Polarized Drell-Yan at COMPASS-II: Transverse Spin Physics Program
AApril 9, 2015 0:33 WSPC/INSTRUCTION FILESPIN2014˙proceedings˙DY
International Journal of Modern Physics: Conference Seriesc (cid:13)
The Authors
Polarized Drell-Yan at COMPASS-II: Transverse Spin Physics Program
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]
Successful realization of polarized Drell-Yan physics program is one of the main goals ofthe second stage of the COMPASS experiment. Drell-Yan measurements with high en-ergy (190 GeV/c) pion beam and transversely polarized NH3 target have been initiatedby a pilot-run in the October 2014 and will be followed by 140 days of data taking in2015. In the past twelve years COMPASS experiment performed series of SIDIS mea-surements with high energy muon beam and transversely polarized deuteron and protontargets. Results obtained for Sivers effect and other target transverse spin dependentand unpolarized azimuthal asymmetries in SIDIS serve as an important input for gen-eral understanding of spin-structure of the nucleon and are being used in numeroustheoretical and phenomenological studies being carried out in the field of transvers-spinphysics. Measurement of the Sivers and all other azimuthal effects in polarized Drell-Yanat COMPASS will reveal another side of the spin-puzzle providing a link between SIDISand Drell-Yan branches. This will be a unique possibility to test universality and key-features of transverse momentum dependent distribution functions (TMD PDFs) usingessentially same experimental setup and exploring same kinematic domain. In this reviewmain physics aspects of future COMPASS polarized Drell-Yan measurement of azimuthaltransverse spin asymmetries will be presented, giving a particular emphasis on the linkwith very recent COMPASS results obtained for SIDIS transverse spin asymmetries fromfour ”Drell-Yan” Q -ranges. Keywords : COMPASS; Drell-Yan; SIDIS; Transverse Spin Azimuthal Asymmetries;PACS numbers: 13.60.-r; 13.60.Hb; 13.88.+e; 14.20.Dh; 14.65.-q.
1. Introduction
Study of spin-dependent azimuthal asymmetries arising in the SIDIS and Drell-Yancross-sections is a powerful method used to access TMD distribution functions ofthe nucleon. Using standard notations the cross-section expression for the leptonoff transversely polarized nucleon SIDIS processes can be written in a following
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 pril 9, 2015 0:33 WSPC/INSTRUCTION FILESPIN2014˙proceedings˙DY Bakur Parsamyan 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 ε is the ratio of longitudinal and transverse photon fluxes and is given as ε =(1 − y − γ y ) / (1 − y + y + γ y ); γ = 2 M x/Q . Target transverse polarizationdependent 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 (see Fig. 1). Each modulation leads to a A w i ( φ h ,φ s ) BT Target-Spin-dependent Asymmetry (TSA) defined as a ratio of the associated structure functionto the azimuth-independent ones. Here the superscript of the asymmetry indicatescorresponding modulation, the first and the second subscripts - respective (”U”-unpolarized,”L”-longitudinal and ”T”-transverse) polarization of beam and target.Five amplitudes which depend only on S T are the Single-Spin Asymmetries (SSA),the other three which depend both on S T and λ (beam longitudinal polarization)are known as Double-Spin Asymmetries (DSA). Amplitude of each modulation isscaled by a ε -dependent so-called depolarization factor. Using similar notations, thegeneral form of the single-polarized ( πN ↑ ) Drell-Yan cross-section (leading orderpart) in terms of angular variables defined in Collins-Soper and target rest frames(see Fig. 1) can be written in the following model-independent way : dσ LO d Ω = α em F q F U (cid:110) θ + sin θA cos 2 ϕ CS U cos 2 ϕ CS + S T (cid:104)(cid:0) θ (cid:1) A sin ϕ S T sin ϕ S + sin θA sin(2 ϕ CS + ϕ S ) T sin (2 ϕ CS + ϕ S )+ sin θA sin(2 ϕ CS − ϕ S ) T sin (2 ϕ CS − ϕ S ) (cid:105)(cid:111) (2) Similarly to the SIDIS case, the superscript of the asymmetry indicates the cor-responding modulation, while ”U”,”L” and ”T” denote the state of the target po-larization. As one can see, in the Drell-Yan cross-section only one unpolarized andthree target transverse spin dependent azimuthal modulations arise at leading order.Within the QCD parton model approach four of the eight SIDIS TSAs haveLeading Order (LO) interpretation (first three SSAs and first DSA in Eq. 1) a and are described by the different convolutions of Transverse Momentum Depen-dent (TMD) twist-two Parton Distribution Functions (PDFs) and FragmentationFunctions(FFs) – . The first two are well-known Sivers (gives access to ”Sivers” a In Eq. 1, Eq. 2 and Table. 1 the LO amplitudes are marked in red and subleading ones - in blue. b In this review FFs in SIDIS and beam PDFs in Drell-Yan are not discussed for brevity. pril 9, 2015 0:33 WSPC/INSTRUCTION FILESPIN2014˙proceedings˙DY
