Transverse spin azimuthal asymmetries in SIDIS at COMPASS: Multidimensional analysis
NNovember 12, 2018 19:10 WSPC/INSTRUCTION FILESPIN2014˙proceedings˙SIDIS
International Journal of Modern Physics: Conference Seriesc (cid:13)
The Authors
Transverse spin azimuthal asymmetries in SIDIS at COMPASS:Multidimensional analysis
Bakur Parsamyan
ICTP - Strada Costiera 11, 34151 Trieste, ItalyINFN sezione di Trieste - Via Valerio 2, 34127 Trieste, ItalyUniversit`a di Torino and INFN sezione di Torino - Via P. Giuria 1, 10125 Torino, [email protected]
COMPASS is a high-energy physics experiment operating at the SPS at CERN. Widephysics program of the experiment comprises study of hadron structure and spectroscopywith high energy muon and hadrons beams. As for the muon-program, one of the im-portant objectives of the COMPASS experiment is the exploration of the transverse spinstructure of the nucleon via spin (in)dependent azimuthal asymmetries in single-hadronproduction in deep inelastic scattering of polarized leptons off transversely polarizedtarget. For this purpose a series of measurements were made in COMPASS, using 160GeV/c longitudinally polarized muon beam and transversely polarized LiD (in 2002,2003 and 2004) and NH (in 2007 and 2010) targets. The experimental results obtainedby COMPASS for unpolarized target azimuthal asymmetries, Sivers and Collins effectsand other azimuthal observables play an important role in the general understanding ofthe three-dimensional nature of the nucleon. Giving access to the entire twsit-2 set oftransverse momentum dependent parton distribution functions and fragmentation func-tions COMPASS data triggers constant theoretical interest and is being widely used inphenomenological analyses and global data fits. In this review main focus is given tothe very recent results obtained by the COMPASS collaboration from first ever multi-dimensional extraction of transverse spin asymmetries. Keywords : COMPASS; SIDIS; Transverse Spin Azimuthal Asymmetries; Multidimen-sional analysis;PACS numbers: 13.60.-r; 13.60.Hb; 13.88.+e; 14.20.Dh; 14.65.-q.
1. Introduction
Using standard notations the cross-section for the lepton off transversely polarizednucleon SIDIS processes (in a single photon exchange approximation) can be written
This is an Open Access article published by World Scientific Publishing Company. It is distributedunder the terms of the Creative Commons Attribution 3.0 (CC-BY) License. Further distributionof this work is permitted, provided the original work is properly cited.1 a r X i v : . [ h e p - e x ] A p r ovember 12, 2018 19:10 WSPC/INSTRUCTION FILESPIN2014˙proceedings˙SIDIS Bakur Parsamyan in a following model-independent way – : dσdxdydzp hT dp hT dφ h dφ S = 2 (cid:20) αxyQ y − ε ) (cid:18) γ x (cid:19)(cid:21) (cid:0) F UU,T + εF UU,L (cid:1) × (cid:40) (cid:112) ε (1 + ε ) A cos φ h UU cos φ h + εA cos 2 φ h UU cos (2 φ h ) + λ (cid:112) ε (1 − ε ) A sin φ h LU sin φ h + S T (cid:104) A sin( φ h − φ S ) UT sin ( φ h − φ S ) + εA sin( φ h + φ S ) UT sin ( φ h + φ S ) + εA sin(3 φ h − φ S ) UT sin (3 φ h − φ S )+ (cid:112) ε (1 + ε ) A sin φ S UT sin φ S + (cid:112) ε (1 + ε ) A sin(2 φ h − φ S ) UT sin (2 φ h − φ S ) (cid:105) + S T λ (cid:104)(cid:113) (1 − ε ) A cos( φ h − φ S ) LT cos ( φ h − φ S )+ (cid:112) ε (1 − ε ) A cos φ S LT cos φ S + (cid:112) ε (1 − ε ) A cos(2 φ h − φ S ) LT cos (2 φ h − φ S ) (cid:105)(cid:41) (1) where ratio of longitudinal and transverse photon fluxes is given as ε = (1 − y − γ y ) / (1 − y + y + γ y ); γ = 2 M x/Q . Target transverse polarization ( S T )dependent part of this general expression contains eight azimuthal modulations inthe φ h and φ S azimuthal angles of the produced hadron and of the nucleon spin,correspondingly. Each modulation leads to a A w i ( φ h ,φ S ) BT Transverse-Spin-dependentAsymmetry (TSA) defined as a ratio of the associated structure function F w i ( φ h ,φ S ) BT to the azimuth-independent one F UU = F UU,T + εF UU,L . Here the superscript of theasymmetry