Review of COMPASS results on transverse-spin effects in SIDIS
RReview of COMPASS results on transverse-spineffects in SIDIS
Nour MAKKE ∗ On behalf of the COMPASS CollaborationUniversità degli studi di Trieste, Via A. Valerio 2, 34127 Trieste, ItalyINFN sezione di Trieste, Padriciano, 99, 34149 Trieste, ItalyE-mail: [email protected]
The transversity parton distribution remains a poorly known cornerstone in the nucleon spin struc-ture. While the Collins effect in spin asymmetries in Semi-Inclusive DIS (SIDIS) is one crucialtool to address the transversity function, the most promising alternative is the azimuthal asym-metry in SIDIS when a hadron pair is detected in the final state. In this case, the chiral-oddtransversity function is coupled to another chiral-odd function, i.e. the hadron-pair interferencefragmentation function (IFF). The measurement of azimuthal asymmetries in hadron-pair pro-duction on a transversely polarised nucleon target has been performed at COMPASS using a 160GeV/c muon beam of CERN’s M2 beam line. Results from the 2007 and 2010 recent measure-ments will be presented and compared to model predictions.
The European Physical Society Conference on High Energy Physics18-24 July, 2013Stockholm, Sweden ∗ Speaker. c (cid:13) Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/ a r X i v : . [ h e p - e x ] A ug eview of COMPASS results on transverse-spin effects in SIDIS Nour MAKKE
1. Introduction
The distribution of transversely polarised quarks in a transversely polarised nucleon, denotedby h ( x ) or ∆ T q ( x ) was first introduced by Ralston and Soper in 1979 [1]. Due to its chiral-oddnature, the transversity is not measurable in inclusive Deep-Inelastic Scattering (DIS). It couldbe assessed in semi-inclusive DIS of leptons off transversely polarised nucleons by measuringsingle-spin azimuthal asymmetries (SSA) of cross-sections, where it couples to another chiral-oddfunction, the spin-dependent fragmentation function. One of the main advantages of SIDIS is thatthe Collins and Sivers effects, as well as the other transverse momentum dependent (TMD) effects,generate different azimuthal asymmetries and thus do not mix. COMPASS [2, 3] and HERMES [4]collaborations presented the first data collected with transversely polarised protons and deuterons in2004 where a clear evidence of transverse SSA’s on proton was observed in the covered kinematics.The model-independent expression for the SIDIS cross-section for transversely polarised tar-get can be written in the following way d σ dxdydzdP hT d ϕ h d ϕ S = (1.1) (cid:20) cos θ − sin θ sin ϕ S (cid:21)(cid:20) α xyQ y ( − ε ) (cid:18) + γ x (cid:19)(cid:21)(cid:0) F UU , T + ε F UU , L (cid:1) × + cos ϕ h (cid:112) ε ( + ε ) A cos ϕ h UU + cos2 ϕ h ε A cos2 ϕ h UU + λ sin ϕ h (cid:112) ε ( − ε ) A sin ϕ h LU + P T (cid:113) − sin θ sin ϕ S sin ϕ S (cid:16) cos θ (cid:112) ε ( + ε ) A sin ϕ S UT (cid:17) + sin ( ϕ h − ϕ S ) (cid:18) cos θ A sin ( ϕ h − ϕ S ) UT +
12 sin θ (cid:112) ε ( + ε ) A sin ϕ h UL (cid:19) + sin ( ϕ h + ϕ S ) (cid:18) cos θ ε A sin ( ϕ h + ϕ S ) UT +
12 sin θ (cid:112) ε ( + ε ) A sin ϕ h UL (cid:19) + sin ( ϕ h − ϕ S ) (cid:18) cos θ (cid:112) ε ( + ε ) A sin ( ϕ h − ϕ S ) UT +
