Left-right asymmetry for meson production in SIDIS process

CPC(HEP & NP), 2009, 33(12): 1354- -1357Chinese Physics CVol. 33, No. 12, Dec., 2009Left-right asymmetry for meson production inSIDIS process'SUN Bo(孙博) SHE Jun(佘俊) ZHANG Bing(张冰) MAO Ya Jun(冒亚军)) MA Bo-Qiang(马伯强)3)(School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking Univereity, Beijing 100871, China )Abstract We analyze the left- right asymmetry in the semi inclusive deep inelastic scattering (SIDIS) processusing a method where no weighting function are used. Considering all favor of quarks, we reanalyze the π*production and extend our calculation on the K* production. The predictions on HERMES, COMPASS andJLab kinematics with transversely polarized nucleon target are shown in this paper.Key words semi-inclusive deep inelastic scattering, transversity, left right asymmetryPACS 13.60.Le, 13.85.Ni, 13.87.Fh1 Introductionvarious weighting functions are used in most analy-sis. After multiplying the weighting function, we canIn 1991, the left -right asymmetry was reported byextract each efect separately. This is the conven-E704 collaboration for the first timel", where largetional way to deal with the SIDIS data. However, inasymmetry was found in p'p→πX process withRef.5, it was pointed out that the selection of the200 GeV transversely polarized beam. Their resultsweighting functions is based on a certain theory, thesuggest that the transverse spin effect is also signifi-“weighting function”method may change if the the-cant even in the high energy region. However, the the-ory changes. The authors suggested to analyze theory based on the naive parton model predicted a vani-SIDIS data using the method at the E704 experimentshing asymmetry. In order to explain these phenom-where no weighting functions were multiplied.As we know, there are other theory which try toena, two mechanisms were proposed. In 1991, Siversprovided a possible mechanism2 that the asymme-explain the lef-right asymmetry, e.g. the valencetry is originated from the quark intrinsic transversequark orbital angular moment effectio, but appar-momentum. This mechanism is now described by aently the weighting functions do not work in theseparton distribution function, the Sivers function; Intheories. Thus we think it is reasonable to adopt the1993, Collins provided another mechanism!3, 日thatno-weighting function method.In Ref. [5], only u and d quarks were consideredthe asymmetry is generated in the hadronization pro-cesses with a spin dependent fragmentation function,in the calculation, however, besides u and d quarks,the Collins function. Although these two mechanisms0 and d quarks are also favored in the fragmenta-are completely diferent, both of them contribute totion process to the π production, so the sea quarkscontribution especially for i and d should not be igthe asymmetry.Contrast to the complexity of the hadron-hadronnored. Considering all Aavors of quarks, we reanalyzecollision proces, we turn our attention to a muchthe πt production and then extend our calculation oncleaner and simpler process, the semi-inclusive deepthe K* production.inelastic scattering (SIDIS) process. Since the con-2 Theoretical descriptiontribution of the Sivers and Collins effects are com-bined during the interaction of high energy particles,On the theoretical side, we adopt the factorizationReceived 7 August 2009中国煤化工* Supported by National Natural Science Foundation of China (107.MYHCNMH Giv Grant PrierorChinese Ministry of Education (305001)1)E-mail: maoyj@pku.edu.cn2) E mail: mabq@phy.pku. edu.cn⑥2009 Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Sciences and the Instituteof Modern Physics of the Chinese Academy of Sciences and IOP Publishing LtdNo. 12.SUN Bo et al: Left-right agymmetry for meson production in SIDIS process1355theorem to describe the cross section. By introduc-0(1), but other terms such as the Collins efect areing various distribution or fragmentation functions,O(sin2 0).0 can be calculated byla!:we can express the cross section for an SIDIS pro-cess explicitly under the r' p framel7,8, in which thez axis is defined as the direction parallel to the ex-sin0=γ\1+r2，γ= 2xMp/Q. (5)changed virtual pboton. However, most of the ex-periment analysis were under the lp frame, i.e. theFor most instance, θ is very small, and the directionlaboratory frame, where z axis is defined as the di-of the virtual photon is very close to the direction ofrection parallel to the beam direction. In order tothe incident beam. That is: the Sivers effect is domi-compare with experiment, we need to transform thenant and other efects are suppressed in our analysis.crOss section from r°p frame to lp frame by a rota-And for convenience, the Collins effect which is nottion of angle 0, θ is the angle between the beam andknown so clearly yet is not considered in our analysis.the virtual photon. Thus the cross section is writtenThe asynmetry can be written as:asl!:drdydqdzdqhdPRLloAuv(r,y,z,Ph1)≈- s|d$fd中% (dosv + do.+....|dfdh douua2cos02s-1-mair0g x{F.D.]-(6)SrcosO; in( -的)F(临D]-3 Numerical calculationsVI- sin'0sin',: M,ST cosθh.时+Before the numerical calculations, we need an in-√1- sin'0sin'φput for the distribution and fragmentation functions.The Sivers function has already been studied by+other terms > = dσv + dosiv +o+.+...