Quasi-real photon contribution to $A_N$ in $\ell p^\uparrow \to \pi\,$ X within a TMD approach

0.3 MB·

by  Umberto D'Alesio

Quasi-real photon contribution to A in (cid:96)p↑ → π X
N
within a TMD approach
7 Umberto D’Alesio∗
1 DipartimentodiFisica,UniversitàdiCagliari,CittadellaUniversitaria,and
0
INFN,SezionediCagliari,I-09042Monserrato(CA),Italy
2
E-mail: [email protected]
n
a
Carlo Flore
J
DipartimentodiFisica,UniversitàdiCagliari,CittadellaUniversitaria,and
2
1 INFN,SezionediCagliari,I-09042Monserrato(CA),Italy
E-mail: [email protected]
]
h
Francesco Murgia
p
- INFN,SezionediCagliari,I-09042Monserrato(CA),Italy
p
e E-mail: [email protected]
h
[
Within a TMD approach we discuss the impact of quasi-real (Weizsäcker-Williams) photon

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contribution to the transverse single-spin asymmetry, A , for the inclusive process (cid:96)p↑ →πX.
v N
3 This study extends a previous one where only the leading-order contribution was taken into ac-
0
count. PredictionsareobtainedadoptingtheSiversandtransversitydistributionsandtheCollins
3
3 fragmentation functions as extracted from fits to the azimuthal asymmetries measured in semi-
0
inclusivedeepinelasticscatteringande+e− annihilationprocesses. Thedescriptionoftheavail-
.
1
abledataisverygood,showingacleargeneralimprovementwithrespecttothepreviousanalysis
0
7 (alreadyquitepromising). ThisresultrepresentsafurthersteptowardsaunifiedTMDtreatment
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ofSSAsin(cid:96)p↑→(cid:96)(cid:48)hX and(cid:96)p↑→hX processes.
:
v
i
X
r
a
QCDEvolution2016
May30-June03,2016
NationalInstituteforSubatomicPhysics(Nikhef),Amsterdam
∗Speaker.
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/
Quasi-realphotoncontributiontoA UmbertoD’Alesio
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1. Introduction
Theissueofthevalidityoffactorizationintermsoftransversemomentumdependentdistribu-
tions(TMDs)forinclusiveprocesseswhereonlyonelargeenergyscaleisdetectedischallenging
andstillunderdebate. ThedescriptionwithinaTMDapproach(aswellasinatwist-threeformal-
ism) of the large data sets for A measured in inclusive pion production in p↑p collisions is the
N
moststrikingexample(seeforinstanceRef.[1]).
In Refs. [2, 3] this issue has been investigated in a somehow simpler inclusive process, still
with a single large energy scale, but very close to the semi-inclusive deep inelastic scattering
(SIDIS) process, for which TMD factorization has been proven [4, 5, 6]. We refer to transverse
single-spinasymmetries(SSAs)forthe(cid:96)p↑→hX process,withthedetection,inthelepton-proton
center of mass (c.m.) frame, of a single large-P final particle, typically a pion. The same pro-
T
cesswasalsoconsideredinRefs.[7,8]intheframeworkofcollinearfactorizationwithtwist-three
correlationfunctions.
TheseSSAswerecomputedassumingtheTMDfactorizationatleadingorder(LO)andusing
the relevant TMDs (Sivers and Collins functions) as extracted from SIDIS and e+e− data. In
particular,inRef.[3]thetheoreticalestimateswerecomparedwithaselection1oftheexperimental
resultsbytheHERMESCollaboration[9],showingagoodagreementinsignandsize.
HerewewanttoextendthisLOstudyincludingthecontributionfromquasi-real(Weizsäcker-
Williams) photon exchange, relevant in the kinematical configuration dominated by small Q2 (for
acompleteandcomprehensivestudyseeRef.[10]). Thiswillallowustoimprovethedescription
of the fully-inclusive data and consider, for the first time, the anti-tagged data set, dominated by
events in which the final lepton has a very small scattering angle. Notice that this data category
was not included in the previous analysis because a simple LO approach (namely via q(cid:96)→q(cid:96)) is
expectedtobenotadequate.