12 sin θ ε A sin2 ϕ h UL (cid:19) + sin ( ϕ h − ϕ S ) (cid:16) cos θ ε A sin ( ϕ h − ϕ S ) UT (cid:17) + sin ( ϕ h + ϕ S ) (cid:18)
12 sin θ ε A sin2 ϕ h UL (cid:19) + P T λ (cid:113) − sin θ sin ϕ S cos ϕ S (cid:18) cos θ (cid:112) ε ( − ε ) A cos ϕ S LT + sin θ (cid:113)(cid:0) − ε (cid:1) A LL (cid:19) + cos ( ϕ h − ϕ S ) (cid:18) cos θ (cid:113)(cid:0) − ε (cid:1) A cos ( ϕ h − ϕ S ) LT +
12 sin θ (cid:112) ε ( − ε ) A cos ϕ h LL (cid:19) + cos ( ϕ h − ϕ S ) (cid:16) cos θ (cid:112) ε ( − ε ) A cos ( ϕ h − ϕ S ) LT (cid:17) + cos ( ϕ h + ϕ S ) (cid:18)
12 sin θ (cid:112) ε ( − ε ) A cos ϕ h LL (cid:19) Here φ h is the angle of the transverse momentum of the outgoing hadron and φ S is the azimuthalangle of the quark spin before the hard scattering. The first and second subscripts indicate thebeam and the target polarisations ( U unpolarised, L longitudinal and T transverse). A total ofeight TMD distribution functions are needed to fully describe the transverse-spin and transverse-momentum structure of the nucleon, leading to eight azimuthal asymmetries in Eq.1.1: five Single-Spin (SSA) and three Double-Spin (DSA) target transverse spin-dependent asymmetries. Becauseof the smallness of the sin θ In the COMPASS kinematics, the impact of the additional terms,represented by sin θ -scaled longitudinal spin amplitudes and θ -angle dependent factors, is sizeableonly in the case of the A cos φ LT DSA which remains sizeably affected by the large A LL amplitude.2 eview of COMPASS results on transverse-spin effects in SIDIS Nour MAKKE
2. Transverse asymmetries in single hadron production
Among these azimuthal asymmetries, the Collins and Sivers are of particular interest. Thecollins asymmetries are generated by the Collins effect in the single hadron production. In thismechanism, the Collins fragmentation function ∆ T D hq , which describes the correlation betweenthe fragmenting quark spin and the momentum of the produced hadron, introduces a left-rightsymmetry in the distributions of hadrons reflected in the hadron yields. The Sivers function ∆ T q (or f q ) arises from a correlation between the transverse momentum of an unpolarised quark in atransversely polarised nucleon and the nucleon spin. At LO, the asymmetries can be written as A Coll = ∑ q e q · ∆ T q · ∆ T D hq ∑ e q · q · D hq , A Siv = ∑ q e q · ∆ T q · D hq ∑ q e q · q · D hq (2.1)The asymmetries are built by comparing the azimuthal distributions of hadrons produced insemi-inclusive DIS on transversely polarised nucleons with opposite spin configurations, in therelevant azimuthal angle and then fitted with the unbind maximum-likelihood method, based onmaximum-likelihood fits with the data unbind in φ h and φ S . more details on the analysis can befound in [6] (and references therein). COMPASS has collected SIDIS data on transversely polarisedtarget with LiD (2002-04 years) and NH (2007-2010 years), with a target polarisation factor ofthe order of 50% and 90% and a dilution factor of the order of 0 .
38 and 0 .
15 respectively. Thekinematic range of the measurement is defined by Q > , 0 . < y < .
