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Letters
B
www.elsevier.com/locate/physletb 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 32 32 33 33 34 34 35 35 36 36 37 37 38 38 39 39 40 40 41 41 42 42 43 43 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55 56 56 57 57 58 58 59 59 60 60 61 61 62 62 63 63 64 64 65 65The
Sivers
asymmetry
in
Drell–Yan
production
at
the
J
/
peak
at COMPASS
M. Anselmino
a,
V. Barone
b,
c,
M. Boglione
a aUniversitàdiTorinoandINFN-Torino,via Giuria 1,10125Torino,Italy bUniversitàdelPiemonteOrientale,VialeT.Michel 11,I-15121Alessandria,Italy cINFN-Torino,via Giuria 1,10125Torino,Italya
r
t
i
c
l
e
i
n
f
o
a
b
s
t
r
a
c
t
Articlehistory:
Received 13 February 2017
Received in revised form 24 April 2017 Accepted 28 April 2017
Available online xxxx Editor: A. Ringwald Keywords: Drell–Yan process
Transverse momentum dependent distribution functions
Sivers effect Single spin asymmetry
The abundant production oflepton pairs via J/ creation atCOMPASS,
π
±p↑→ J/X→ +−X,allowsameasurementofthetransversesinglespinasymmetry,ANJ/,generatedbytheSiverseffect.The crucialissueofthesignchangeoftheSiversfunctioninDrell–Yanleptonpairproduction,withrespectto SemiInclusiveDeepInelasticScatteringprocesses,canbeaddressedinadifferentcontext.Assumingthat theSiversasymmetryisrelatedtoauniversaland intrinsicpropertyoftheproton,predictionsforthe expectedmagnitudeof ANJ/,whichturnsouttobelarge,aregiven.Acomparisonwiththesuggested measurement ofthissingle spin asymmetry– an importantquantityby itself – should givevaluable information.
©2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
Thedistribution,in momentumspace, of unpolarizedquarksandgluonsinside a transverselypolarizednucleon, firstintroduced by Sivers[1,2],isoneoftheeightleading-twistTransverseMomentumDependentPartonicDistributionFunctions(TMD-PDFs),whichcanbe accessedthroughexperimentsandencodeourinformationonthe3-Dimensionalnucleonstructure.TheSiversdistributionforunpolarized quarks(orgluons)withtransversemomentumk⊥insideaprotonwith3-momentump andspin S ,isdefinedas
ˆ
fq/p↑(
x,
k⊥)
=
fq/p(
x,
k⊥)
+
1 2Nf q/p↑
(
x,
k⊥)
S· ( ˆ
p× ˆ
k⊥)
=
fq/p(
x,
k⊥)
−
k⊥ mp f1T⊥q(
x,
k⊥)
S· ( ˆ
p× ˆ
k⊥) ,
(1)where fq/p
(
x,
k⊥)
istheunpolarizedTMD-PDFandNfq/p↑
= (−
2k⊥/
mp)
f1T⊥q istheSiversfunction.The Sivers function is one of the bestknown polarized TMD-PDFs andhas a clearexperimental signature [3–5].It is of particular interestforseveralreasons;one expectsittoberelatedtofundamentalintrinsicfeaturesofthenucleonandtobasicQCDproperties.In fact,theSivers distributionrelatesthemotionofunpolarizedquarks andgluonstothenucleonspin S ;then,inorderto builda scalar, parityinvariantquantity,S mustcoupletotheonlyotheravailablepseudo-vector,thatisthepartonorbitalangularmomentum,Lqor Lg. AnotherpeculiarfeatureoftheSiversdistributionisthatitsoriginatpartoniclevelcanbetracedinQCDinteractionsbetweenthequarks (or gluons) active in inelastic high energy interactions andthe nucleon remnants [6,7]; thus, it is expected to be process dependent andhaveoppositesigninSemiInclusiveDeepInelasticScattering(SIDIS)andDrell–Yan(D–Y)processes[8,9].Thisimportantprediction remainstobetested.