2. Formalism
InRefs.[2,3],towhichwereferthereaderforalldetails,astudyofSSAsin(cid:96)p↑→πX pro-
cesseswithinaTMDapproachwaspresented,restrictingtoaleading-orderapproximation. Here,
stillwithinthesameapproach,wewanttoconsidertheimpactofquasi-realphotonexchange. As
pointedoutinRef.[11]thiscontribution,atleastinacollinearapproachandforunpolarizedcross
sections, represents in most cases only a small part of the next-to-leading order (NLO) calcula-
tions. On the other hand in a TMD scheme, as for the twist-three approach, NLO corrections are
not available for such a process and it is then worth to see to what extent the quasi-real photon
exchange could play a role in the computation of spin asymmetries. On top of that, by including
transversemomentumeffectstheestimatesofunpolarizedcrosssectionsareenhancedw.r.t.those
computedinacollinearframework.
Weconsiderthetransversesingle-spinasymmetry,A ,fortheprocessp↑(cid:96)→hX intheproton-
N
leptonc.m. frame(withthepolarizedprotonmovingalongthepositiveZ axis)
cm
dσ↑(PPP )−dσ↓(PPP ) dσ↑(PPP )−dσ↑(−PPP )
T T T T
A = = , (2.1)
N dσ↑(PPP )+dσ↓(PPP ) 2dσunp(PPP )
T T T
1Onlydataforinclusiveeventsinthebackwardtargethemisphereandtaggedeventswereconsidered.
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Quasi-realphotoncontributiontoA UmbertoD’Alesio
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where PPP is the transverse momentum of the final hadron. Notice that for a generic transverse
T
polarization, SSS , along an azimuthal direction φ in the chosen reference frame, in which the ↑
T S
directionisgivenbyφ =π/2,onehas:
S
A(φ ,S )=SSS ·(pppˆ ×PPPˆ )A =S sinφ A , (2.2)
S T T T N T S N
where pppistheprotonmomentum.
Assuming the validity of the TMD factorization scheme for the process p↑(cid:96)→hX, in which
P =|PPP |istheonlylargescaledetected, asdiscussedinRefs.[2,3], inaleading-orderapproxi-
T T
mationthemaincontributiontoA comesfromtheSivers[12,13]andCollins[14]effectsandone
N
has[15,16,1]:
(cid:90) dxdz
∑ d2kkk d3ppp δ(ppp ·pppˆ(cid:48))J(p )δ(sˆ+tˆ+uˆ)[Σ(↑)−Σ(↓)]q(cid:96)→q(cid:96)
16π2xz2s ⊥ ⊥ ⊥ q ⊥
q
A = , (2.3)
N (cid:90) dxdz
∑ d2kkk d3ppp δ(ppp ·pppˆ(cid:48))J(p )δ(sˆ+tˆ+uˆ)[Σ(↑)+Σ(↓)]q(cid:96)→q(cid:96)
16π2xz2s ⊥ ⊥ ⊥ q ⊥
q
with(droppingnegligiblecontributionsfromotherTMDs)
[Σ(↑)−Σ(↓)]q(cid:96)→q(cid:96) = 1∆Nf (x,k )cosφ (cid:2)|Mˆ0|2+|Mˆ0|2(cid:3)D (z,p )
2 q/p↑ ⊥ 1 2 h/q ⊥
+ h (x,k )Mˆ0Mˆ0∆ND (z,p )cos(φ(cid:48)+φh) (2.4)
1q ⊥ 1 2 h/q↑ ⊥ q
and
[Σ(↑)+Σ(↓)]q(cid:96)→q(cid:96)= f (x,k )(cid:2)|Mˆ0|2+|Mˆ0|2(cid:3)D (z,p ). (2.5)
q/p ⊥ 1 2 h/q ⊥
All functions and all kinematical and dynamical variables appearing in the above equations
areexactlydefinedinRef.[2]anditsAppendicesandinRef.[16].
