Charmed Hadron Production at RHIC

Transcription

1 KOBE-FHD-2-1 (hep-ph/21144) Charmed Hadron Prodution at RHIC Kazumasa OHKUMA 1), a) 1,2), b), Toshiyuki MORII and 1), ) Satoshi OYAMA 1) Graduate Shool of Siene and Tehnology, Kobe University Nada, Kobe , JAPAN 2) Faulty of Human Development, Kobe University Nada, Kobe , JAPAN ABSTRACT To extrat information about polarized gluon distribution in the proton, harmed hadron, atually Λ, produtions at RHIC experiment are studied. We found that the spin orrelation asymmetry between the initial proton and the produed Λ is enable us to distinguish parameterization models of polarized gluons. Talk presented by K. OHKUMA at 3rd Cirum-Pan-Paifi Symposium on High Energy Spin Physis, Beijing, China,Ot. 8-13, 21 (talk on Ot. 11, 21) a) address: ohkuma@radix.h.kobe-u.a.jp b) address: morii@kobe-u.a.jp ) address: satoshi@radix.h.kobe-u.a.jp

2 1 Introdution Sine the surprising EMC measurement 1 of the polarized struture funtion of proton g p 1 (x, Q2 ) was reported more than ten-years ago, the spin struture of the proton is still mysterious problem being alled the proton spin puzzle 2. As is well known, a proton is not an elementary but ompound partile and thus, its spin is arried by its onstituents as desribed by a sum rule, 1 2 = 1 2 Σ G <L z > qg (1) where 1 2 on the left side means a spin of the proton, while Σ, G and <L z > qg represent the amount of the proton spin arried by the onstituent quarks, gluons and their orbital angular momenta, respetively. An extensive study on polarized struture funtions of nuleons brought about a rather good information of valene quark distributions in the proton, However, knowledge of G and <L z > qg is still poor beause it is very diffiult to diretly extrat its information from existing experimental data. In this work, we are interesting in the polarized gluon distribution G. So far, to extrat its information, many proesses depending on the gluon interations have been proposed and studied. Here, to study the polarized gluon distribution in a proton, we propose another proess, p p Λ X, whih ould be observed in forthoming BNL-RHIC experiment. In this proess, Λ is dominantly produed via fragmentation of a harm quark originated from gluon gluon fusion 1. Thus, its ross setion is diretly proportional to the gluon distribution in the proton. Moreover, the Λ ombined light u and d quarks. Hene, the Λ is omposed of a heavy quark and antisymmetrially spin is basially arried by a harm quark through gluon gluon fusion. Therefore, observation of the spin of the produed Λ us information about the polarized gluons in the proton gives 1 Sine harm quarks are tiny ontents in the proton, the gluon gluon fusion proess is dominant for harm quark prodution. 2

3 2 Spin Correlation Asymmetry To get information of G, we introdue the spin orrelation asymmetry of the target proton and produed Λ baryon, 3 = dσ dσ dσ dσ dσ dσ dσ dσ d σ/dx dσ/dx, (X = η or p ), (2) T where dσ, for example, denotes the spin-dependent differential ross setion with the positive heliity of the target proton and the negative heliity of the produed Λ baryon. η and p T mean pseudo-rapidity and transverse momentum of produed Λ, respetively. Moreover, aording to quark-parton model, d σ/dx anbeexpressedas d σ Y max 1 1 dx = G pa Y min x min x min g a (x a,q 2 ) G pb g b (x b,q 2 ) D Λ (z) a b d ˆσ dˆt Jdx adx b dy, (X, Y = η or p T (X Y )), (3) where G pa g a (x a,q 2 ), G pb g b (x b,q 2 )and D Λ (z) represent the unpolarized gluon distribution funtion, the polarized gluon distribution funtion and the spin-dependent fragmentation funtion of the outgoing harm quark deaying into a polarized Λ,respetively. d ˆσ/dˆt is the spin orrelation differential ross setion in the subproess and J is the Jaobian whih transforms the variables z and ˆt into η and p T. 3 Numerial Calulation To numerially estimate, we use, as input parameters, m.25 GeV, m p =.938 GeV and m Λ =2.28 GeV. 4 We limit the integration region of η and p T of produed Λ as 1.3 η 1.3 and3gev p T 15(4) GeV for s = 2(5) GeV in order to get rid of the ontribution of the diffrative Λ prodution and also the Λ 3

4 prodution through a single harm quark prodution via W boson exhange and W boson prodution. In addition, we take the GRSV1 5 and 6 parameterization models for the polarized gluon distribution funtion and GRV98 7 for the unpolarized one. Though both of GSRSV1 and models exellently reprodue the experimental data on the polarized struture funtion of nuleons g 1 (x), the polarized gluon distributions for those models are quite different. In other words, the data on polarized struture funtion of nuleons g 1 (x) alone are not enough to distinguish the model of gluon distributions. Sine the proess is semi-inlusive, the fragmentation funtion of a harm quark to Λ is neessary to do numerial alulation. For the unpolarized fragmentation funtion, we use Peterson fragmentation funtion 8, D Λ (z). However,sinewehavenodata, at present, about polarized fragmentation funtion for the polarized Λ prodution, we take the following ansatz for the polarized fragmentation funtion D Λ (x), D Λ (z) =C Λ D Λ, where C Λ is sale-independent spin transfer oeffiient. In this analysis, we study two ases: (A) C Λ = 1 (non-relativisti quark model) and (B) C Λ = z (Jet fragmentation model 9 ). Numerial results of are shown in Fig. 1 and Fig. 2. As shown in Fig. 1 and Fig. 2, is rather sensitive to the model of the polarized gluon distribution funtions. Therefore, the proess disussed here ould provide good information about the distribution of the polarized gluons in a nuleon. Espeially, the η dependene of at s=2gev is the most effetive to distinguish the parameterization models of polarized gluon beause the magnitude of a numerial value of is larger than others. 4 Summary To extrat information of polarized gluon distribution in the proton, we have proposed an interesting proess; p p Λ X and alulated the spin orrelation asymmetry,, defined by Eq.(2). We found that in this proess, is rather sensitive to the parameterization models of polarized gluon, and thus, proess is quite promising for testing 4

5 the models of polarized gluon distribution. Error estimation is important and now is undergoing. To get better knowledge of G, we need more detailed information about the spin-dependent fragmentation funtion of a harm quark to Λ GeV p T 15GeV η 1.3 GRSV1.5 GRSV η p T Figure 1: as a funtion of η (left panel) and p T (right panel) at s=2gev..2 3GeV p T 3GeV GRSV η 1.3 GRSV η p T Figure 2: as a funtion of η (left panel) and p T (right panel) at s=5gev. REFERENCES [1] J. Ashman et al. [European Muon Collaboration], Phys. Lett. B22, 63 (1988); Nul. Phys.B328,1 (1989). [2] For a review see: 5

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