9, 0 . < x < . W > z > . x , the hadron fractional energy z and the hadrontransverse momentum p hT in Figs.1 and 2. Collins asymmetries:
The pion asymmetries, which are very similar to the published unidenti-fied hadron ones [5, 6], show a zero signal in the sea region and a significant non-zero signal inthe valence region with opposite sign for π + and π − . This intuitively indicates that the Collinsfragmentation functions have the same magnitude and opposite sign [7] since A π + Coll , p = e u h u H ⊥ , f av + e d h d H ⊥ , un f , A π − Coll , p = e u h u H ⊥ , un f + e d h d H ⊥ , f av Neglecting the d quark contribution because of its small charge weight, | A π + Coll , p | (cid:39) | A π − Coll , p | impliesthat H f av ⊥ = − H un f ⊥ . In the kaon case, the asymmetry show a similar trend, although affected bylarge statistical uncertainties, in particular for K + which shows a significant trend towards negativevalues at high x . These results surprisingly agree with the existing measurements by the HERMESexperiment [8] which has a different kinematic coverage than COMPASS, i.e. the COMPASS Q is larger by a factor 2-3 wrt HERMES one in the last x bin. The same measurement have beenperformed using a deuterium target and published in [2, 9] where all asymmetries were found tobe compatible with zero. This is intuitively interpreted as a cancellation between the u and d quarkcontribution in an isoscalar target. Since A π + Coll , d = A π − Coll , d (cid:39) ( h u + h d )( e u H ⊥ , f av + e d H ⊥ , un f ) , weconclude that the transversity h u and h d have the same size and opposite sign.3 eview of COMPASS results on transverse-spin effects in SIDIS Nour MAKKE
Figure 1:
The Collins asymmetries for pions (top) and kaons (bottom) measured using a transversely po-larised proton target at COMPASS.
Figure 2:
The Sivers asymmetries for pions (top) and kaons (bottom) measured using a transversely po-larised proton target at COMPASS. eview of COMPASS results on transverse-spin effects in SIDIS Nour MAKKE
Sivers asymmetries
The Sivers asymmetries for negative pions and kaons are compatible withzero, in contrast with positive pions and kaon asymmetries where a significant signal extends theoverall measured x range and increases with z . The K + asymmetry is intriguinly larger than π + asymmetry. This suggests a rather significant role of the sea quarks. At variance with the Collinscase, the COMPASS Sivers asymmetries are smaller than HERMES’s ones [4] by a factor of two,giving insights of the Q evolution of the Transverse Momentum Dependent (TMD) functions. Inthe case of a deuterium target, all measured Sivers asymmetries are compatible with zero. This isnaively interpreted, in the framework of the parton model, as due to opposite Sivers functions for u and d quarks. Other 6 asymmetries
The other six "beyond Collins and Sivers" asymmetries ( A cos ( φ h − φ S ) LT , A sin φ S UT , A sin ( φ h − φ S ) UT , A sin ( φ h − φ S ) UT , A cos φ h LT , A cos ( φ h − φ S ) LT ) have been also measured by COMPASS on deuteriumand proton targets for charged unidentified hadrons as function of x , z and p hT . These asymmetriesare consistent with zero within the statistical accuracy except for A cos ( φ h − φ S ) LT and A sin φ S UT where thereis an evidence of a non-zero signal. Fig.3 shows the A cos ( φ h − φ S ) LT compared to theoretical predictionsfrom [10], [11] and [12] demonstrating a good level of agreement between theory and experimentalmeasurements within the reached statistical accuracy. Figure 3: "Beyond Collins and Sivers" asymmetries A − LT cos ( φ h − φ S ) and A sin φ S UT recently measured at COM-PASS using a transversely polarised proton target..
3. Transverse asymmetries in hadron pair production
An alternative approach to assess the transversity function is in dihadron production in SIDIS(Fig. 4). The dihadron asymmetries of unidentified h + h − and identified ( π + π − , π + K − , K + π − , K + K − ) hadron pairs were measured using the full data set collected using a deuterium ( LiD)target during 2002-04 and on a proton (NH ) target during 2007 and 2010. The measurement isdone in the same kinematic range however there additional cuts are applied in this case: each ofthe selected hadron pairs has to have z > . x F > . ρ mesons are rejected by a cut on the missingenergy in the reaction, i.e. E miss > R T > .