In order to include also possible contributions from quasi-real photon exchange we rely on
the well-known Weizsäcker-Williams (WW) approximation. Without entering into many details
weonlyrecallthatinsuchanapproximationtheincomingleptonisconsideredasasourceofreal
photons (with their proper distribution), which then enter the hard scattering process. In other
words,weadoptthefollowingfactorizationformulafortheWWcontributiontotheprocess(cid:96)p→
hX:
(cid:90)
σWW((cid:96)p→hX)= dyf (y)σ(γp→hX), (2.6)
γ/(cid:96)
where f (y) is the number density of photons inside the lepton, carrying a lepton-momentum
γ/(cid:96)
fractiony(p =yp )andσ(γp→hX)isthecrosssectionfortheprocessγp→hX initiatedbya
γ (cid:96)
realphoton. Inparticular,followingRef.[11],weadopttheexpression
(cid:34) (cid:32) (cid:33) (cid:35)
α 1+(1−y)2 µ2
f (y)= ln −1 +O(α2), (2.7)
γ/(cid:96) 2π y y2m2
(cid:96)
where α is the electromagnetic coupling constant, µ the factorization scale (set in the following
equal to P ) and m the lepton mass. Once again for a generic polarized process adopting the
T (cid:96)
helicity formalism one can calculate all possible contributions in terms of TMDs (see Ref. [10]
for all details). Here we simply remark that even for the real-photon initiated process only the
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Quasi-realphotoncontributiontoA UmbertoD’Alesio
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SiversandtheCollinseffectscouldgivepotentiallysizeablecontributionstothenumeratorofA ,
N
whileonceagainonlytheunpolarizedTMDsplayaroleinthedenominator. Atvariancewiththe
leading-order analysis, where there is only one partonic channel, namely q(cid:96)→q(cid:96), here we have
to consider the following channels: qγ →qg and gγ →qq¯. This means that when we refer to the
SiverseffectalsothecontributionfromthegluonSiversfunctionhastobetakenintoaccount.
Wecanthenrewritetheasymmetryunderconsiderationinthefollowingway:
d∆σLO+d∆σWW
A = , (2.8)
N 2[dσLO+dσWW]
where d∆σLO and [2dσLO] are nothing else than the numerator and the denominator in Eq. (2.3),
whilefortheWWpiecesonehastomakethefollowingreplacement:
[Σ(↑)±Σ(↓)]q(cid:96)→q(cid:96) → [Σ(↑)±Σ(↓)]qγ→qg+[Σ(↑)±Σ(↓)]qγ→gq
+ [Σ(↑)±Σ(↓)]gγ→qq¯+[Σ(↑)±Σ(↓)]gγ→q¯q (2.9)
(cid:82)
andperformafurtherconvolutionoveryvia dy/y. Moreexplicitly,wehave
[Σ(↑)−Σ(↓)]qγ→qg = f (y)(cid:110)1∆Nf (x,k )cosφ (cid:2)|Mˆ0|2+|Mˆ0|2(cid:3)qγ D (z,p )
γ/(cid:96) 2 q/p↑ ⊥ 1 2 h/q ⊥
(cid:111)
+ h (x,k )[Mˆ0Mˆ0]qγ∆ND (z,p )cos(φ(cid:48)+φh) (2.10)
1q ⊥ 1 2 h/q↑ ⊥ q
[Σ(↑)+Σ(↓)]qγ→qg = f (y)f (x,k )(cid:2)|Mˆ0|2+|Mˆ0|2(cid:3)qγ D (z,p ) (2.11)
γ/(cid:96) q/p ⊥ 1 2 h/q ⊥
[Σ(↑)−Σ(↓)]qγ→gq = 1 f (y)∆Nf (x,k )cosφ (cid:2)|Mˆ0|2+|Mˆ0|2(cid:3)qγ D (z,p ) (2.12)
2 γ/(cid:96) q/p↑ ⊥ 1 3 h/g ⊥
[Σ(↑)+Σ(↓)]qγ→gq = f (y)f (x,k )(cid:2)|Mˆ0|2+|Mˆ0|2(cid:3)qγ D (z,p ) (2.13)
γ/(cid:96) q/p ⊥ 1 3 h/g ⊥
[Σ(↑)−Σ(↓)]gγ→qq¯ = 1 f (y)∆Nf (x,k )cosφ (cid:2)|Mˆ0|2+|Mˆ0|2(cid:3)gγ D (z,p ) (2.14)
2 γ/(cid:96) g/p↑ ⊥ 2 3 h/q ⊥
[Σ(↑)+Σ(↓)]gγ→qq¯ = f (y)f (x,k )(cid:2)|Mˆ0|2+|Mˆ0|2(cid:3)gγ D (z,p ), (2.15)
γ/(cid:96) g/p ⊥ 2 3 h/q ⊥
where,besidesacommonoverallfactorequalto16π2αα ,
s
(cid:2)|Mˆ0|2+|Mˆ0|2(cid:3)qγ = 16e2sˆ2+uˆ2, (cid:2)Mˆ0Mˆ0(cid:3)qγ = 16e2, (cid:2)|Mˆ0|2+|Mˆ0|2(cid:3)qγ = 16e2sˆ2+tˆ2 (2.16)
1 2 3 q −sˆuˆ 1 2 3 q 1 3 3 q −sˆtˆ
(cid:2)|Mˆ0|2+|Mˆ0|2(cid:3)gγ =2e2uˆ2+tˆ2. (2.17)
2 3 q uˆtˆ
Notice that the Mandelstam invariants for the photon-parton subprocess have to be defined using
p =yp andthatfortheprocessgγ →q¯qonehasthesameexpressionsasinEqs.(2.14)and(2.15)
γ (cid:96)
withD replacedbyD .
