SSpin Physics at COMPASS
Christian Schill on behalf of the COMPASS collaboration
Physikalisches Institut der Albert-Ludwigs-Universit¨at Freiburg,Hermann-Herder Str. 3, 79104 Freiburg, Germany.E-mail:
Abstract.
The COMPASS experiment is a fixed target experiment at the CERN SPS usingmuon and hadron beams for the investigation of the spin structure of the nucleon and hadronspectroscopy. The main objective of the muon physics program is the study of the spin ofthe nucleon in terms of its constituents, quarks and gluons. COMPASS has accumulated dataduring 6 years scattering polarized muons off longitudinally or transversely polarized deuteron( LiD) or proton (NH ) targets.Results for the gluon polarization are obtained from longitudinal double spin crosssection asymmetries using two different channels, open charm production and high transversemomentum hadron pairs, both proceeding through the photon-gluon fusion process. Also, thelongitudinal spin structure functions of the proton and the deuteron were measured in parallelas well as the helicity distributions for the three lightest quark flavours.With a transversely polarized target, results were obtained with proton and deuteron targetsfor the Collins and Sivers asymmetries for charged hadrons as well as for identified kaons andpions. The Collins asymmetry is sensitive to the transverse spin structure of the nucleon, whilethe Sivers asymmetry reflects correlations between the quark transverse momentum and thenucleon spin.Recently, a new proposal for the COMPASS II experiment was accepted by the CERNSPS which includes two new topics: Exclusive reactions like DVCS and DVMP using themuon beam and a hydrogen target to study generalized parton distributions and Drell-Yanmeasurements using a pion beam and a polarized NH target to study transverse momentumdependent distributions.
1. Introduction
COMPASS is a fixed target experiment at the CERN SPS accelerator with a wide physicsprogram focused on the nucleon spin structure and on hadron spectroscopy. COMPASSinvestigates the spin structure of the nucleon in semi-inclusive deep-inelastic scattering. Alongitudinally polarized 160 GeV muon beam is scattered off a longitudinally or transverselypolarized NH or LiD target. The scattered muon and the produced hadrons are detected in a50 m long wide-acceptance forward spectrometer with excellent particle identification capabilities[1]. A variety of tracking detectors are used to cope with the different requirements of positionaccuracy and rate capability at different angles. Particle identification is provided by a largeacceptance RICH detector, two electromagnetic and hadronic calorimeters, and muon filters.The polarized LiD target is split into two cylindrical cells along the beam direction. Thetwo cells are polarized in opposite direction. The polarized NH target consists of three cells(upstream, central and downstream) of 30, 60 and 30 cm length, respectively. The upstream anddownstream cells are polarized in the same direction while the middle cell is polarized oppositely. a r X i v : . [ h e p - e x ] J a n igure 1. Inclusive, π ± and K ± longitudinal double-spin asymmetries on the proton (filledcircles: COMPASS results from Ref. [2]). For comparison the HERMES results from Ref. [4](open circles) and the DSSV fit prediction from Ref. [6] are shown.