COMPASS-DY: Transverse Spin Physics Program April 5, 2015 0:20 WSPC/INSTRUCTION FILESPIN2014˙proceedings˙DY S T qq T H a ( P a ) x ˆ y ˆ z ˆ φ S θ CS ℓ P a , CS P b , CS x ˆ CS z ˆ CS y ˆ CS ℓ ′ φ CS y z x l S T φ h φ S q SIDIS Drell-Yan p T l' p The first two are well-known Sivers (gives access to ”Sivers” PDF f ⊥ q T ) and Collins(gives access to ”transversity” PDF h q ) asymmetries. The other two A sin(3 φ h − φ s ) UT and A cos( φ h − φ s ) LT LO TSAs are related to the h ⊥ q T (pretzelosity) and g q T (worm-gear) DFs, correspondingly. The remaining four SIDIS asymmetries are higher-twisteffects, however they can be expressed in terms of twist-two PDFs being interpretedas Cahn kinematic corrections to twist-two spin effects on the transversely polarizednucleon (suppressed with respect to the leading twist ones by ∼ M/Q ) (for detailssee: , - ).Within the same QCD parton model approach, Drell-Yan TSAs are also in-terpreted in terms of TMD PDFs. In this case the asymmetries are related to theconvolution of two TMD PDFs: one of the beam and one of the target hadron. Quot-ing only the target nucleon PDFs: the A sin ϕ s T , A sin(2 ϕ CS − ϕ s ) T and A sin(2 ϕ CS + ϕ s ) T giveaccess to the ”Sivers” f ⊥ q T , ”transversity” h q and ”pretzelosity” h ⊥ q T , distributionfunctions, respectively. Within the concept of universality (process-independence)of TMD PDFs it appears that same parton distributions functions can be accessedboth in SIDIS and Drell-Yan (see the Table. 1 for the complete list). SIDIS ‘ → N ↑ TMD PDF DY πN ↑ (LO) A cos 2 φ h UU , A cos φ h UU h ⊥ q A cos 2 ϕ CS U A sin( φ h − φ s ) UT , A sin φ s UT , A sin(2 φ h − φ s ) UT f ⊥ q T A sin ϕ S T A sin( φ h + φ s − π ) UT , A sin φ s UT h q A sin(2 ϕ CS − ϕ S ) T A sin(3 φ h − φ s ) UT , A sin(2 φ h − φ s ) UT h ⊥ q T A sin(2 ϕ CS + ϕ S ) T A cos( φ h − φ s ) LT , A cos φ s LT , A cos(2 φ h − φ s ) LT g q T DP DY
Therefore, DY measurements at COMPASS will be intriguingly complementaryto the COMPASS SIDIS results and will give an unprecedented opportunity to ac-
Fig. 1. SIDIS and Drell-Yan frameworks and notations..
PDF f ⊥ q T ) and Collins (gives access to ”transversity” PDF h q ) asymmetries , .The other two A sin(3 φ h − φ s ) UT and A cos( φ h − φ s ) LT LO TSAs are related to the h ⊥ q T (pret-zelosity) and g q T (worm-gear) DFs, correspondingly – , , ). The remaining fourSIDIS asymmetries are suppressed with respect to the leading twist ones by ∼ M/Q and are subleading or higher-twist effects , , . However applying wildly adoptedso-called ”Wandzura-Wilczek approximation” this higher twist objects can be sim-plified to twist-two level (see Refs. 2, 7 for more details). The whole set of eightSIDIS asymmetries has been already measured at COMPASS for both deuteron andproton targets (See Refs. 8–15 and references therein). Within the same QCD par- Table 1. Nucleon TMD PDFs accessed via SIDIS and Drell-Yan TSAs.SIDIS (cid:96) → N ↑ TMD PDF DY πN ↑ (LO) A cos 2 φ h UU , A cos φ h UU h ⊥ q A cos 2 ϕ CS U A sin( φ h − φ s ) UT , A sin φ s UT , A sin(2 φ h − φ s ) UT f ⊥ q T A sin ϕ S T A sin( φ h + φ s − π ) UT , A sin φ s UT h q A sin(2 ϕ CS − ϕ S ) T A sin(3 φ h − φ s ) UT , A sin(2 φ h − φ s ) UT h ⊥ q T A sin(2 ϕ CS + ϕ S ) T A cos( φ h − φ s ) LT , A cos φ s LT , A cos(2 φ h − φ s ) LT g q T double-polarized DY ton model approach, Drell-Yan TSAs are also interpreted in terms of TMD PDFs.In this case the asymmetries are related to the convolution of two TMD PDFs:one of the beam and one of the target hadron. Again, quoting only the target nu-cleon PDFs: the A sin ϕ s T , A sin(2 ϕ CS − ϕ s ) T and A sin(2 ϕ CS + ϕ s ) T give access to the ”Sivers” f ⊥ q T , ”transversity” h q and ”pretzelosity” h ⊥ q T , distribution functions, respectively.Within the concept of generalized universality c of TMD PDFs it appears that sameparton distributions functions can be accessed both in SIDIS and Drell-Yan (seethe Table. 1 for the complete list). Therefore, DY measurements at COMPASSwill be intriguingly complementary to the COMPASS SIDIS results and will givean unprecedented opportunity to access TMD PDFs via two mechanisms and test c Time-reversal modified process-independence. pril 9, 2015 0:33 WSPC/INSTRUCTION FILESPIN2014˙proceedings˙DY Bakur Parsamyan their universality and key features (for instance, predicted Sivers and Boer-MuldersPDFs sign change) using essentially same experimental setup.