h/q h/q¯
Somecommentsareinorder: theWWcontributionsareoforderαα ;thestructuresarevery
s
similar to those appearing in the LO case; the Collins effect enters only in the channel qγ →qg;
thegluonSiverseffectappearsinthechannelsgγ →qq¯andgγ →q¯q.
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3. Results
InthisSectionweshowaselectionofourresultsbothfortheunpolarizedcrosssectionsandthe
SSAs,withspecialattentiontoHERMESkinematics. Foramorecomprehensivestudy,including
alsopredictionsforongoingandfutureexperimentswereferthereadertoRef.[10].
In our computation of the SSAs, based on the TMD factorization, we consider two different
setsofSiversandCollinsfunctions(thelattercoupledtothetransversitydistribution),aspreviously
obtainedinaseriesofpapersfromfitsofSIDISande+e− data[17,18,19,20].
These sets, besides some different initial assumptions, differ in the choice of the collinear
fragmentationfunctions(FFs). Moreprecisely,forthefits[17]and[18](SIDIS1set)weadoptthe
KretzersetforthecollinearFFs[21]. Forthefits[19]and [20](SIDIS2set)weadoptanotherset
ofFFs,namelytheonebydeFlorian,SassotandStratmann(DSS)[22]. TheSIDIS1andSIDIS2
setsarewellrepresentativeoftheextractionsandtheiruncertainties. ConcerningthegluonSivers
function we adopt the recent extraction of Ref. [23] (notice that we have a corresponding gluon
SiversfunctionassociatedtoeachSIDISset).
LetusstartwiththeunpolarizedcrosssectionsforHERMESset-up,wheretheincominglep-
tonmovesalongthe+Z axisinthelepton-protoncenterofmassframe. Thismeansthat,defining
√ cm
asusualx =2P / s(withP thelongitudinalmomentumofthefinalhadron),positive(negative)
F L L
valuesofx correspondtothebackward(forward)protonhemisphere.
F
InFigs.1and2wepresentourestimatesfortheunpolarizedcrosssectionsforπ+ production
√
at s(cid:39)7.25GeV,respectivelyatfixedx =0.2asafunctionofP ,andatfixedP =1.4GeVas
F T T
afunctionofx . Thebluedash-dottedlinesrepresenttheLOcontribution,whilethesolidredlines
F
include also the WW term. As one can see the quasi-real photon contribution is more important
at lower P values at fixed x and is around 60-70% of the total at fixed P . In particular, see
T F T
Fig. 2, it is asymmetric in x , being more important for positive x values. This is apparently
F F
counterintuitive,sinceforx >0theleptonisscatteredmainlyinthebackwardregionwhereone
F
wouldexpectalesserrolefromquasi-realphotonexchange. Ontheotherhandforlargepositivex ,
F
thatfortheHERMESset-upmeansthatthepionisproducedinthebackward protonhemisphere,
|uˆ|(cid:28)|tˆ|andwhiletheLOpiecegoeslike1/Q2≡1/tˆ2,thepartoniccrosssectionforthesubprocess
qγ →qg (see Eq. (2.16), first relation) goes like 1/sˆuˆ. Notice that the difference in size between
thetwocomputations,basedondifferentFFsets,isduetothemoreimportantroleofthegluonFF
intheDSSset.
Let us now move to the predictions for the SSAs. In order to compare our estimates with
HERMESdatasomefurthercommentsonthekinematicalconfigurationsandthenotationsadopted
in their analysis are necessary. As already pointed out above in HERMES set-up [9] the lepton
is assumed to move along the positive Z axis, so that the processes to be considered here are
cm
(cid:96)p↑→hX,ratherthan p↑(cid:96)→hX. Inthisreferenceframethe↑(↓)directionisstillalongthe+Y
√ cm
(−Y ) axis as in Ref. [2] and, as we keep the usual definition of x =2P / s, only its sign is
cm F L
reversed.
