Table Of ContentFebruary7,2008 7:51 ProceedingsTrimSize: 9inx6in vandernat˙proc
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TWO-HADRON SINGLE TARGET-SPIN ASYMMETRIES:
2
FIRST MEASUREMENTS BY HERMES
n
a
J
6 P.B. VAN DER NAT, K. GRIFFIOEN
(ONBEHALF OFTHE HERMES COLLABORATION)
1
v Nationaal Instituut voor Kernfysica en Hoge-Energiefysica (NIKHEF),
9 P.O. Box 41882, 1009 DB Amsterdam, The Netherlands
0
0
1 Single target-spin asymmetries in semi-inclusive two-pion production were mea-
0 sured for the first time by the HERMES experiment, using a longitudinally po-
5 larized deuterium target. These asymmetries relate to the unknown transver-
0 sitydistributionfunctionh1(x)through,alsounknown,interferencefragmentation
/ functions. The presented results are compared with a model for the dependence
x
of one of these interference fragmentation functions on the invariant mass of the
e
pionpair.
-
p
e
h
1. Introduction
:
v
i Of the three leading-twist quark distributions, the quark number density,
X
the quark helicity and the quark transversity distribution, only the latter
r
a one is so far unmeasured. The main reasonfor this is its chiral-odd nature
which requires a secondchiral-oddobject to couple to the transversitydis-
tributioninordertomakeitaccessibletomeasurements. Onecandidatefor
such a chiral-odd fragmentation function is the so-called Collins fragmen-
tationfunctionappearinginpionleptonproduction. Thishasbeenstudied
by the HERMES experiment using a longitudinally polarized target1, and
recently using a transversely polarized target2.
Anotherwayofaccessingtransversityisofferedbyinterferencefragmen-
tationfunctions,whichappearinsingletarget-spinasymmetriesintwo-pion
semi-inclusivedeep-inelasticscattering(DIS).Oneoftheadvantagesofthis
methodisthatthe azimuthalmomentoftheasymmetryisdirectlypropor-
tional to products of distribution and fragmentation functions, whereas in
the case of one-hadron semi-inclusive DIS, these products are convoluted
withthetransversemomentumofthedetectedhadron. Althoughtheinter-
ference fragmentation functions themselves are as yet unknown, they can
be cleanly measured in e+e− experiments, such as Belle3 and Babar.
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)10.6
d-0
~k dn(0.4
~k′ ~q P~1 dnsi1
P~h dnsi00.2
si 0
S~⊥ P~2
-0.2
S~ φR⊥
-0.4
-0.6
0.50.550.60.650.70.750.80.85M0.pp9 [0G.9e5V]1
Figure 1. Left: kinematic planes, where φR⊥ is the angle between the plane spanned
bytheincident(~k)andscatteredlepton(~k′)andtheplanespannedbythetwodetected
pions(P~1 andP~2,withP~h≡P~1+P~2). Right: thefactorsinδ0sinδ1sin(δ0−δ1),where
the s- and p-wave phase shifts (δ0 and δ1) were obtained from pion-nucleon scatter-
ing experiments8. This factor shows the invariant mass dependent part of H1∢,sp, as
predictedbyJaffeet al.5.
2. Single Spin Asymmetry
The transversitydistribution canbe accessedexperimentallyby measuring
the single target-spin asymmetry, defined as:
1 N→(φ )/N→−N←(φ )/N← σ
A (φ )= R⊥ d R⊥ d = UL, (1)
UL R⊥ |P |N→(φ )/N→+N←(φ )/N← σ
L R⊥ d R⊥ d UU
where N→ (N←) is the number of π+π− pairs detected with target spin
antiparallel(parallel)tothedirectionofthebeammomentum. Thesenum-
bers are normalized to the corresponding number of DIS events, N→ and
d
N←, respectively and the entire ratio is divided by P , the longitudinal
d L
target polarization. The asymmetry is evaluated as a function of the az-
imuthalangleφ ,whichisshowninFig. 1. Inthelastterm,σ andσ
R⊥ UL UU
arethepolarizedandunpolarizedcrosssections,respectively. Accordingto
Bacchetta et al.6 σ can be written at sub-leading twist asa:
UL
σUL ∼Xe2qsinφR⊥sinθ(cid:2)K1|Sk|hL−K2|S⊥|h1(cid:3)(cid:0)H1∢,sp+H1∢,ppcosθ(cid:1),
q
(2)
whereK1 andK2 arekinematic factorsb andθ isthe anglebetweenthe di-
rectionofemissionofthepionpairinitscenter-of-massframeandP~ inthe
h
hadronic frame (see Fig. 1). Eq. 2 introduces the two-hadron interference
aEq. 2 was derived using the Wandzura-Wilczek approximation and is valid at low
invariantmassMππ ofthepionpair
bSeethearticlebyBacchetta et al.6 forthefullexpression.
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fragmentation functions H∢,sp and H∢,pp. They decribe the interference
1 1
betweendifferentproductionchannelsofthepionpair: H∢,sp relatestothe
1
interferencebetweens-andp-wavestatesandH∢,pp totheinterferencebe-
1
tween two p-wave states. Both functions can be used separately to extract
information on the transversity distribution h1(x). In the present analysis
the sinφ -momentof the asymmetry, AsinφR⊥ has been studied, which is
R⊥ UL
onlysensitive toH∢,sp,because inevaluatingAsinφR⊥ the integralis taken
1 UL
over the polar angle θ.