Infact,onemightstillwonderwhethertheSiverseffectoriginatesdirectlyfromanintrinsicpropertyoftheproton,ratherthanbeing mediatedthroughinitialorfinal stateinteractions, whichleadtotheopposite signsinSIDISandD–Yprocesses[6–9].Itistempting to relatetheSivers effect,atleastforvalencequarks,to theirorbital motion,which,inturn,mustbelinked tothe parentprotonspin.In suchacaseoneexpectsauniversalityoftheSivers asymmetry.Thus,itisimportanttofindprocessesinwhichmeasurableSingleSpin AsymmetriescanbegeneratedbytheSiversasymmetricdistribution(1)andstudythem.
E-mailaddress:boglione@to.infn.it(M. Boglione). http://dx.doi.org/10.1016/j.physletb.2017.04.074
0370-2693/©2017 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.
1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 32 32 33 33 34 34 35 35 36 36 37 37 38 38 39 39 40 40 41 41 42 42 43 43 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55 56 56 57 57 58 58 59 59 60 60 61 61 62 62 63 63 64 64 65 65
Usually, theSivers distribution can be accessed through thestudy ofazimuthal asymmetries inpolarized SIDISandD–Y processes. Thesehavebeenclearlyobservedinthelastyears,inSIDIS,by theHERMES [3]andCOMPASS[4]Collaborations,allowingextractionsof theSIDISSivers function [10–12].However, noinformationcould be obtainedontheD–Y Siversfunction, asnopolarizedD–Yprocess hadeverbeenmeasured.
AsymmetriesrelatedtotheSiverseffectcanalsobemeasuredinthesocalledgeneralised D–Yprocesses[13,14],thatisthecreationof leptonpairsviavectorbosons, p p
→
W±X→
±ν
X and p p→
Z0X→
+−X . AlsointhiscaseoneexpectsaSiversfunctionopposite tothatobservedinSIDIS.
Recently, firstfew data fromD–Yweak boson productionatRHIC, p↑p
→
W±/
Z0X , have becomeavailable [15].Theyshow some azimuthalasymmetrywhichhints,withlargeerrorsandsizeableuncertainties,atasignchangebetweentheSiversfunctionobservedin thesegeneralisedD–YprocessesandtheSIDISSivers function,although muchcautionisstillnecessary[16].MoredataongenuineD–Y processes,π
±p↑→
γ
∗X→
+−X , areexpectedsoonfromtheCOMPASSCollaboration.However,alsointhiscase,duetotheenergyof theCOMPASS experiment,
√
s=
18.
9 GeV,andtheacceptedsaferegionforD–Y events,M4 GeV/
c2,where M is theinvariant mass ofthe lepton pair, only a limited numberof events,and consequently large statisticalerrors, are expected, asit is confirmedby first data[17].FollowingRefs.[18,19]weproposeheretomeasuretheleptonpairproductionatCOMPASSatthepeakofthe J
/
production,where thenumberofeventsisgreatlyenhanced.Noticethatthespin-parityquantumnumbersof J/
arethesameasforaphoton.LetusstartfromtheusualD–Yprocess.AccordingtotheTMDfactorisationscheme,thecrosssectionforthisprocess,
h1
h2→
q q X¯
→
+
−X , inwhichonemeasuresthefour-momentum
q of
theleptonpair,canbewritten,atleadingorder,as[20,21]:d
σ
h1h2→+−X dy dM2d2q T= ˆ
σ
0 q e2q d2k⊥1d2k⊥2δ
2(
k⊥1+
k⊥2−
qT)
fq/h¯ 1(
x1,k⊥1) fq/h2(
x2,k⊥2) (2)wherethe
qrunsoverallrelevantquarksandantiquarksandwehaveadoptedtheusualvariables: q= (
q0,qT,
qL)
q2=
M2 y=
1 2ln q0+
qL q0−
qL s= (
p1+
p2)2·
(3)The fq/h
(
x,
k⊥)
aretheunpolarizedTMD-PDFsande
q2σ0
ˆ
isthecrosssectionfortheq
q¯
→
+−process: e2q
σ
ˆ
0=
e2q4
π α
29M2
·
(4)k⊥1 andk⊥1 arethepartontransversemomenta,whilethepartonlongitudinalmomentumfractionsaregivenat
O (
k⊥/
M)
,by x1,2=
M√
se ±y so that x F=
2 qL√
s=
x1−
x2=
x1−
M2 s x1=
M2 s x2−
x2,
y=
1 2ln x1 x2=
lnx1√
s M·
(5)Eq.(2)holdsinthekinematicalregion:
q2T
M2 k⊥qT.