，(1)HERMES and COMPASS Collaborations[10,川, butat that time, only the information of u and d quarkswhere we use a compact notation:could be extracted. Recently, besides the chargedFlwfD]= Sedp_dk_8(pr- kx-Pa1/2)pion production, neutral pion and charged kaon az-imuthal asymmetries were also analyzed by HER-w(pI,k)f*(x,pH)Df(,z2h2)，(2)MES and COMPASS Collaboration[12, 13). Thanks tothese experiment, the parameters of the Sivers func-andtion were improved, and besides the u and d quarksthe Sivers function for the sea, quarks were extracted1-y- =y2n2h=Pr/|P%1| (3) for the first timel4. For the fragmentation func~-1-y+元u +jv2ntions, all recent analysis were based exclusively onthe single inclusive ete- annihilation (SIA) data. InThe angles 幅and中的are definedas: 幅=咖一these experiments, it is impossible to distinguish“va-φ，φ=φ。-φ, where φ denotes the orientationlence" from“sea”" without assumptions. Fortunately,angle of the lepton plane.the measurements coming from both proton-protonThe left-right aymmetry in this paper is definedcollisions and deep inelastic lepton-nucleon scatter-a8ing have matured enough to yield cormplementary in-1 N(4b,)-N(ψ。 +π)1 da↑-dσt, (4formation on the fragmentation process in the lastSr N(4.)+N(ψ。+π)Sr dat + datfew years. Using these data, individual fragmenta-where Sr is the transverse polarization of the target,tion functions for all favors quarks as well as gluonsψ。is the azimuthal angle of the spin vector. Since nowere extracted in a global analysis15l.weighting functions are applied here, we cannot inte-It should be pointed out that, although an uni-grate the produced hadron over the whole space, or itversa中国煤化工lent distributionsmust lead to a vanishing result. Similar to the E704we choose theexperiment, we limit the detected region in a certain SiversYHCNMHGcess.range, e.g. -π/4 to π/4. As the target spin changesUsing the parametrization mentioned above, wefrom up to down, a left -right asymmetry is obtained. present our prediction on HERMES experiment forAfter integral over φ，we find that Sivers effect isa proton target, on Compass experiment for proton,1356Chinese Phyics C (HEP & NP)Vol. 33neutron and deuteron targets, on JLab experimentfor proton and neutron targets.ProtonFirstly, we reanalyze the results on π production~0.for different experiments, these results are shown inig. 1- Fig. 4. In Fig. 1, we make a comparisonwith the results obtained in Ref. [5], It can be foundthat the sea quarks have an observable contributionto the asymmetry, especially suppress the asymmetryNeutronat large x and z region. Then we extend our calcula-tion to the K* production, the results are shown inFig. 5一Fig. 8. Notice that the Sivers distributions-0of the i and s quarks given in Ref. [14] are extremelysmall but with a large uncertainty where even theirsign are not determined within the error, so it must0.2 00.8 0.2.4 0.6 0.8lead a large uncertainty to our prediction on K- pro-duction.Fig. 3. Similar as Fig. 1, but at JLab kinemat-ics with a beam energy of 6 GeV.气o.1F0.10.20.4 0.6 0.2 0.4 0.6 0.8Fig. 1. The r and z-dependence of the left-rightasymmetry for π# production on HERMESkinematics. Solid lines for π+ and dashed linesfor π . Thick curves are our results and thincurves are results from Ref. [5].-0.2-与「2 0.40.8 0.2 0.4 0.6 0.80.05Fig.4. Similar as Fig. 1, but at JLab kinemat-ics with a beam energy of 12 GeV.Neulron冬1F-0.1Deuteron中国煤化工z0.8 0.8-0.05-DH.CNMHGFig. 5. The T and z-dependence of the left-right10asymmetry for K* production on HERMESkinematics. Solid lines for K+ and dashedFig.2. Similar as Fig. 1, but at COMPASS kinematics.lines for K- .No. 12SUN Bo et al: Left-right asymmetry for meson production in SIDIS process1357Proton与0.1-..05-Neutron0.1-0.102-Deuteron0.602 0.4 0.6 0.8Fig. 8. Similar as Fig. 5, but at JLab kinemat-ics with a beam energy of 12 GeV.-0.05-4 ConclusionFig. 6. Similar as Fig. 5, but at COMPASS kinematics.Following the method in Ref. [5], we reanalyze theleft-right asymmetry in the SIDIS process with the5new Sivers and fragmentation functions, all flavorsof quarks are considered in our analysis. We foundthe contribution of sea quarks should not be ignoredin πt production, although their Sivers distributionsare small. The asymmetry on K* production are alsopresented in this paper. It should be cautious thatthe results for K- production might be not accurateenough, and the parametrization of 0 and s quarksneed further constrained.-0.2-00.2O.0.6 0.20.4 0.6 0.Fig.7. Similar as Fig. 5, but at JLab kinemat-ics with a beam energy of 6 GeV.References8 Bacchetta A, Diehl M, Goekeb K, Metzb A, MuldersP J,Schlegel M. JHEP, 2007, 0702: 0939 Diehl M, Sapeta S. Eur. Phys. J. C, 2005, 41: 5151 Adams DLet al. Phys. Lett. B, 1991, 261: 20110 Anselmino M, Boglione M, D'Alesio U, Leader E, Murgfia2 Sivers D w. Phys. Rev. D, 1990, 41: 83; Sivers D w. Phys.F. Phys. Rev. D, 2005, 71: 014002Rev. D, 1991, 43: 26111 Anselmino M et al. Phys. Rev. D, 2005, 72: 0940073 CollinsJC. Nucl. Phys. B, 1993, 396: 16112 Diefenthaler M (HERMES). arXiv: 0706.22424 Collins J C, Heppelmann s P, Ladinsky G A. Nucl. Phys.13 Martin A (COMPASS). Czech. J. Phys, 2006, 56: F33;B, 1994, 420: 565hep-ex/0702002. Alekseev M et al (COMPASS). arXiv:5 SHEJ, MAO Y, MA B Q. Phys. Lett. B, 2008, 866: 3554 Ar180 |中国煤化工，s9:. 893 Boros C, LIANG z T, MENG T C. Phys. Rev. Lett., 1993,de2007, 75: 114010Y台.CNMH(7 Kotzinian A. Nucl. Phys. B, 1995, 441: 23416 Bormiun巴u, muucioi山. siu. . wyo. 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