2. COMPASS: SIDIS – Drell-Yan ”bridge”
During it’s first phase in 2002-2010 COMPASS has made series of SIDIS TSA mea-surements using 160 GeV/c longitudinally polarized muon beam and transverselypolarized LiD and
N H targets (See Refs. 8–15 and references therein). New mea-surements for TSAs, but this time with Drell-Yan reaction are foreseen in 2015 with190 GeV/c π − beam and transversely polarized polarized N H -target , .Certainly, both sets of COMPASS results from SIDIS and Drell-Yan will becomea subject of global fits and phenomenological comparison. For this purpose the bestoption is to explore SIDIS data in more differential way extracting the asymmetriesin the same four Q kinematic regions (which implies also different x -coverage)which were selected for the COMPASS Drell-Yan measurement program , : • < Q / ( GeV/c ) < low mass ” (3) • < Q / ( GeV/c ) < .
25 ” intermediate mass ” • . < Q / ( GeV/c ) <
16 ”
J/ψ mass ” • Q / ( GeV/c ) >
16 ”
High mass ” . In the left plot in Fig. 2 COMPASS SIDIS x : Q kinematical phase-space is shownas divided in four ”Drell-Yan” Q -ranges. Here the most promising for DY-studiesis the so-called ”high mass” range which is expected to be free from backgroundand corresponds to the valence-quark region where the Drell-Yan asymmetries areexpected to reach their largest values , . On the right plot COMPASS SIDIS Q > GeV /c ) and Drell-Yan ”high mass” overlapping distributions are demonstrated. April 4, 2015 23:54 WSPC/INSTRUCTION FILESPIN2014˙proceedings˙DY Bakur Parsamyan cess TMD PDFs via two mechanisms and test their universality and key features(for instance, predicted Sivers and Boer-Mulders PDFs sign change) using essen-tially same experimental setup. Certainly, at some point both sets of COMPASSresults from SIDIS and Drell-yan will be a subject of global fits and phenomenolog-ical comparison. For this purpose the best option is to explore SIDIS data in moredifferential way extracting the asymmetries in the same four Q kinematic regions(which implies also different x -coverage) which were selected for the COMPASSDrell-Yan measurement program : • < Q / ( GeV /c ) < low mass ” (3) • < Q / ( GeV /c ) < .