(6)Inthecaseinwhichoneofthehadrons,say
h
2↑,ispolarized,Eq.(2)simplymodifiesbyreplacing fq/h2(
x2,
k⊥2)
withˆ
fq/h↑2(
x2,
k⊥2)
as giveninEq.(1).WethenhavetheSiverssingletransversespinasymmetry:AN
=
dσ
h1h↑2→+−X−
dσ
h1h↓2→+−X dσ
h1h↑2→+−X+
dσ
h1h↓2→+−X≡
dσ
↑−
dσ
↓ dσ
↑+
dσ
↓ (7)=
qe2q d2k⊥1d2k⊥2δ
2(
k⊥1+
k⊥2−
qT)
S· ( ˆ
p2× ˆ
k⊥2)
fq/h¯ 1(
x1,
k⊥1)
Nf q/h↑2(
x2,
k⊥2)
2qe2q d2k ⊥1d2k⊥2δ
2(
k⊥1+
k⊥2−
qT)
fq/h¯ 1(
x1,k⊥1)fq/h2(
x2,k⊥2)·
(8)Whentheleptonpairproductionoccursvia
q
q annihilation¯
intoavectormesonV rather thanavirtualphotonγ
∗,Eqs.(2),(4)and(8) stillhold,withthereplacements[18]:16
π
2α
2e2 q→ (
gqV)
2(
gV)
2 1 M4→
1(
M2−
M2 V)
2+
M2V2V
,
(9) whereg
Vq and
g
V arethe V vector couplingstoq
q and¯
+
− respectively.
V isthewidthofthevectormesonandthenewpropagator isresponsibleforalargeincreaseinthecrosssectionat
M
2=
M2V. Wethenhave: AVN
=
q(
gqV)
2 d2k⊥1d2k⊥2δ
2(
k⊥1+
k⊥2−
qT)
S· ( ˆ
p2× ˆ
k⊥2) fq/h¯ 1(
x1,k⊥1) Nf q/h↑2(
x2,k⊥2) 2q(
gV q)
2 d2k ⊥1d2k⊥2δ
2(
k⊥1+
k⊥2−
qT)
fq/h¯ 1(
x1,k⊥1) fq/h2(
x2,k⊥2)·
(10)Wepropose touse Eq.(10)forleptonpairproductionatCOMPASS,
π
±p↑→
+−X , atthe J
/
peak, M2=
M2J/.There areseveral reasonswhichmakethischannelveryinterestingandpromising,aswellassomereasonsofattentionandcaution.
1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 32 32 33 33 34 34 35 35 36 36 37 37 38 38 39 39 40 40 41 41 42 42 43 43 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55 56 56 57 57 58 58 59 59 60 60 61 61 62 62 63 63 64 64 65 65
1) At COMPASSenergyonehas
x1
x2=
M2J/
/
s 0.
027.Duetothisrelationbothx1
andx2
mustbegreaterthan0.027andoneofthem mustbegreaterthan√
0.
0270.
16.Atsmallvaluesofx
F ory one hasapproximatelyx
1x20.
16.Itisthenreasonabletoexpectthat themainchannelforthe J/
productionisindeedq
q annihilation¯
(ratherthangluonfusion).Theexactelementarymechanismthroughwhichthe
q
q give¯
origintothe J/
isstillnotclear(see,forexample,Refs.[22,23]).Wedo notattemptanyexplanationofsuch amechanism:itssubtleties andcomplicationsare simplyhiddenintheunknown couplings gVq.In theexpressionofthespinasymmetry,Eq.(10),suchcouplingscancel:exactly,iftheydonotdependontheflavour
q or,
approximately,if oneflavourdominates.Thiswillbethecaseforthe J/
productioninπ
p interactions. Althoughwedonotattemptapredictionforthe crosssection,weareconfidentthattheexpression(10)oftheasymmetryisadequateenoughtostudytheSiverseffectin J/
production atCOMPASS.2) The COMPASS data,whichhavebeentakenin2015andarepresently beinganalysed,referto the
π
−p↑→
+−X process at
√
s=
18.
