New results on transverse spin asymmetries from COMPASS
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Owned by the authors, published by EDP Sciences, 2018
New results on transverse spin asymmetries from COMPASS
Bakur Parsamyan , , a Dipartimento di Fisica Generale, Università di Torino, Torino, Italy INFN, Sezione di Torino, Via P. Giuria 1, I-10125 Torino, Italy
Abstract.
One of the important objectives of the COMPASS experiment is the exploration of transversespin structure of nucleon via spin (in)dependent azimuthal asymmetries in semi-inclusive deep inelasticscattering (SIDIS) of polarized leptons (and soon also Drell-Yan (DY) reactions with π − ) o ff trans-versely polarized target. For this purpose a series of measurements were made in COMPASS, using160 GeV / c longitudinally polarized muon beam and polarized LiD and NH targets and are foreseenwith 190 GeV / c π − beam on polarized NH . The experimental results obtained by COMPASS for az-imuthal e ff ects in SIDIS play an important role in the general understanding of the three-dimensionalnature of the nucleon and are widely used in theoretical analyses and global data fits. Future first everpolarized DY-data from COMPASS compared with SIDIS results will open a new chapter probing gen-eral principles of QCD TMD-formalism. In this review main focus will be given to the very recentCOMPASS results obtained for SIDIS transverse spin asymmetries from four "Drell-Yan" Q -ranges. Using standard notations SIDIS cross-section can bewritten in a following model-independent way [1], [2]: d σ dxd y dzdP hT d ϕ h d ψ = (cid:34) α x y Q y − ε ) (cid:32) + γ x (cid:33)(cid:35) F UU (1) × (cid:110) + (cid:112) ε (1 + ε ) A cos φ h UU cos φ h + ε A cos2 φ h UU cos 2 φ h + λ (cid:104) (cid:112) ε (1 − ε ) A sin φ h LU sin φ h (cid:105) + S L (cid:104) (cid:112) ε (1 + ε ) A sin φ h UL sin φ h + ε A sin2 φ h UL sin 2 φ h (cid:105) + S L λ (cid:104) √ − ε A LL + (cid:112) ε (1 − ε ) A cos φ h LL cos φ h (cid:105) + S T (cid:20) A sin ( φ h − φ S ) UT sin ( φ h − φ S ) + ε A sin ( φ h + φ S ) UT sin ( φ h + φ S ) + ε A sin ( 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 ( φ h − φ S ) UT sin (2 φ h − φ S ) (cid:21) + S T λ (cid:20) (cid:113)(cid:0) − ε (cid:1) 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 ( φ h − φ S ) LT cos (2 φ h − φ S ) (cid:21)(cid:27) a e-mail: [email protected] where, F UU = F UU , T + ε F UU , L and ψ is the labora-tory azimuthal angle of the scattered lepton (in DISkinematics d ψ ≈ d φ S ). Target transverse polariza-tion dependent part of this general expression con-tains eight azimuthal modulations in the φ h and φ S az-imuthal angles of the produced hadron and of the nu-cleon spin, correspondingly, see Fig. 1. Each modula-tion leads to a A w i ( φ h ,φ s ) BT Target-Spin-dependent Asym-metry (TSA) defined as a ratio of the associated struc-ture function to the unpolarized ones. Here the super-script of the asymmetry indicates corresponding mod-ulation, the first and the second subscripts - respective("U"-unpolarized,"L"-longitudinal and "T"-transverse)polarization of beam and target. Five amplitudes whichdepend 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 modula-tion is scaled by a ε -dependent so-called depolarizationfactor where: ε = − y − γ y − y + y + γ y , γ = MxQ (2)Using similar notations, the general form of the single-polarized ( π N ↑ ) Drell-Yan cross-section (leading orderpart) in terms of angular variables defined in Collins-Soper frame (Fig. 1) can be written in the following a r X i v : . [ h e p - e x ] N ov PJ Web of Conferences 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 Figure 1.