07 GeV ensures a well defined5 eview of COMPASS results on transverse-spin effects in SIDIS
Nour MAKKE azimuthal angle φ R . The full statistics collected using a proton target consists of 45 . · h + h − pairs, of which 28 · are identified as pion pairs. The deuteron sample consists of 5 . · h + h − . Figure 4:
Simplified scheme of the dihadron production mechanism: The incoming and the scattered leptonswith their 3-momenta l and l’ define the scattering plane (gray). φ S is the azimuthal angle of the fragmentingquark spin S . The 3-momenta of both hadrons define the lepton plane (blue). The corresponding ξ i valuesare used in the normalisation of the difference vector R , i.e. R = ( z p − z p ) / ( z + z ) = ξ p − ξ p . φ R is the azimuthal angle of R and R T is its component perpendicular to the 3-momentum of the virtual photon. Figs. 5(a)(top) and 6 show respectively the asymmetries for unidentified and identified hadronpair asymmetries measured using an isoscalar target. The asymmetries are found to be consistentwith zero within the statistical accuracy. Furthermore no specific trend is visible in any of the x , z or M inv dependences, in agreement with the existing theoretical models predictions and inline with the COMPASS measurement of the Collins asymmetry on deuterium. This observationcan be interpreted as an almost complete cancellation between the up ( h u ) and down ( h d ) quarktransversity on isoscalar target which is predicted by the available theoretical models [13, 14].The first COMPASS measurement of the dihadron asymmetry of h + h − pairs on a proton target wasperformed using the data collected in 2007 and shown in Fig.5(a) (bottom) as a function of x , z and M inv . While no specific trend is visible versus z , a large asymmetry up to -10% is measured in thevalence x -region and a significant negative signal versus M inv is measured around the ρ mass of0.77 (GeV/c) . In order to improve the results in terms of statistics and to allow further analyses, thefull beam time in 2010 was dedicated to collect data again on a transversely polarised target. Theasymmetry measurement based on 2010 data set showed a very good agreement and consistencywith the results from 2007 and therefore a recently new analysis was performed by combining both2007 and 2010 data sets. COMPASS has the particle identification facility using a Ring ImagingCherenkov detector and ensures a very good separation of the particle types in the momentumrange [3 GeV,50 GeV]. The resulting asymmetries for identified dihadron are shown in Fig.6. Thepion pair asymmetry shows a significant negative signal up to -6% in the valence x -region and apronounced peak around the ρ mass in it’s M inv dependence. The kaon pair asymmetry is mostlydominated by large statistical uncertainties and is compatible with zero in almost all kinematic binsexcept at large M inv . For mixed pairs ( π + K − and K + π − ), the asymmetries are consistent with zero.A comparison between COMPASS π + π − asymmetry and existing measurement by the HER-MES experiment [15] and theoretical model predictions by Bacchetta et al. [13] and Ma et al. eview of COMPASS results on transverse-spin effects in SIDIS Nour MAKKE [14] is shown in Fig.5(b). COMPASS and HERMES measured π + π − asymmetries agree in thecommonly covered x range despite the different Q coverage in each x bin. The experimental trendin x and the observed peak around the ρ mass are well reproduced in both model predictions.However, the agreement in z and the remaining mass regions is rather poor. (a) 2002-04 (top) and 2007 (bottom) h + h − pairs asymmetries measured using a trans-versely polarised deuteron and proton targets respectively compared with model produc-tions [13, 14].(b) π + π − asymmetries from combined 2007 and 2010 proton data in comparison withHERMES data [15] and model predictions [13, 14] in the valence region ( x > . Figure 5:
Hadron pair asymmetries on transversely polarised deuteron and proton targets at COMPASS.
4. Conclusion
An overview of COMPASS investigation on transverse-spin effects and transverse momentum-dependent effects in SIDIS has been presented. A full set of recent results on the eight azimuthalasymmetries, of pions and kaons, measured by scattering 160 GeV muon beam off a transverselypolarised target in 2007 and 2010 were presented and discussed. While the results of collins andSivers on deuteron are compatible with zero, a non-zero effect is observed when using a protontarget. This observation is deeper investigated via a multi-dimensional analysis of the full data set.A significant signal is also observed in dihadron production, highlighting a non-zero transversityfunction for up and down quarks. 7 eview of COMPASS results on transverse-spin effects in SIDIS
Nour MAKKE
Figure 6:
New Hadron pair asymmetries measured at COMPASS using a transversely polarised deuteron(2003/04) and proton (2007/10) targets using the RICH for particle identification in the range [3,10 GeV].
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