9 GeV.Theirinterestingfeatureisthatthedominantcontributiontotheasymmetry(10)isgivenbyau quark¯
fromtheπ
− andau
quarkfromtheproton,bothofthemvalencequarks.Allothercontributionswouldalwaysinvolveaseaquarkand,inthecentralrapidity region,arestronglysuppressed.3) Other productionmechanismsof J
/
mightcontribute,likegluon fusion.However,whilethey mightenhance theunpolarizedcross section,thedenominatorof AVN,itisveryunlikelythattheysignificantlyaffectthenumeratorof AVN;infactthegluonSiversfunctionis expectedtobesmall,ifnotzero[24].Thus,suchcontributionsmightdecreasethevalueof AVN,buttheycannotaltertheconclusionthat itmainlyoriginatesfromthevalencequarkSiversfunctions.
Thenwehave,forcentralrapidity
π
−p↑→
J/
X→
+−X processes: ANJ/
(
π
−;
x1,
x2,
qT)
d2k ⊥1d2k⊥2δ
2(
k⊥1+
k⊥2−
qT)
S· ( ˆ
p2× ˆ
k⊥2)fu/¯ π−(
x1,k⊥1) Nfu/p↑(
x2,k⊥2) 2d2k ⊥1d2k⊥2δ
2(
k⊥1+
k⊥2−
qT)
fu/¯ π−(
x1,
k⊥1)
fu/p(
x2,
k⊥2)
(11)and,for
π
+p↑→
J/
X→
+−X processes: ANJ/
(
π
+;
x1,
x2,
qT)
d2k ⊥1d2k⊥2δ
2(
k⊥1+
k⊥2−
qT)
S· ( ˆ
p2× ˆ
k⊥2)fd/¯π+(
x1,k⊥1) Nfd/p↑(
x2,k⊥2) 2d2k ⊥1d2k⊥2δ
2(
k⊥1+
k⊥2−
qT)
fd/¯π+(
x1,
k⊥1)
fd/p(
x2,
k⊥2)
·
(12)Noticethatthevariables
x1
andx2 arerelatedtoeachotherandone canuseonlyoneofthemorthevariablex
F or y, seeEq.(5)with M2=
M2J/.
Eqs.(11)and(12)canbefurtherevaluatedadopting,asusual,aGaussianfactorizedformbothfortheunpolarizeddistributionandthe Siversfunctions,asinRef.[10]:
fq/p
(
x,
k⊥)
=
fq(
x)
1π
k2⊥
e −k2⊥/ k2⊥ (13)
Nfq/p↑
(
x,
k⊥)
=
2N
q(
x)
h(
k⊥)
fq/p(
x,
k⊥)
(14) h(
k⊥)
=
√
2e k⊥ M1 e−k2⊥/M21,
(15)wherethe fq
(
x)
are theunpolarized PDFs, M1 is a parameter which allows thek
⊥ Gaussian dependence ofthe Sivers function to be differentfrom that of the unpolarized TMDs andN
q(
x)
is a function which parameterisesthe factorized x dependence of the Sivers function.ThesamefunctionalformasinEq.(13),withthesamevalueofk2⊥
,isassumedfortheunpolarizedquarkdistributioninsidea pion.