SIDIS and Drell-Yan frameworks and notations. model-independent way [3]: d σ LO d Ω = α em Fq F U (cid:110) + cos θ + sin θ A cos2 ϕ CS U cos 2 ϕ CS (3) + S L sin θ A sin2 ϕ CS L sin 2 ϕ CS + S T (cid:104)(cid:16) + cos θ (cid:17) A sin ϕ S T sin ϕ S + sin θ A sin(2 ϕ CS + ϕ S ) T sin (2 ϕ CS + ϕ S ) + sin θ A sin(2 ϕ CS − ϕ S ) T sin (2 ϕ CS − ϕ S ) (cid:105)(cid:111) Similarly to the SIDIS case, the superscript of theasymmetry indicates the corresponding modulation.As in Eq. 1 "U","L" and "T" denote the state of thetarget polarization. As one can see, in the Drell-Yancross-section only one unpolarized and three targettransverse spin dependent azimuthal modulations ariseat leading order.Within the QCD parton model approach four of theeight SIDIS TSAs have Leading Order (LO) interpre-tation (first three SSAs and first DSA in Eq. 1) and aredescribed by the di ff erent convolutions of TransverseMomentum Dependent (TMD) twist-two distributionfunctions (DFs) and fragmentation functions(FFs) .The first two are well-known Sivers (gives accessto "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, corre-spondingly. The remaining four SIDIS asymmetriesare higher-twist e ff ects, however they can be expressedin terms of twist-two PDFs being interpreted as Cahnkinematic corrections to twist-two spin e ff ects on thetransversely polarized nucleon (suppressed with re-spect to the leading twist ones by ∼ M / Q ) (for detailssee: [2],[4]-[6]). In Eq. 1, Eq. 3, Table. 1 and Table. 2 the "twist-2" (LO) ampli-tudes are marked in red and those which have higher twist interpre-tation - in blue
Within the same QCD parton model approach,Drell-Yan TSAs are also interpreted in terms of TMDPDFs. In this case the asymmetries are related to theconvolution of two TMD PDFs: one of the beam andone of the target hadron. 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, respec-tively. Within the concept of universality (process-independence) of TMD PDFs it appears that same par-ton distributions functions can be accessed both inSIDIS and Drell-Yan (see the Table. 1 for the completelist). Table 1.
Nucleon TMD PDFs accessed via SIDIS andDrell-Yan asymmetries
SIDIS (cid:96) → N ↑ TMD PDF DY π N ↑ (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 DYTherefore, DY measurements at COMPASS will beintriguingly complementary to the COMPASS SIDISresults and will give an unprecedented opportunityto access TMD PDFs via two mechanisms and testtheir universality and key features (for instance, pre-dicted Sivers and Boer-Mulders PDFs sign change)using essentially same experimental setup. Certainly,at some point both sets of COMPASS results fromSIDIS and Drell-yan will be a subject of global fitsand phenomenological comparison. For this purposethe best option is to explore SIDIS data in more dif-ferential way extracting the asymmetries in the samefour Q kinematic regions (which implies also di ff erent x -coverage) which were selected for the COMPASSDrell-Yan measurement program [3]: • < Q / ( GeV / c ) < lo w mass ” (4) • < Q / ( GeV / c ) < .
25 ” intermediate mass ” • . < Q / ( GeV / c ) <
16 ” J /ψ mass ” • Q / ( GeV / c ) >
16 ” Hi g h mass ” . Here the most promising is the so-called "high mass"range which is expected to be free from backgroundand corresponds to the valence-quark region wherethe Drell-Yan asymmetries are expected to reachtheir largest values [3]. SIDIS TSAs extracted fromaforementioned " Q -ranges" will serve not only forfuture SIDIS-DY comparison, but, exploring two-dimensional x : Q -behaviour of the asymmetries, they RANSVERSITY 2014 can be used also as a better input for TMD-evolutionstudies and related SIDIS-DY predictions [7],[8]. Inthis review COMPASS results for all SIDIS TSAs ex-tracted from four Drell-Yan Q -ranges will be dis-cussed. ( a . u . ) / dxd Q h N d 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 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 æ x Æ <4 /(GeV/c) /(GeV/c) /(GeV/c) /(GeV/c) Q +/- Proton 2010 data h -2 -1 æ y Æ -2 -1 æ z Æ -2 -1 æ T p Æ -2 -1 æ W Æ -2 -1 æ Q Æ x 0.2 0.4 0.6 0.8 y z (GeV/c) T p ) W (GeV/c (GeV/c) Q Figure 2.
