Arestov, Yu I

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 STATE RESEARCH CENTER OF RUSSIAINSTITUTE FOR HIGH ENERGY PHYSICSIHEP 2001-3Yuri I. ArestovTWIST-2 POLARIZED FRAGMENTATIONFUNCTION IN THE OPEN CHARMPRODUCTION IN DISTalk given at Spin2000, Osaka, Japan,October 16-21, 2000Protvino 2001UDK 539.12.142 m–24AbstractArestov Yu.I. Twist-2 Polarized Fragmentation Function in the Open Charm Production in DIS : IHEPPreprint 2001-3. – Protvino, 2001. – p. 3, ﬁgs. 4.To extract the polarized fragmentation function G1, the transmitted polarization parameter DLLhas been considered in the semi-inclusive leptoproduction process e−↑ + p → e− + Λ+c↑ + X with bothlongitudinally polarized electron and charmed lambda. The polarization transfer dˆLL for the lepton-gluonsubprocess e−↑ + g → e− + Q↑Q¯ was carefully studied, and it appeared to be sizable. The quantitativeestimates of dˆLL were made at the gluon momentum fraction xg = 0.2.aNNOTACIQaRESTOW ‘.i. pOLQRIZOWANNAQ FUNKCIQ FRAGMENTACII TWISTA-2 W OBRAZOWANII OTKRYTOGO ˆARMA WDIS.: pREPRINT ifw— 2001-3. – pROTWINO, 2001. – 3 S., 4 RIS.dLQ OPREDELENIQ POLQRIZOWANNOJ FUNKCII FRAGMENTACII G1 TWISTA-2 RASSMATRIWAETSQ PARA-METR PEREDANNOJ POLQRIZACII DLL W POLUINKL@ZIWNOM PROCESSE e−↑ + p → e− + Λ+c↑ +X S POLQRI-ZOWAANYMI “LEKTRONAMI I Λ+. dETALXNO IZUˆENA PEREDAˆA POLQRIZACII OT e−↑ K TQVELOMU KWARKUW LEPTON-GL@ONNOM PODPROCESSE e−↑ + g → e− + Q↑Q¯, GDE ONA OKAZYWAETSQ ZNAˆITELXNOJ. sDELANYKOLIˆESTWENNYE OCENKI dˆLL PRI IMPULXSE GL@ONA xg = 0.2.c© State Research Center of RussiaInstitute for High Energy Physics, 2001The polarized charmed lambda production is considered in SIDIS reactione−↑ + p→ e− +Λ+c↑ +X (1)with the longitudinally polarized lepton beam shown in ﬁg. 1 in the LO approximation. Thepolarization transmission parameter DLL is deﬁned asDLL =σ++ + σ−− − σ+− − σ−+σ++ + σ−− + σ+− + σ−+, (2)where the subscripts {++} etc. relate to the helicity states of the lepton and Λ+c .In the absense of the initial polarization, Λ+c may be polarized only transversely to theproduction plane. A longitudinal component of the Λ+c polarization vector may arise due to thelongitudinal lepton polarization in the initial state.The polarization transmission coeﬃcient which can be measured experimentally relates tothe fragmentation function G1(z, µ2) (FF) through the following expression:DLL ∼ G(xg) · dˆLL ·G1, (3)→e-p Λc+Gγe-c-cFig. 1. The SIDIS reaction (1).where G(xg) is the gluon distribution in the (unpolarized)proton and dˆLL is the polarization transmission coeﬃcientin the heavy quark pair production in the lepton–gluonscatteringe−↑ + g → e− +Q↑Q¯. (4)In order to plan measurements of the unknown FF G1, itwould be instructive to know the range of the values ofdˆLL in subprocess (4). The matrix element of reaction (4)incorporates the contributions of u-channel (QQ¯ conﬁgu-ration in Fig. 1), t-channel with the permuted Q’s and theinterference term. Below these contributions are referredto as uu, tt and tu terms.As is seen from Fig. 2, the dLL properties may bequite diﬀerent depending on t or u-channel that is onthe QQ¯ conﬁguration in the diagram. The azimuthal an-gle φ counts from the lepton scattering plane. The total1φ-dependence integrated over pT exhibits a remarkable behaviour with a deep minimum atφ = 1800 and a positive maximum at φ = 00 (3600). The maximum of the absolute value ofdLL may reach 0.3.Apart from pT dependence it can be interesting to track down the dˆLL dependence on EQ,the quark energy, and on cos(Q, q), the cosine of the scattering angle in respect to the virtualphoton direction. In Fig. 3 the corresponding two- and one-dimensional plots are shown in tworegions: φ = 0± 300 and φ = 180± 300.Finally, Fig. 4 presents the quark energy EQ dependence of the polarization coeﬃcient dˆLLintegrated in separate hemispheres in respect to the virtual photon momentum. It is seen thatat the reasonable values of the quark energy, the coeﬃcient dˆLL appears to be sizable.From the above consideration, it follows that the model expectations for the fragmentationfunction G1 (see (3)) may be quite reasonable because the underlying subprocess exhibits thelarge values of dˆLL in some regions of the phase space.Received January 19, 2001Fig. 2. dˆLL versus pT and φ for (from up to down) tt, uu, tu and total terms.2Fig. 3. dˆLL dependence on the quark energy EQ and (Q,q) angle (see the text).Fig. 4. The quark energy dependence of dˆLL in the forward and backward hemispheres.3‘.i.aRESTOWpOLQRIZOWANNAQ FUNKCIQ FRAGMENTACII TWISTA-2 W OBRAZOWANII OTKRYTOGOˆARMA W DIS.oRIGINAL-MAKET PODGOTOWLEN S POMO]X@ SISTEMY LaTEX.rEDAKTOR e.n.gORINA. tEHNIˆESKIJ REDAKTOR n.w.oRLOWA.pODPISANO K PEˆATI 29.01.2001. fORMAT 60× 84/8. oFSETNAQ PEˆATX.pEˆ.L. 0.37. uˆ.-IZD.L. 0.3. tIRAV 160. zAKAZ 50. iNDEKS 3649.lr ß020498 17.04.97.gnc rf iNSTITUT FIZIKI WYSOKIH “NERGIJ142284, pROTWINO mOSKOWSKOJ OBL.iNDEKS 3649p r e p r i n t 2001-3, i f w —, 2001

Twist-2 Polarized Fragmentation Function in the Open Charm Production in DIS

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