2. Longitudinal Spin Structure of the Nucleon
The longitudinal spin structure of the nucleon is investigated by measuring double spinasymmetries in inclusive (DIS) and semi-inclusive (SIDIS) deep-inelastic scattering on alongitudinally polarized target. SIDIS asymmetries, where pions and kaons are detected, aresensitive to the individual quark flavours. The most recent proton asymmetries measured in2007 [2, 3] are shown in figure 1 together with the results from the HERMES experiment [4, 5].From the semi-inclusive asymmetries, a leading order QCD extraction of the polarized partondistribution functions is possible. The measured asymmetries A h ( x, z ) for a hadron h canbe written as the product of polarized parton distribution functions ∆ q ( x ) and fragmentationfunctions D hq ( z ), summed over all quark q and anti-quark ¯ q flavours: A h ( x, z ) = (cid:80) q, ¯ q e · ∆ q ( x ) · D hq ( z ) (cid:80) q, ¯ q e · q ( x ) · D hq ( z ) (1)The fragmentation functions are taken from the parametrization of DSS [8]. For the unpolarizedparton distribution functions q ( x ) in the denominator the MRST parametrization [9] is used.In a least-squares fit to the ten inclusive and semi-inclusive asymmetries from proton- anddeuteron data, the quark helicity distributions for u − , d − and s − quarks are extracted. Sinceit was observed that in the measured x -range the extracted strange and anti-strange quarkhelicity distributions are compatible, the assumption ∆ s = ∆¯ s has been made to further reducethe number of parameters. The results of the fit are then shown in figure 2. The curves infigures 1 and 2 are the results of a global fit of the DSSV group using previously existing dataat Next-to-Leading Order (NLO) [6, 7].The u -quark helicity distribution is positive with its maximum in the valence quark regionand the d -quark distribution is negative in the same x -region. The anti-quark distributions ∆¯ u and ∆ ¯ d do not show a significant x -dependence. ∆¯ u is consistent with zero, while ∆ ¯ d is slightlynegative. The flavour asymmetry of the helicity distribution of the sea, ∆¯ u − ∆ ¯ d has beenextracted from the fit. The first moment determined in the x -range of the experimental data, is igure 2. Quarkhelicity distributions x ∆ u , x ∆ d , x ∆¯ u , x ∆ ¯ d and x ∆ s at Q = 3 (GeV/c) asa function of x . Thebands show the sys-tematic uncertainty ofthe measurement. Thecurves are predictionsof DSSV calculated atNLO [6].found to be (cid:90) . . (∆¯ u − ∆ ¯ d ) dx = − . ± . stat. ) ± . syst. ) (2)and therefore compatible with zero. The model prediction ∆¯ u − ∆ ¯ d (cid:39) ¯ d − ¯ u of [10, 11] is notconfirmed by the experimental data. New COMPASS data on a longitudinally polarized protontarget have been collected in 2011 and will allow the statistical precision of the measurementsto be increased.
3. Gluon polarization in the nucleon
At COMPASS, the gluon polarization is directly measured by determining the longitudinaldouble-spin asymmetry in the photon-gluon fusion process (PGF). PGF events are searched forin two different channels: the open charm production channel, where an outgoing charm quarkis identified by the production of D mesons and the high- p T hadron pair channel, where the twooutgoing quarks hadronize with high transverse momentum. The open charm channel providesa clean signature of PGF but with limited statistics. For the high- p T channel, statistics is large,but the background from other processes is higher.Open-charm events are selected by reconstructing D and D ∗ mesons from their decayproducts. For this analysis, all data collected on LiD and NH from 2002 until 2007 have beenused. The particle identification is performed using the RICH detector. For the D ∗ sample,the D mesons are tagged by the detection of a low momentum pion from the D ∗ → D + π S decay. For untagged events, the decay channel D → K+ π has been used. The total number ofD mesons is about 14.000 (10.000) and 46.000 (19.000) in the D ∗ and D samples collected on LiD (NH ) targets.The final result for the gluon polarization from open charm production is given by theweighted mean of the results for D and D ∗ as [12]∆ g/g = − . ± . stat. ) ± . syst. ) (3)with < x > = 0 .