COMPASS x: Q phase-space with indicated fourDrell-Yan Q -ranges (top). COMPASS multidimensionalkinematical "map" (bottom). Asymmetries were extracted from COMPASS 2010 -transversely polarized proton data. In general, eventselection procedure as well as asymmetry extractionand systematic uncertainty definition techniques ap-plied for this analysis are identical to those used forrecent COMPASS results on Collins, Sivers and otherTSAs [9]-[6].The DIS events are selected by applying standardcuts: Q > GeV / c ) , 0 . < x < . . 9. Two more cuts were applied on hadronic vari-ables: p T > . / c and z > . 2. In COMPASSkinematics "0 . < z < . 2" and " z > . 2" data samplescontain nearly same number of events and in order toimprove the statistical accuracy and clarify the trends, TSAs have also been studied in extended " z > . x : Q phase-space was divided into four sub-ranges by selecting four Drell-Yan Q -bins Fig. 2 (top)according to Eq. 4. Multidimensional map of COM-PASS kinematical dependencies as extracted from thedata is presented in Fig. 2 (bottom).All TSAs were measured as functions of x , z , p T and W ( W -dependencies are omitted in this review forbrevity) both for positive and negative hadrons. In -2 -1 æ D Æ ) S j - h j sin( D ) S j - h j ), sin(3 p - S j + h j sin( D ) S j - h j , sin(2 S j sin D +/- h <4 /(GeV/c) preliminaryCOMPASS ) S j - h j cos( D ) S j - h j , cos(2 S j cos D Proton 2010 data -2 -1 012 <6.25 /(GeV/c) -2 -1 012 <16 /(GeV/c) -2 -1 x >16 /(GeV/c) Q z 0.5 1 1.5 2 2.5 (GeV/c) T p Figure 3. Mean depolarization factors. accordance with Eq. 1 "physics" asymmetries for thegiven modulation w ( φ h , φ s ) are related with the "raw"ones obtained from the fit (as amplitudes of the corre-sponding azimuthal modulations), through the follow-ing relations: A w ( φ h ,φ s ) UT = A w ( φ h ,φ s ) UT , ra w f | P T | D w ( φ h ,φ s ) ( y ) and A w ( φ h ,φ s ) LT = A w ( φ h ,φ s ) LT , ra w f λ | P T | D w ( φ h ,φ s ) ( y ) where P T , f and D w ( φ h ,φ s ) ( y ) are the meanvalues (extracted from the data in the given kinematicalbin) of the transverse polarization of the target (w.r.tbeam axis), target polarization dilution factor and ofthe corresponding depolarization factor (Fig. 3).Last important detail was already described in pre-vious COMPASS reviews [11],[12] and here will beaddressed only briefly. In the Eq. 1 target transversepolarization ( S T ) is defined relative to the virtual pho-ton momentum direction (most natural basis from thetheory point of view) while, in experiment transversepolarization of the target is defined relative to the beam PJ Web of Conferences (incoming lepton) direction. As it was demonstratedin [1],[13] this di ff erence, in particular, influences az-imuthal distributions in the final state. In the appropri-ately modified expression for the SIDIS cross-sectionfor transversely (w.r.t. lepton beam) polarized target[11],[12] one can find new sin θ -scaled terms and θ -dependent factors ( θ is the angle between γ ∗ -directionand initial lepton momenta in lab. frame) and see thatsome TSAs are getting mixed up with longitudinal spinasymmetries (LSA). Anyway, since θ is rather small inCOMPASS kinematics the influence of the additionalterms and factors can be neglected in most of the cases.Essentially, one can can derive following relation be-tween the correct TSAs and those extracted from thefit using "Eq. 1"-approach and therefore mixed withspecific LSAs because of the γ ∗ p → lp transition: A T ≈ A T , f it − C ( ε ) A L . Mixed TSAs and LSAs andcorresponding C ( ε, θ )-factors are presented in Table. 