Insuchacasethek⊥ integrationscanbeperformedanalyticallyinEqs.(11)and(12),obtaining:
ANJ/
(
π
−;
x2,qT)
=
k 2 S
2
[
k2S+
k2⊥]
2 exp−
q2T 2k2⊥
k2 ⊥
−
k2Sk2⊥
+
k2S×
√
2 e qT M1×
2N
u(
x2)S· ( ˆ
p2× ˆ
qT)
(16)≡
ANJ/(
π
−;
x2,
qT)
S· ( ˆ
p2× ˆ
qT)
(17) and ANJ/(
π
+;
x2,
qT)
=
k2S
2
[
k2S+
k2⊥]
2 exp−
q2T 2k2⊥
k2⊥
−
k2Sk2⊥
+
k2S×
√
2 e qT M1×
2N
d(
x2)
S· ( ˆ
p2× ˆ
qT)
(18)≡
ANJ/(
π
+;
x2,qT)
S· ( ˆ
p2× ˆ
qT)
(19) wherek2S
=
M 2 1k2⊥
M12
+
k2⊥·
(20)NoticethattheunpolarizedPDFscancelout.
ANJ/
(
π
±;
x2,
qT)
istheamplitude oftheazimuthalmodulationintheangledefinedby S· ( ˆ
p2× ˆ
qT)
.Forexample,takingtheproton movinginthe−ˆ
z directionandS≡ ↑
along+ ˆ
y,intheπ
−
p c.m. frame,onehasS· ( ˆ
p2× ˆ
qT)
= −
cosφ
,whereφ
istheazimuthalangle1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 32 32 33 33 34 34 35 35 36 36 37 37 38 38 39 39 40 40 41 41 42 42 43 43 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55 56 56 57 57 58 58 59 59 60 60 61 61 62 62 63 63 64 64 65 65
Fig. 1. Plots
of
ANJ/(π−;xN,qT)(left) and ANJ/(π+;xN,qT)(right) versus xN, at qT=1 GeV/c.These estimates are obtained according to Eqs.
(16)–(19)of the text(x2≡xN), using the parameters of the Sivers function given in Ref.[12]. The uncertainty of these parameters generates the shaded areas.
Fig. 2. Plots
of
ANJ/(π−;xN,qT)(left) and A J/N (π+;xN,qT)(right) versus qT, at xN=0.1. These estimates are obtained according to Eqs.(16)–(19)of the text (x2≡xN),
using the parameters of the Sivers function given in Ref.[12]. The uncertainty of these parameters generates the shaded areas.
ofthe J
/
.Measurementsof ANJ/(
π
−;
x2,
qT)
and ANJ/(
π
+;
x2,
qT)
give a directaccess, respectively,toN
u(
x2)
andN
d(
x2)
,andthe correspondingSiversfunctions,Eq.(14).Asapossibletestofthe(non)universalityoftheSiversfunctionwegiveanestimateof ANJ/
(
π
−;
x2,
qT)
andA
NJ/(
π
+;
x2,
qT)
,based on theSivers functionsextracted fromSIDISdata.All quantities necessaryto compute the two asymmetriescan be found inRef. [12] (Eq. (40)andthirdcolumnofTable III),takingintoaccountonlythevalencequarkcontributions.Theprocessweareconsideringis,atthepartoniclevel,morecomplicatedthantheusualcontinuumD–Yleptonpairproductionviaa qq
¯
→
γ
∗ annihilation.Theargumentsbasedoninitialversus finalstateinteractions inSIDISandD–Yprocesses[6–9]mightnotholdin thiscase.Thus,wedonotchangethesignoftheSIDISSiversfunctions.Ourestimatesareactuallymadeassumingtheuniversalityofthe Siverseffect,thinking ofitasgeneratedby intrinsicpropertiesofthenucleons;one mightthink,forexample,oftheSivers asymmetric distribution(1)asatypicalfeatureofquarksorbitinginsidethenucleon.Comparisonwithdatawillconfirmornotthisassumption.InFig. 1weplot ANJ/
(
π
−;
xN,
qT)
(leftplot) and ANJ/(
π
+;
xN,
qT)
(rightplot),atq
T=
1 GeV/
c, asfunctionsofx
N intheexpected kinematicalregionoftheCOMPASSexperiment.Forabetterreadingwedenotebyx
N thelongitudinalmomentumfractionofthenucleon carried by the quark, defined as x2 in the text. The uncertainty bandscorrespond to the uncertainty in the knowledge of the Sivers functionsfromRef.[12].Similarly,inFig. 2weplottheasymmetries,forx
N=
0.