11 at a scale µ ≈
13 (GeV/c) .In the high- p T hadron pair channel, other competitive processes contribute to the asymmetry.These are the leading order process γ + q → q and the QCD-Compton process γ + q → γ + q ( g + q ).esolved photons are strongly suppressed by selecting events with Q > . A neuralnetwork is then used to assign for each event a probability for the three processes (PGF, QCD-Compton or LO), trained on the results of a Monte Carlo simulation [13]. The preliminary resultfor the gluon polarization for high- p T hadron pairs with Q > is∆ g/g = 0 . ± . stat. ) ± . syst. ) (4)at < x g > = 0 . +0 . − . at an average scale of µ = 3(GeV/c) . The result has been measuredin three bins of x g to check for a possible x g dependence of the gluon polarization. It isdisplayed in figure 3 together with the measurements of SMC [14] and HERMES [15, 16] andtwo parameterizations from a COMPASS NLO QCD analysis of the world data [17]. The resultsfavor small values of ∆ g/g . Figure 3. ∆ g/g measure-ments from open-charm andhigh- p T hadron pairs as afunction of x . The COM-PASS results are comparedto results of SMC [14] andHERMES [15, 16]. Thecurves are two parameteri-zations from a COMPASSNLO QCD fit with ∆ g > g <
4. Transversity and TMDs
Single spin asymmetries in semi-inclusive deep-inelastic scattering (SIDIS) off transverselypolarized nucleon targets have been under intense experimental investigation over the past fewyears [18, 19, 20, 21, 22]. They provide new insights into QCD and the nucleon structure. Forinstance, they allow the determination of the third leading-twist quark distribution function∆ T q ( x ), the transversity distribution [23, 24]. Additionally, they give insight into the partontransverse momentum distribution and angular momentum [25].The measurement of transverse spin effects in semi-inclusive deep-inelastic scattering is animportant part of the COMPASS physics program. In part of the years 2002-2004 data weretaken by scattering a 160 GeV muon beam on a transversely polarized deuteron target. In 2007and 2010, additional data were collected on a transversely polarized proton target.In semi-inclusive deep-inelastic scattering the transversity distribution ∆ T q ( x ) can bemeasured in combination with the chiral odd Collins fragmentation function. According toCollins, the fragmentation of a transversely polarized quark into an unpolarized hadron generatesan azimuthal modulation of the hadron distribution with respect to the lepton scattering plane[23].In Fig. 4 the results for the Collins asymmetry on the proton target are shown as a functionof x , z , and p T for positive and negative hadrons [18]. For small x up to x = 0 .
05 the measuredasymmetry is small and statistically compatible with zero, while for the last points an asymmetry igure 4.
Collinsasymmetry on aproton target forpions (upper row)and kaons (lowerrow) as a functionof x , z and p T [18]. The bandsshow the system-atic uncertainty ofthe measurement.different from zero is visible. The asymmetry increases up to about 8% with opposite sign fornegative and positive hadrons. This result confirms the measurement of a sizable Collins functionand transversity distribution.COMPASS has measured the Collins asymmetries on a deuteron target as well. They areall compatible with zero [21]. From this measurement the opposite sign of u - and d - quarktransversity has been derived. Both, proton and deuteron data sets have been employed inglobal fits taking into account the Collins fragmentation function from BELLE and the Collinsasymmetries from COMPASS and HERMES to obtain constrains to the transversity distributionfor u - and d -quarks [26].Another azimuthal asymmetry is related to the Sivers effect. The Sivers asymmetry arisesfrom a coupling of the intrinsic transverse momentum −→ k T of unpolarized quarks with thespin of a transversely polarized nucleon [27]. The correlation between the transverse nucleonspin and the transverse quark momentum is described by the Sivers distribution function∆ T q ( x, −→ k T ). Since the Collins and Sivers asymmetries are independent azimuthal modulationsof the cross section for semi-inclusive deep-inelastic scattering, both asymmetries are determinedexperimentally from the same dataset.In Fig. 5 the results for the Sivers asymmetry on the proton are shown as a function of x , z ,and p T . The Sivers asymmetry for negative hadrons is small and statistically compatible withzero. For positive hadrons the Sivers asymmetry is positive [18]. The Sivers asymmetry on thedeuteron target is small and compatible with zero, which is due to the opposite sign of the u − and d − quark Sivers function [21]. Figure 5.
Siversasymmetry on aproton target forpositive and nega-tive hadrons as afunction of x , z and p T from [18]. . Outlook Recently, the COMPASS II proposal [28] was submitted to improve the knowledge of themomentum structure of the nucleon towards a three dimensional picture. For this a seriesof new measurements is planned. A study of generalized parton distributions (GPD) will bedone using exclusive reactions like deeply virtual Compton scattering (DVCS) and deeply virtualmeson production (DVMP) [29, 30]. Drell-Yan processes will be used for a complementary studyof transverse momentum dependent distributions (TMD) using a transversely polarized target[31]. At very low momentum transfers Primakoff reactions can be used to extract pion and kaonpolarizabilities. The COMPASS II proposal was approved on December 2010 for an initial datataking of three years.
Acknowledgments
This work has been supported in part by the German BMBF.
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