2 Table 2. Mixed "T" and "L" amplitudes and C ( ε, θ )-factors TSA C ( ε, θ )-factor LSA A sin( φ h − φ s ) UT , A sin( φ h + φ s − π ) UT sin θ √ ε (1 + ε )2 A sin φ h UL A sin(2 φ h − φ s ) UT sin θε √ ε (1 + ε ) A sin 2 φ h UL A cos( φ h − φ s ) LT sin θ √ ε (1 − ε )2 √ ( − ε ) A cos φ h LL A cos φ s LT sin θ √ ( − ε ) √ ε (1 − ε ) A LL It can be demonstrated that for all transverse asym-metries except A cos ϕ S LT DSA the impact of TSA-LSAmixing can be neglected. This is justified by the small-ness of C ( ε, θ )-factors in COMPASS kinematics (Fig.4(top)) and since also contributing LSAs are measured(or estimated) to be small [14]. The case of A cos ϕ S LT asymmetry is peculiar since it is a ff ected by a large A LL amplitude [15] and here mixing e ff ect cannot beneglected. In order to correct the A cos ϕ S LT asymmetrythe A LL values evaluated in accordance with [16] wereused. Corresponding A LL curves are shown in Fig.4(bottom) compared with the COMPASS data pointsfrom [15], demonstrating close agreement. Results for Sivers asymmetry from z > . z > . x , z and p T ).For negative hadrons some hints of a negative ampli-tude can be seen at lowest Q -range for intermedi-ate z values while at relatively large x and Q there -2 -1 æ ) q , e C ( Æ ) p - S j + h j sin( A ) S j - h j sin( A ) S j - h j sin(2 A ) S j - h j cos( A +/- h <4 /(GeV/c) preliminaryCOMPASS S j cos A ) S j - h j , cos(2 S j ), sin S j - h j sin(3 A Proton 2010 data -2 -1 /(GeV/c) -2 -1 /(GeV/c) -2 -1 x >16 /(GeV/c) Q z 0.5 1 1.5 2 2.5 (GeV/c) T p LL A COMPASS Proton 2007 (PLB 693(2010)) -2 -1 + h PRD74:074015(2006) =0.10 m =0.15 m =0.20 m =0.25 m <4 /(GeV/c) /(GeV/c) /(GeV/c) /(GeV/c) Q -2 -1 x - h z (GeV/c) T p Figure 4. Top: mean C ( ε, θ )-factors from Table. 2. Bottom: A LL asymmetry, COMPASS data [15] and predictions [16]. are indication for a positive signal. Asymmetry ap-pears to be slightly smaller for z > . z > . 2. Comparing points from same x -bins, but dif-ferent Q -ranges one can see that within statistical ac-curacy there’s no clear and strong Q -dependence forthe e ff ect. Nevertheless, decreasing with Q trend canbe noted in some bins. For Collins e ff ect, clear signal is visible both for pos-itive and negative hadrons (but with opposite sign)at relatively large x values Fig. 6 (top). Asymmetrygrows with x , z and p T , but with some "instabilities" RANSVERSITY 2014 (see for instance saddle-shaped trends in two middle Q -ranges). No clear Q dependence was observed. -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 -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 Figure 5. Sivers asymmetry: z > . z > . A cos ( φ h − φ S ) LT asymmetry The A cos( φ h − φ s ) LT is the only leading-twist LT-amplitude.It provides access to g q T ( x , k T ) "worm gear" PDF, which describes longitudinal polarization of quarks intransversely polarized nucleon. In the Fig. 7 resultsfor this asymmetry are shown together with predic-tion curves evaluated in accordance with [17]. A clearsignal is detected for positive and negative hadrons atlarge x and Q values. Within given statistical accuracypredictions are in agreement with experimental points. A sin ( φ S ) UT asymmetry The A sin( φ s ) UT asymmetry is a sub-leading twist e ff ect. Atfirst order it can be described by Collins and Siversmechanisms only, but suppressed by a factor of Q − and by a factor of ∼ | p T | with respect to them. Thisis the only "higher-twist" e ff ect which shows non-zerotrends. Results for this asymmetry are presented inFig. 