ApredictionwasgivenbyJaffeetal.5 fortheinvariant-massbehaviorof
H∢,sp in terms of s- and p-wave phase shifts. Fig. 1 shows that according
1
to this model the asymmetry would change sign approximately at the ρ0
mass. Note, however, that this model does not predict the size or sign of
the asymmetry.
Two distribution functions appear in Eq. 2: the transversity distri-
bution h1 and the subleading-twist function hL, which is related to h1
througha Wandzura-Wilzcek relation. The contribution of these functions
is proportionalto the target polarization components transverse (S ) and
⊥
parallel(S ) to the virtual photon direction, respectively. In the data pre-
k
sentedherethevalueofS increasesfrom3%ofS atlowxto9%athigh
⊥ k
x. For the present analysis data were taken during the period 1998-2000
with a longitudinally polarized deuterium (gas) target. The averagetarget
polarization was 0.84 ± 0.04.
3. Results
In Fig. 2 the sinφ -momentc AsinφR⊥ is plotted versus the invariant
R⊥ UL
mass of the pion paird M in panels of increasing x (= Q2/(2Mν)) and z
ππ
(z ≡E /ν). The size of the asymmetries is onthe orderof a few percent.
ππ
Forallpanels the asymmetriesarenotinconsistentwithzerogiventhe size
ofthe statisticalerrors. Nosignificantx- orz-dependenceisobserved. The
shape of the asymmetries versus the invariant mass has been compared
with the model prediction shown in Fig. 1. This was done by fitting the
following function to the data:
f(Mππ)=c1P(Mππ)+c2 (3)
cUsing the definition of φR⊥ shown in Fig. 1, AsUinLφR⊥ will differ by a sign, com-
pared with the situation where the azimuthal angle is defined according to the Trento
conventions4.
dForthesepreliminaryresults,allhadrontypeswereanalyzedassumingtheywerepions.
Thecorrespondinguncertainty isnotincludedinthequoted systematicerror.
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⊥R 0.06 eeedddÕÕÕ ÕÕÕ eee''' hhh+++hhh--- XXX HHHEEERRRMMMEEESSS PPPRRREEELLLIIIMMMIIINNNAAARRRYYY
fsinAUL0.04
0.02
0
-0.02
-0.04 r0 r0 r0
-0.06 s0s0s0y.y.y.000sss222... 3 3 3uuu <<<nnn cccxxx... <<<=== 000000......000000444000666777 <<<<<<xzxzxz>>>>>> ====== 000000......444000555333666 000...000444666 <<< xxx <<< 000...000777666 <<<<<<xzxzxz>>>>>> ====== 000000......444000999555999 xxx >>> 000...000777666 <<<<<<zzzxxx>>>>>> ====== 000000......555111000333
0.40.50.60.70.80.9 1 1.1 0.40.50.60.70.80.9 1 1.1 0.40.50.60.70.80.9 1 1.1
Mpp [GeV]
⊥R 0.06 eeddÕÕ ÕÕ ee'' hh++hh-- XX HHEERRMMEESS PPRREELLIIMMIINNAARRYY
fsinAUL0.04
0.02
0
-0.02
-0.04 r0 r0
-0.06 s0s0y y <<ss zz.. uu<<nn 00cc....55 ==22 00..000077 <<<<xxzz>>>> ==== 0000....3300887700 00..5522 << zz << 11 <<<<xxzz>>>> ==== 0000....6600448811
0.40.50.60.70.80.9 1 1.1 0.40.50.60.70.80.9 1 1.1
Mpp [GeV]
Figure 2. The asymmetry-moment AsUinLφR⊥ as a function of the invariant mass Mππ
fordifferentx-bins(top)andz-bins(bottom).
whereP(M )containstheinvariant-massdependencefromthemodelpre-
ππ
diction and c1 and c2 are free parameters of the fit. The resulting curves
areincludedinFig. 2. These curvesshowthatinallpanels,the resultsare
consistent with the model. In the mid-x and low-z region the data give a
hint for a sign change of the asymmetry at the ρ0 mass.
Starting in 2002, HERMES has been taking data with a transversely
polarized hydrogen target, with an average polarization of 0.78 ± 0.04,
which can result in much larger asymmetries. Data-taking will continue
until the summer of 2005. The analysis of these data is ongoing and first
results are expected in the near future.
References
1. A.Airapetian et al. (HERMES), Phys. Lett. B 562, 182 (2003).
2. A.Airapetian et al.(HERMES),Phys. Rev. Lett. (inpress), hep-ex/0408013.
3. R.Seidl (Belle) these proceedings.
4. A.Bacchetta et al.,hep-ph/0410050 (2004)
5. R.L.Jaffe, X. Jin, and J. Tang. Phys. Rev. Lett. 80, 1166 (1998).
6. A.BacchettaandM.Radici,ProceedingsofDIS’2004(2004),hep-ph/0407345.
7. A.BacchettaandM.Radici,Phys.Rev.D67,094002(2003),hep-ph/0407345.
8. P.Estabrooks and A.Martin, Nucl. Phys. B79, 301 (1974).