TheazimuthaldependentcrosssectionmeasuredbyHERMESisdefinedas[9]:
dσ =dσ [1+S Asinψsinψ], (3.1)
UU T UT
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Quasi-realphotoncontributiontoA UmbertoD’Alesio
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HERMES, unpol. cross section HERMES, unpol. cross section
104 104
LO + WW LO + WW
LO LO
2V]103 2V]103
e e
G G
b/ b/
p p
P [h102 P [h102
3d 3d
σ/ σ/
3d l p -> π+ X 3d l p -> π+ X
E h101 E h101
xF = 0.2 xF = 0.2
Kretzer DSS
100 100
1 1.2 1.4 1.6 1.8 2 2.2 1 1.2 1.4 1.6 1.8 2 2.2
PT [GeV] PT [GeV]
√
Figure1:Unpolarizedcrosssectionatx =0.2asafunctionofP for(cid:96)p→π+X,atHERMES, s=7.25
F T
GeV,adoptingtwosetsforthefragmentationfunctions: Kretzerset(left)andDSSset(right).
HERMES, unpol. cross section HERMES, unpol. cross section
350 350
LO + WW LO + WW
l p -> π+ X LO l p -> π+ X LO
300 300
PT=1.4 GeV PT=1.4 GeV
2eV] 250 Kretzer 2eV] 250 DSS
G G
pb/ 200 pb/ 200
P [h P [h
3d 150 3d 150
σ/ σ/
3E dh 100 3E dh 100
50 50
0 0
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
xF xF
Figure 2: Unpolarized cross section at P =1.4 GeV as a function of x for (cid:96)p→π+X, at HERMES,
√ T F
s=7.25GeV,adoptingtwosetsforthefragmentationfunctions: Kretzerset(left)andDSSset(right).
where
sinψ =SSSˆ ·(PPPˆ ×kkkˆ) (3.2)
T T
coincides with our sinφ of Eq. (2.2), as ppp and kkk (respectively, the proton and the lepton 3-
S
momenta)areoppositevectorsinthelepton-protonc.m. frame. Wethenhave
Asinψ(x ,P )=Ap↑(cid:96)→hX(−x ,P ), (3.3)
UT F T N F T
where Ap↑(cid:96)→hX is the SSA as given in Eqs. (2.1) and (2.8), and Asinψ is the quantity measured by
N UT
HERMES[9].
In the following we will consider both the fully-inclusive data as well as the sub-sample of
anti-taggeddata(withnodetectionofthefinallepton)for(cid:96)p→πX processesatlargeP . Inboth
T
casesthereisonlyonelargescale(neededforaperturbativecalculation), theP ofthefinalpion.
T
ForthisreasonweonlylookatthosedataatP ≥1GeV.
T
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Quasi-realphotoncontributiontoA UmbertoD’Alesio
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Noticethat,atvariancewithSIDISazimuthalasymmetries,oneisnotabletoseparatethesin-
glecontributionstoA oftheSiversandCollinseffects,thatinprinciplecouldcontributetogether.
N
Our predictions for Asinψ compared with HERMES data are shown in Figs. 3 (inclusive data
UT
set, vs. x at P =1.1 GeV) and 4 (anti-tagged data set, vs. P at x =0.2). More precisely, we
F T T F
show the quark Sivers and Collins contributions, adopting the SIDIS 1 (left panels) and SIDIS 2
(rightpanels)sets,atLO(bluedot-dashedlines)andatLO+WW(redsolidlines),aswellasthe
totalresultaddingthecontributionfromthegluonSiversfunction(greendottedlines). Theoverall
statistical uncertainty band, also shown, is the envelope of the independent statistical uncertainty
bands on the Sivers and Collins functions for quarks, obtained following the procedure described
inAppendixAofRef.[19].
inclusive [backward target hemisph.] inclusive [backward target hemisph.]
0.2 0.2
LO
l p -> π+ X l p -> π+ X LO+WW (q)
LO+WW (q+g)
PT=1.1 GeV PT=1.1 GeV
0.15 0.15
ψ ψ
sinAUT 0.1 sinAUT 0.1
0.05 0.05
SIDIS 1 SIDIS 2
0 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6
xF xF
inclusive [backward target hemisph.] inclusive [backward target hemisph.]
0.1 0.1
LO
l p -> π- X l p -> π- X LO+WW (q)
LO+WW (q+g)
PT=1.1 GeV PT=1.1 GeV
0.05 0.05
ψ ψ
sinAUT 0 sinAUT 0
-0.05 -0.05
SIDIS 1 SIDIS 2
-0.1 -0.1
0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6
xF xF
√
Figure 3: The theoretical estimates for Asinψ vs. x at s(cid:39)7.25 GeV and P =1.1 GeV for inclusive
UT F T
π+(upperpanels)andπ−(lowerpanels)productionin(cid:96)p↑→πX processes,comparedwiththeHERMES
data[9]. Seetextandlegendfordetails.
