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February7,2008 7:51 ProceedingsTrimSize: 9inx6in vandernat˙proc 5 0 0 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. 1 February7,2008 7:51 ProceedingsTrimSize: 9inx6in vandernat˙proc 2 )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. February7,2008 7:51 ProceedingsTrimSize: 9inx6in vandernat˙proc 3 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 distribution 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, compared with the situation where the azimuthal angle is defined according to the Trento conventions4. dForthesepreliminaryresults,allhadrontypeswereanalyzedassumingtheywerepions. Thecorrespondinguncertainty isnotincludedinthequoted systematicerror. February7,2008 7:51 ProceedingsTrimSize: 9inx6in vandernat˙proc 4 ⊥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).