indicates corresponding modulation, the first and the second subscripts- respective (”U”-unpolarized,”L”-longitudinal and ”T”-transverse) polarization ofbeam and target. Five amplitudes which depend only on S T are the target Single-Spin Asymmetries (SSA), the other three which depend both on S T and λ (beamlongitudinal polarization) are known as Double-Spin Asymmetries (DSA).In the QCD parton model approach four (marked in red) out of eight trans-verse spin asymmetries have Leading Order (LO) or leading ”twist” interpreta-tion and are described by the convolutions of twist-two Transverse-Momentum-Dependent (TMD) Parton Distribution Functions (PDFs) and FragmentationFunctions (FFs) – . These are the famous A sin ( φ h + φ S ) UT ”Sivers” and A sin ( φ h + φ S ) UT ”Collins” effects , and A sin(3 φ h − φ S ) UT single-spin asymmetry (related to h ⊥ q T (”pret-zelosity”) PDF – ) and A cos( φ h − φ S ) LT DSA (related to g q T (”worm-gear”) distribu-tion function – , , ).Remaining four (marked in blue) asymmetries ( A sin( φ s ) UT and A sin(2 φ h − φ s ) UT SSAsand A cos( φ s ) LT and A cos(2 φ h − φ s ) LT DSAs) are so-called ”higher-twist” effects. Corre-sponding structure functions contain terms at sub-leading order in Q − which in-volve a mixture of twist-two and induced by quark-gluon correlations twist-threeparton distribution and fragmentation functions , , . However, applying wildlyadopted so-called ”Wandzura-Wilczek approximation” this higher twist objects canbe simplified to twist-two level (see Refs. 2, 4 for more details).In general, TSAs being convolutions of different TMD functions are known tobe complex objects a priori dependent on the choice of kinematical ranges andovember 12, 2018 19:10 WSPC/INSTRUCTION FILESPIN2014˙proceedings˙SIDIS Multidimensional TSAs at COMPASS multidimensional kinematical phase-space. Thus, ideally, asymmetries have to beextracted as multi-differential functions of kinematical variables in order to revealthe most complete multivariate dependence. In practice, available statistics oftenis too limited for such an ambitious approach and investigating dependence of theasymmetries on some specific kinematic variable one is forced to integrate overall the others. Presently, one of the hottest topics in the field of spin-physics isthe study of TMD evolution of various PDFs and FFs and related asymmetries.Different models predict from small up to quite large ∼ /Q suppression of theQCD-evolution effects attempting to describe available experimental observationsand make predictions for the future ones , , . Additional experimental measure-ments exploring different Q domains for fixed x -range are necessary to furtherconstrain the theoretical models. The work described in this review is a unique andfirst ever attempt to explore behaviour of TSAs in the multivariate kinematicalenvironment. For this purpose COMPASS experimental data was split into five dif-ferent Q ranges giving an opportunity to study asymmetries as a function of Q at fixed bins of x . Additional variation of z and p T cuts allows to deeper exploremulti-dimensional behaviour of the TSAs and their TMD constituents.
2. Analysis and COMPASS multi-dimensional concept
The analysis was carried out on COMPASS data collected in 2010 with transverselypolarized proton data. General, event selection procedure as well as asymmetryextraction and systematic uncertainty definition techniques applied for this analysisare identical to those used for recent COMPASS results on Collins, Sivers and otherTSAs – . General sample is defined by the following standard DIS cuts: Q > GeV /c ) , 0 . < x < . . < y < . hadronic selections: p T > . z > . Q -dependence the x : Q phase-space covered byCOMPASS experimental data has been divided into 5 × Q -ranges are the following ones: Q / ( GeV /c ) ∈ [1; 1 . , [1 .
7; 3] , [3; 7] , [7; 16] , [16; 81] a . In addition, each of this samples has beendivided into five z and five p T (GeV/c) sub-ranges defined as follows: z > . z > .
2, 0 . < z < .