Some comments are in order. Let us start with the fully-inclusive case, Fig. 3: the inclusion
oftheWWcontributionimprovessignificantlytheagreementwiththedata(rememberthatinthis
kinematical region it is the dominant part in the unpolarized cross sections); the Collins effect
is always tiny or negligible (both in the LO and WW contributions); the differences between the
predictions adopting the SIDIS 1 and the SIDIS 2 sets are due to the different behaviour of the
corresponding Sivers functions; the contribution coming from the gluon Sivers function is almost
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anti-tagged [backward target hemisph.] anti-tagged [backward target hemisph.]
0.25 0.15
LO
l p -> π+ X l p -> π+ X LO+WW (q)
0.2 LO+WW (q+g)
xF = 0.2 xF = 0.2
0.1
0.15
ψ ψ
sinAUT 0.1 sinAUT 0.05
0.05
0
0
SIDIS 1 SIDIS 2
-0.05 -0.05
0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
PT [GeV] PT [GeV]
anti-tagged [backward target hemisph.] anti-tagged [backward target hemisph.]
0.1 0.1
LO
l p -> π- X l p -> π- X LO+WW (q)
LO+WW (q+g)
xF = 0.2 xF = 0.2
0.05 0.05
ψ ψ
sinAUT 0 sinAUT 0
-0.05 -0.05
SIDIS 1 SIDIS 2
-0.1 -0.1
0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
PT [GeV] PT [GeV]
√
Figure4: ThetheoreticalestimatesforAsinψ vs.P at s(cid:39)7.25GeVandx =0.2forinclusiveπ+(upper
UT T F
panels)andπ−(lowerpanels)productionin(cid:96)p↑→πX processes,comparedwiththeHERMESanti-tagged
data[9]. Seetextandlegendfordetails.
negligible for the SIDIS 2 set, while for the SIDIS 1 set is relatively more important, reducing
the agreement with the data2. Concerning the anti-tagged data set, Fig. 4, we could observe that:
onceagaintheWWcontributionleadstoaverygooddescriptionofthedata(evenifsomesizeable
discrepancyfortheπ+ dataremains). ThegluonSiverseffectisnegligible,exceptfortheSIDIS1
set in π− production. However, one has to keep in mind that this kinematical region probes the
stillpoorlyconstrainedlarge-xbehaviouroftheSiversfunctions(thedominantcontribution). This
is the reason of the wider error bands. Quite interestingly a very recent extraction of the Sivers
functionsfromSIDISdataseemstoreducesignificantlythediscrepanciesbetweenthetheoretical
predictionsandtheanti-taggeddataset,seeRef.[10].
4. Conclusions
The issue of TMD factorization and universality is crucial for our understanding of SSAs in
QCD. Here we have further pursued the idea, already discussed in a previous study, for assessing
thevalidityofaTMDschemeininclusiveprocessesinwhichasinglelarge-P particleisproduced.
T
2NoticethatthereisstillalargeuncertaintyinthegluonSiversfunctionextractioninthelarge-xregion.
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Quasi-realphotoncontributiontoA UmbertoD’Alesio
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We have computed the single spin asymmetry A , for the (cid:96)p↑ →hX process, as generated by the
N
SiversandtheCollinsfunctions,whichhavebeenextractedfromSIDISande+e− data[17,18,19,
20]. Doing so, we adopt a unified TMD factorized approach, valid for (cid:96)p→(cid:96)hX and (cid:96)p→hX
processes, in which, consistently, we obtain information on the TMDs and make predictions for
A .
N
Inthepresentanalysiswehaveextendedthisstrategy,includingthecontributionofquasi-real
photon exchange, expected to be important when the final lepton is scattered at small angles. We
haveindeedobtainedthatforHERMESkinematicstheWWcontributiontotheunpolarizedcross
section is huge, reaching more than 70%, and therefore dominating over the LO term. Moreover,
andmoreimportantly,wehaveshownhowthedatadescriptionoftheSSAsobservedatHERMES,
concerning their size, sign and behaviour, (already quite satisfying at LO) is definitely improved
whenoneincludestheWWpiece. Thisseemscorroboratingtheoverallapproach.
U.D.thankstheorganizersfortheirkindinvitationtosuchaniceandfruitfulworkshop.
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