-p T sample for which a parton f from the nucleon interacts with a parton f γ from a resolved photon. Recalling that we use a deuteron target, A 1 is the inclusive virtual-photon-deuteron asymmetry and ∆f /f (∆f γ /f γ ) is the polarization of quarks or gluons in the deuteron (photon). The contributions of the leading and low-p T processes cannot be calculated in the same way, since there is no hard scale allowing the factorization of their asymmetries A leading and A low−p T (low transverse momentum, and Q 2 < 1 (GeV/c) 2 events). However, the asymmetry for this kind of events is small as indicated by previous measurements of A 1 at low Q 2 [17]. Moreover, the leading and lowp T processes together account for only 7% of the high-p T sample. For these two reasons, we neglected their contributions. The fraction of photon-gluon fusion events in the sample is of the order of 30%, see Fig. 2. The analyzing powerâ PGF LL is calculated using the leading-order expressions for the polarized and unpolarized partonic cross-sections and the parton kinematics for each PGF event in the high-p T Monte Carlo sample. In average, we obtain â PGF LL /D = −0.93, so that the contribution of PGF to the high-p T asymmetry is −0.29 × ∆G/G.
The contribution of QCD Compton events to the high-p T asymmetry is evaluated from a parametrization of the virtual-photon-deuteron asymmetry A 1 based on a fit to the world data [2,18]. This asymmetry is calculated for each event at the momentum fraction x q of the quark, known in the simulation. The estimated contribution of the QCD Compton scattering to the high-p T asymmetry is 0.006.
The parton from a resolved photon interacts either with a quark or a gluon from the nucleon. In the latter case, the process is sensitive to the gluon polarization ∆G/G. The analyzing powersâ f f γ LL are calculated in pQCD at leading order [19]. The polarizations of the u, d and s quarks in the deuteron ∆f /f are calculated using the polarized parton distribution functions from Ref. [20] (GRSV2000) and the unpolarized parton distribution functions from Ref. [21] (GRV98, also used as an input for PYTHIA), all at leading order. The polarizations of quarks and gluons in the virtual photon ∆f γ /f γ are unknown be-cause the polarized PDFs of the virtual photon have not yet been measured. Nevertheless, theoretical considerations provide a minimum and a maximum value for each ∆f γ , in the so-called minimal and maximal scenarios [22]. As the analyzing powers are positive for all considered channels, the two scenarios correspond to extreme values for the contribution of the resolved-photon processes to the high-p T asymmetry, 0 + 0.012 × ∆G/G and 0.002 + 0.078 × ∆G/G, respectively. Here, the term proportional to ∆G/G comes from the processes involving a gluon from the nucleon.
Our analysis is restricted to leading order, and the systematic error has to take into account next-to-leading-order effects. Their order of magnitude is estimated by repeating the analysis several times with modified Monte Carlo parameters: the renormalization and factorization scales were multiplied and divided by two, and the parton shower mechanism was deactivated. The systematic error is obtained from the difference in the corresponding values for ∆G/G, 0.004 (0.011) in the minimal (maximal) scenario.
Another source of systematic error is the tuning of the PYTHIA parameters. Since our event selection relies on a cut in transverse momentum, the relevant parameters are those which determine the amount of transverse momentum acquired by the outgoing hadrons in the soft parts of the reaction: the intrinsic transverse momentum of the partons in the nucleon and in the resolved photon, and the parameters describing the hadronization. These parameters were scanned independently over a range in which the agreement between the simulation and real data remains reasonable. This results in several values for ∆G/G, all based on the same measured high-p T asymmetry of Eq. (5). The value of ∆G/G appears to depend predominantly on the width of the intrinsic-transversemomentum distribution for the partons in the photon. Varying this parameter between 0.1 GeV/c and 1 GeV/c leads to a 30% variation of the fraction of photon-gluon fusion R PGF . Note that the resulting systematic errors are proportional to the high-p T asymmetry, which implies that a statistical fluctuation of the measured high-p T asymmetry modifies the systematic errors. This was taken into account by performing the systematic study for A /D + σ stat (A /D) and A /D − σ stat (A /D) as well, quoting the largest value for the systematic error. Finally, the systematic error on ∆G/G is 0.018 and 0.052 in the minimal and maximal scenarios, respectively.