2, 0 . < z < . . < z < . p T > .
1, 0 . < p T < .
75, 0 . < p T < .
3, 0 . < p T < .
75 and p T > .
75. Usingvarious combinations of aforementioned cuts and ranges, asymmetries have beenextracted for following ”3D” and ”4D” configurations: 1) x -dependence in Q - z and Q - p T grids. 2) Q -dependence in x - z and x - p T grids. 3) Q - (or x -) dependence in x - p T (or Q - p T ) grids for different choices of z -cuts.Another approach was used to focus on z - and p T -dependences in different x -ranges. For this study the two-dimensional z : p T phase-space has been divided into a < Q / ( GeV/c ) <
81 selection repeats the definition of the so-called ”high-mass” range: mostpromising domain for future COMPASS–Drell-Yan TSA-analyses , . ovember 12, 2018 19:10 WSPC/INSTRUCTION FILESPIN2014˙proceedings˙SIDIS Bakur Parsamyan × x -bins: 0 . < x < .
7, 0 . < x < . . < x < . x - z - p T ” grid. In the next section several examples of COMPASSpreliminary results obtained for multi-dimensional target transverse spin dependentazimuthal asymmetries are presented. x -3 -2 -1
10 1 ( G e V / c ) Q ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d ( a . u . ) / dxd Q h N d preliminaryCOMPASS Proton 2010 data <81 /(GeV/c) /(GeV/c) /(GeV/c) /(GeV/c) /(GeV/c) -3 -2 -1
10 1110 > 1 /(GeV/c) Q z ( G e V / c ) T p ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d ( a . u . ) T / d z dp h N d preliminaryCOMPASS Proton 2010 data Fig. 1. COMPASS x : Q (right) and z : p T (left) phase space coverage.
3. Results
As an example of ”3D” Sivers effect, two extracted configurations are quoted in theFig. 2. In the top plot x -dependence of the asymmetry for positive and negativehadrons is shown in cells of two-dimensional grid of Q and p T exploring the ”3D: Q - p T - x ” behaviour. Sizable Sivers asymmetry is observed for positive hadronstending to increase with p T , while for negative hadrons there are some indicationsfor a positive signal at relatively large x and Q . The bottom plot draws the Q dependence in a ”3D: x - z - Q ” configuration and serves as a direct input for TMD-evolution related studies. In fact, in several x-bins there are some hints for possible Q -dependence for positive hadrons (decrease) more evident at large z bins.In Fig. 3 Collins asymmetry is shown in ”3D: Q - z - x ” (top) and ”3D: x - z - p T ” (bottom) grids. Clear ”mirrored” behaviour for positive and negative hadronamplitudes is being observed in most of the bins. Amplitudes tend to increase inabsolute value with both z and p T .Another SSA which is found to be non-zero at COMPASS is the A sin( φ s ) UT termwhich is presented in Fig. 4 (top) in ”3D: x - z - p T ” configuration. Here the mostinteresting is the large z -range were amplitude is measured to be sizable and nonzero both for positive and negative hadrons.The bottom plot in the Fig. 4 is dedicated to the A cos( φ h − φ S ) LT DSA exploredin ”3D: Q - z - x ” grid and superimposed with the theoretical curves from Ref. 13.This is the only DSA which appears to be non-zero at COMPASS and the last TSAfor which a statistically significant signal has been detected. Remaining four asym-metries are found to be small or compatible with zero within available statisticalaccuracy and to be in agreement with available predictions , , .ovember 12, 2018 19:10 WSPC/INSTRUCTION FILESPIN2014˙proceedings˙SIDIS Multidimensional TSAs at COMPASS -2 -1 -0.100.1 + h - h ) S f - h f s i n ( U T A <1.7 /(GeV/c) T p -2 -1 -0.100.1 preliminaryCOMPASS /(GeV/c)<0.75; z>0.1 T -2 -1 -0.100.1 Proton 2010 data /(GeV/c)<0.3; z>0.1 T -2 -1 -0.100.1 /(GeV/c)<0.75; z>0.1 T -2 -1 -0.100.1 >0.75 GeV; z>0.1 T p -2 -1 -0.100.1 ) S f - h f s i n ( U T A <3 /(GeV/c) -2 -1 -0.100.1 -2 -1 -0.100.1 -2 -1 -0.100.1 -2 -1 -0.100.1 -2 -1 -0.100.1 ) S f - h f s i n ( U T A <7 /(GeV/c) -2 -1 -0.100.1 -2 -1 -0.100.1 -2 -1 -0.100.1 -2 -1 -0.100.1 -2 -1 -0.100.1 ) S f - h f s i n ( U T A <16 /(GeV/c) -2 -1 -0.100.1 -2 -1 -0.100.1 -2 -1 -0.100.1 -2 -1 -0.100.1 -2 -1 -0.100.1 x ) S f - h f s i n ( U T A <81 /(GeV/c) -2 -1 -0.100.1 x -2 -1 -0.100.1 x -2 -1 -0.100.1 x -2 -1 -0.100.1 x -0.0500.05 + h - h ) S f - h f s i n ( U T A T z>0.1; p -0.0500.05 ) S f - h f s i n ( U T A -0.0500.05 ) S f - h f s i n ( U T A -0.0500.05 ) S f - h f s i n ( U T A -0.0500.05 ) S f - h f s i n ( U T A -0.0500.05 ) S f - h f s i n ( U T A -0.0500.05 ) S f - h f s i n ( U T A -0.0500.05 ) S f - h f s i n ( U T A -0.0500.05 (GeV/c) Q ) S f - h f s i n ( U T A -0.0500.05 preliminaryCOMPASS >0.1 GeV/c T z>0.2; p -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 (GeV/c) Q -0.0500.05 Proton 2010 data >0.1 GeV/c T -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 (GeV/c) Q -0.0500.05 >0.1 GeV/c T -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 (GeV/c) Q -0.0500.05 >0.1 GeV/c T -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 (GeV/c) Q Fig. 2. Sivers asymmetry in ”3D”: Q - p T - x (top) and x - z - Q (bottom). ovember 12, 2018 19:10 WSPC/INSTRUCTION FILESPIN2014˙proceedings˙SIDIS Bakur Parsamyan -2 -1 -0.100.1 + h - h ) p - S f + h f s i n ( U T A <1.7 /(GeV/c) T z>0.1; p -2 -1 -0.100.1 preliminaryCOMPASS >0.1 GeV/c T z>0.2; p -2 -1 -0.100.1 Proton 2010 data >0.1 GeV/c T -2 -1 -0.100.1 >0.1 GeV/c T -2 -1 -0.100.1 >0.1 GeV/c T -2 -1 -0.100.1 ) p - S f + h f s i n ( U T A <3 /(GeV/c) -2 -1 -0.100.1 -2 -1 -0.100.1 -2 -1 -0.100.1 -2 -1 -0.100.1 -2 -1 -0.100.1 ) p - S f + h f s i n ( U T A <7 /(GeV/c) -2 -1 -0.100.1 -2 -1 -0.100.1 -2 -1 -0.100.1 -2 -1 -0.100.1 -2 -1 -0.100.1 ) p - S f + h f s i n ( U T A <16 /(GeV/c) -2 -1 -0.100.1 -2 -1 -0.100.1 -2 -1 -0.100.1 -2 -1 -0.100.1 -2 -1 -0.100.1 x ) p - S f + h f s i n ( U T A <81 /(GeV/c) -2 -1 -0.100.1 x -2 -1 -0.100.1 x -2 -1 -0.100.1 x -2 -1 -0.100.1 x -0.100.1 + h - h ) p - S f + h f s i n ( U T A all x0.10
4. Conclusions
The first ever multidimensional extraction of the whole set of target transversespin dependent azimuthal asymmetries has been done at COMPASS with protondata collected in 2010. Various multi-differential configurations has been tested ex-ploring x : Q : z : p T phase-space. Particular attention was given to probes of possible Q -dependence of TSAs, serving a direct input to TMD-evolution related studies.Several interesting observations have been made studying the results obtained forSivers, Collins, A cos ( φ h − φ S ) LT and A sin ( φ S ) UT asymmetries. Other four asymmetries werefound to be compatible with zero within given statistical accuracy. These resultscombined with past and future data of other collaborations will give a unique op-portunity to access the whole set of TMD PDFs and test their multi-differentialnature and key features.Bakur Parsamyan undertook this work with the support of the ICTP TRIL Pro-gramme, Trieste, Italy. References
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