25 ” intermediate mass ” • . < Q / ( GeV /c ) <
16 ”
J/ψ mass ” • Q / ( GeV /c ) >
16 ”
High mass ” . ( 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 > 16 /(GeV/c) Q < 16 /(GeV/c) /(GeV/c) /(GeV/c) -3 -2 -1
10 1110 > 1 /(GeV/c) Q -2 -1 Drell-Yan (MC)SIDIS (2010 proton data) x Q ( G e V / c )
2. Data analysis details
One of the important objectives of the COMPASS experiment is the explorationof transverse spin structure of nucleon via spin (in)dependent azimuthal asymme-tries in semi-inclusive deep inelastic scattering (SIDIS) of polarized leptons (andsoon also Drell-Yan (DY) reactions with π − ) off transversely polarized target. Forthis purpose a series of measurements were made in COMPASS, using 160 GeV/c COMPASS preliminary / dxd Q / dxd Q / dxd Q / dxd Q ( a . u . ) ( a . u . ) ( a . u . ) ( a . u . ) hhhh dddd NNNN Q ( G e V / c ) -3 -2 -1 x Fig. 2. COMPASS x : Q phase-space with indicated four Drell-Yan Q -ranges. SIDIS TSAs extracted from all four aforementioned ” Q -ranges” together withCOMPASS recent results for multi-differential analysis will serve not only forfuture SIDIS-DY comparison, but, exploring two-dimensional x : Q -behaviour ofthe asymmetries, they can be used also as a better input for TMD-evolution studiesand related SIDIS-DY predictions , , .pril 9, 2015 0:33 WSPC/INSTRUCTION FILESPIN2014˙proceedings˙DY COMPASS-DY: Transverse Spin Physics Program Results for Sivers asymmetry are presented in Fig. 3. A clear positive signal isobserved for positive hadrons (growing with x , z and p T ). For negative hadronssome hints of a negative amplitude can be seen at lowest Q -range for intermediate z values while at relatively large x and Q there are indication for a positive signal. -2 -1 -0.0500.05 + h - h <4 /(GeV/c) ) S j - h j s i n ( U T A -0.0500.05 preliminaryCOMPASS Proton 2010 data -0.0500.05 -2 -1 -0.0500.05 <6.25 /(GeV/c) ) S j - h j s i n ( U T A -0.0500.05 -0.0500.05 -2 -1 -0.0500.05 <16 /(GeV/c) ) S j - h j s i n ( U T A -0.0500.05 -0.0500.05 -2 -1 -0.0500.05 x >16 /(GeV/c) Q ) S j - h j s i n ( U T A -0.0500.05 z -0.0500.05 (GeV/c) T p Fig. 3. SIDIS Sivers asymmetry from Drell-Yan Q -ranges. Comparing points from same x -bins, but different Q -ranges one can see thatwithin statistical accuracy there is no clear and strong Q -dependence for the ef-fect. Nevertheless, decreasing with Q trend can be noted in some bins which hasbeen confirmed also by the recent more detailed multidimensional analysis . It isinteresting to mention that for planned Drell-Yan measurements Sivers asymmetryin the ”high mass”-range is expected to have approximately same statistical accu-racy as it’s SIDIS-analogue extracted from COMPASS proton-2010 data ( ≈ , , .Even if Sivers effect in Drell-Yan is a flagship measurement for COMPASS-II, otherTSAs and their links with SIDIS ”analogues” from Table. 1 are also very importantfor general TMD PDF-studies. In the Fig. 4 mean values for all eight SIDIS-TSAsare quoted as measured in four Drell-Yan Q -ranges.pril 9, 2015 0:33 WSPC/INSTRUCTION FILESPIN2014˙proceedings˙DY Bakur Parsamyan -0.02 -0.01 0 0.01 0.02 preliminaryCOMPASS proton 2010 data ) S j - h j sin(UT A ) p - S j + h j sin(UT A ) S j - h j sin(3UT A S j sinUT A ) S j - h j sin(2UT A ) S j - h j cos(LT A S j cosLT A ) S j - h j cos(2LT A æ A Æ + h - h <4 (GeV/c) » æ x Æ z > 0.2 -0.1 -0.05 0 0.05 0.1 preliminaryCOMPASS proton 2010 data ) S j - h j sin(UT A ) p - S j + h j sin(UT A ) S j - h j sin(3UT A S j sinUT A ) S j - h j sin(2UT A ) S j - h j cos(LT A S j cosLT A ) S j - h j cos(2LT A æ A Æ + h - h <6.25 (GeV/c) » æ x Æ z > 0.2 -0.1 -0.05 0 0.05 0.1 preliminaryCOMPASS proton 2010 data ) S j - h j sin(UT A ) p - S j + h j sin(UT A ) S j - h j sin(3UT A S j sinUT A ) S j - h j sin(2UT A ) S j - h j cos(LT A S j cosLT A ) S j - h j cos(2LT A æ A Æ + h - h <16 (GeV/c) » æ x Æ z > 0.2 -0.1 -0.05 0 0.05 0.1 preliminaryCOMPASS proton 2010 data ) S j - h j sin(UT A ) p - S j + h j sin(UT A ) S j - h j sin(3UT A S j sinUT A ) S j - h j sin(2UT A ) S j - h j cos(LT A S j cosLT A ) S j - h j cos(2LT A æ A Æ + h - h >16 (GeV/c) Q 0.233 » æ x Æ z > 0.2 Fig. 4. Mean SIDIS TSAs in four Drell-Yan Q -ranges (left to right)
3. Conclusions
In 2015 COMPASS experiment will start collecting first ever transversely polar-ized Drell-Yan data. Recently COMPASS has provided first input for future directSIDIS-DY studies. Using COMPASS proton 2010 transvers data all eight SIDISTSAs were extracted from four Q -ranges selected for the COMPASS Drell-Yanprogram. These results combined with future polarized Drell-Yan data from COM-PASS will give a unique opportunity to access TMD PDFs via two processes andtest their universality and key features sticking to the same x : Q kinematical range.Bakur Parsamyan undertook this work with the support of the ICTP TRIL Pro-gramme, Trieste, Italy. References
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