1 (correspondingtox1
≡
xπ=
0.
3 andx
F=
0.
2),versus qT. InbothcasestheSivers asymmetriescanbe large,withawell definedsign, drivenby thesignoftheSiversfunctionsoftheproton valencequarks,u quark
for ANJ/(
π
−)
andd quark
for ANJ/(
π
+)
.Notice thatwithintheuncertaintybandstheexpectedmagnitudesof ANJ/(
π
−)
and ANJ/(
π
+)
mightsizeablyvary,keepinghoweveradefinitesign.Inordertoobtainabetterstatistics,onecouldgatherdataoverthefullrangeof
q
T forwhichEq.(6)holds;thentheasymmetriesare givenbyEqs.(11)and(12)withnumeratoranddenominatorintegratedoverq
T from0upto,say,2 GeV/c.In conclusion, we propose a simple measurement of the single transverse spin asymmetry AN in the channel
π
±p↑→
J/
X→
+
−X , forwhichabundant datahave beenalreadycollected by theCOMPASS Collaboration.If, aswe expect atthe kinematicsof the experiment,the asymmetryismainlygeneratedby theSiversdistributionofunpolarizedvalencequarksinsidethepolarizedproton,its signrevealsthesignofthecorrespondingSiversfunction.
Wegivesomeestimatesfortheasymmetryinasimplifiedfactorizedschemewhichavoidsthecomplicationsoftheactualknowledge ofthepartonicinteractionswhichcouplea
q
q pair¯
tothe J/
.Wedonotattempt, andcannotgive,anypredictionforthecrosssection oftheprocess,buttheexpressionoftheasymmetryismuchsimplerandwelldefined, duetocancellationsofunknownquantities.Our mainassumptionisindeedthedominanceoftheq
q channel.¯
Admittedly,ourresultsfortheasymmetrymightbetoooptimisticasother production mechanism might increase the denominator of Eq. (7): however, we do believe that any measured asymmetry should be relatedtothequarkSiverseffect.Ourestimatesaregivenassuming thesameSivers functionsasthoseextractedfromSIDIS, withoutanysignchange.Wedonottake intoaccounttheir possibleTMD evolution: the Q2 region oftheSIDISdata,afew GeV2,isnotfar fromthe M2
J/ valuerelevant here. Moreover, we expect that,while TMD evolution mightbe relevantfor crosssections,it doesnot affectmuch the value oftheir ratios, whichappearin theasymmetries.Adetailedstudyofthe issuesrelatedtothe phenomenologicalimplementationofTMD evolution in
1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 32 32 33 33 34 34 35 35 36 36 37 37 38 38 39 39 40 40 41 41 42 42 43 43 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55 56 56 57 57 58 58 59 59 60 60 61 61 62 62 63 63 64 64 65 65
SIDISprocessesatCOMPASS kinematics, stronglydominated by non-perturbativeeffects,can be found inRef. [25],where estimatesof theirimpactisgiven.
Anexperimental confirmation ofour estimatedsigns wouldfavour the universalityof the Sivers functions. An opposite signmight indicate that the argument according to which the Sivers functionsin SIDIS and D–Y processes must be opposite holds also for this process,
π
±p↑→
J/
X→
+−X . Inanycasethemeasurementof ANJ/ atCOMPASSisinterestingandworthbeingperformed.
Acknowledgements
WeareverygratefultoBakurParsamyanforusefuldiscussionsontheCOMPASSphysicsprogrammeandresults. M.A.andM.B. acknowledgesupportfromthe“ProgettodiRicercaAteneo/CSP”(code TO-Call3-2012-0103).
References
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[3] A. Airapetian, et al., Observation of the Naive-T-odd Sivers effect in deep-inelastic scattering, Phys. Rev. Lett. 103 (2009) 152002, http://dx.doi.org/10.1103/PhysRevLett.103. 152002, arXiv:0906.3918.
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