Result and conclusion
The values for the gluon polarization in the minimal and maximal scenarios are ∆G G max = 0.031 ± 0.089(stat) ± 0.014(exp. syst) ± 0.052(MC. syst).
This leads to the central value where the difference between the two scenarios has been included in the systematics, and where all systematics have been added quadratically. Let us recall that the systematic error covers an uncertainty on R PGF of up to 30%. Gluons are probed at an average scale µ 2 and an average momentum fraction of the gluons x g , which are both obtained from the simulation where the parton kinematics is known. For the scale, we obtain in average  [14], and HERMES [23]. The horizontal bar on each point represents the range in x g . The curves show various parametrizations from NLO fits in the MS scheme at µ 2 = 3 (GeV/c) 2 : GRSV2000 [20] (3 curves, please see text for details), AAC03 [24], and LSS05 sets 1 and 2 [25].
The distribution of x g is asymmetric, with a different r.m.s. width on the left and on the right, x g = 0.095 +0.08 −0.04 . For these two quantities, the average was obtained by weighting each event by its sensitivity to the gluon polarization, c.f. Eq. (6).
Our value for the gluon polarization is compared with previous direct measurements from the SMC [14] and HERMES [23] experiments in Fig. 3. The SMC measurement uses high-p T events at Q 2 > 1 (GeV/c) 2 , where the contribution of the resolved-photon processes is small. The HERMES result was derived from data mostly at low Q 2 , but the contribution of the resolved-photon processes to the asymmetry was neglected. Note that these experimental determinations are based on a leading-order analysis. Figure 3 also shows three distributions of ∆G/G as a function of x g from Ref.
[20] (GRSV2000), resulting from QCD fits to the world g 1 data at NLO. They correspond to three hypotheses on the gluon polarization at µ 2 = 0.40 (GeV/c) 2 : maximal polarization (max), best fit to the data (std), and zero polarization (min). The distributions are then evolved radiatively to µ 2 = 3 (GeV/c) 2 where their first moments are 2.5, 0.6 and 0.2, respectively. Our result clearly favors parametrizations with a low gluon polarization.
More recent NLO distributions of ∆G/G from Ref. [24] (AAC03) and Ref. [25] (LSS05, sets 1 and 2) are displayed as well. Although these curves strongly differ in shape, the values at x g = 0.095 are quite close and all within 1.5 σ above our measured value. The first moment ∆G at the scale µ 2 = 3 (GeV/c) 2 is equal to 0.8 for AAC03, and to 0.26 (0.39) for LSS05 set 1 (set 2).
When the singlet axial matrix element a 0 was found to be much smaller than the contribution to the nucleon spin expected in the naive quark-parton model, it was suggested that the difference could be accounted for by a large contribution of the gluon spin [26,27,28]. Indeed, in the so-called AB [29] or JET [30] renormalization schemes, the contribution of the quark spins to the nucleon spin becomes ∆Σ = a 0 + N f (α s /2π)∆G where N f is the number of active flavors. At Q 2 = 3 (GeV/c) 2 , a value of ∆G of about 3 would be required to obtain the expected ∆Σ of the order of 0.6. The small value of ∆G/G at x g = 0.095 from our measurement cannot by itself rule out the possibility of the first moment ∆G being as large as 3, since the shape of ∆G(x g ) is poorly known. However, the fact that our point is lower than fitted parameterizations, leading to values of ∆G around or below unity, makes the hypothesis of a large ∆G unlikely.
In summary, we have measured the gluon polarization at x g = 0.095 and µ 2 ≃ 3 (GeV/c) 2 and found a result compatible with zero, with a statistical error and a systematic error smaller than 0.1. The gluon polarization was extracted from the longitudinal spin asymmetry obtained for low-Q 2 events in which a pair of high-p T hadrons is produced. The present analysis, for the first time, takes into account the contribution from the polarized structure of the virtual photon.