6 (bottom). There are several bins at relativelylarge x and Q values where a negative signal can beseen for negative hadrons. For positive hadrons asym-metry appears to be small and compatible with zero ev-erywhere, except few large z bins at Q < GeV / c ) . A sin (3 φ h − φ S ) UT , A sin (2 φ h − φ S ) UT , A cos ( φ S ) LT and A cos (2 φ h − φ S ) LT asymmetries Remaining four asymmetries are found to be compat-ible with zero within statistical accuracy. This canbe explained by di ff erent kinematical suppressions towhich they are a ff ected. For instance, the A sin (2 φ h − φ S ) UT , A cos ( φ S ) LT and A cos (2 φ h − φ S ) LT "higher-twist" terms have Q − -suppression [1], [2], while A sin (3 φ h − φ S ) UT leading orderamplitude is suppressed by a ∼ | p T | scale-factor [1],[2],[18]. In Fig. 7 data-points for the A cos ( φ S ) LT asymme-try are shown as extracted from the fit compared withpoints corrected for A LL -mixing (see Sec. 2). COMPASS provided first input for future direct SIDIS-DY studies. All eight SIDIS TSAs were extractedfrom four Q -ranges selected for the COMPASS futureDrell-Yan program and two z -selections using proton2010 transverse data. Sizable e ff ects were observedfor Sivers and Collins amplitudes and clear indicationsof non-zero asymmetries were taken for the 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 statisti-cal accuracy. These results combined with future firstever polarized Drell-Yan data from COMPASS willgive a unique opportunity to access TMD PDFs viatwo processes and test their universality and key fea-tures sticking to the same x : Q kinematical range. PJ Web of Conferences -2 -1 -0.1-0.0500.050.1 + h - h <4 /(GeV/c) ) p - S j + h j s i n ( U T A -0.1-0.0500.050.1 preliminaryCOMPASS Proton 2010 data -0.1-0.0500.050.1 -2 -1 -0.1-0.0500.050.1 <6.25 /(GeV/c) ) p - S j + h j s i n ( U T A -0.1-0.0500.050.1 -0.1-0.0500.050.1 -2 -1 -0.1-0.0500.050.1 <16 /(GeV/c) ) p - S j + h j s i n ( U T A -0.1-0.0500.050.1 -0.1-0.0500.050.1 -2 -1 -0.1-0.0500.050.1 x >16 /(GeV/c) Q ) p - S j + h j s i n ( U T A -0.1-0.0500.050.1 z -0.1-0.0500.050.1 (GeV/c) T p -2 -1 -0.0500.05 + h - h <4 /(GeV/c) S 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 s i n U T A -0.0500.05 -0.0500.05 -2 -1 -0.0500.05 <16 /(GeV/c) S 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 s i n U T A -0.0500.05 z -0.0500.05 (GeV/c) T p Figure 6. Collins (top) and A sin φ S UT (bottom) asymmetries References [1] A. Kotzinian, Nucl. Phys. B , 234 (1995)[ arXiv:hep-ph/9412283 ].[2] A. Bacchetta, M. 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[COMPASS], CERN-SPSC-2010-014. -2 -1 -0.2-0.100.10.2 + h - h <4 /(GeV/c) ) S j - h j c o s ( LT A -0.2-0.100.10.2 preliminaryCOMPASS Proton 2010 data -0.2-0.100.10.2 =0.10 m =0.15 m =0.20 m PRD73:114017(2006) -2 -1 -0.2-0.100.10.2 <6.25 /(GeV/c) ) S j - h j c o s ( LT A -0.2-0.100.10.2 -0.2-0.100.10.2 -2 -1 -0.2-0.100.10.2 <16 /(GeV/c) ) S j - h j c o s ( LT A -0.2-0.100.10.2 -0.2-0.100.10.2 -2 -1 -0.2-0.100.10.2 x >16 /(GeV/c) Q ) S j - h j c o s ( LT A -0.2-0.100.10.2 z -0.2-0.100.10.2 (GeV/c) T p -2 -1 -0.2-0.100.10.2 <4 /(GeV/c) S j c o s LT A -0.2-0.100.10.2 preliminaryCOMPASS Proton 2010 data -0.2-0.100.10.2 (corrected) + h (corrected) - h (observed) + h (observed) - h -2 -1 -0.2-0.100.10.2 <6.25 /(GeV/c) S j c o s LT A -0.2-0.100.10.2 -0.2-0.100.10.2 -2 -1 -0.2-0.100.10.2 <16 /(GeV/c) S j c o s LT A -0.2-0.100.10.2 -0.2-0.100.10.2 -2 -1 -0.2-0.100.10.2 x >16 /(GeV/c) Q S j c o s LT A -0.2-0.100.10.2 z -0.2-0.100.10.2 (GeV/c) T p Figure 7. 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