Charmed Hadron Prodution in Polarized pp Collisions oshiyuki Morii Λ and Kazumasa Ohkuma Λ Division of Sienes for Natural Environment, Faulty of Human Development, Kobe University, Nada, Kobe 657-851, JAPAN Eletroni address:morii@kobe-u.a.jp Department of Physis, Faulty of Engineering, Yokohama National University, Hodogaya, Yokohama 24-851, JAPAN Eletroni address:ohkuma@phys.ynu.a.jp Abstrat. o extrat information about polarized gluons in the proton, prodution of harmed hadrons, in partiular, Λ + baryon in pp ollisions was studied. We alulated the transverse momentum distribution and the pseudo-rapidity distribution of the spin orrelation asymmetry between the initial proton and the produed Λ +. hose statistial sensitivities were also alulated under the ondition of RHIC experiment. We found that the pseudo-rapidity distribution of is promising for testing the model of polarized gluons in the proton and also the spin-dependent fragmentation model of a harm quark deaying into Λ + baryon. INRODUCION he Relativisti Heavy Ion Collider (RHIC) at Brookhaven National Laboratory has just started to explore the internal struture of proton. One of the important purposes of those RHIC experiments is to study the behavior of polarized gluons in the proton. As is well known, the proton spin is given by the sum of the spin arried by quarks Σ and gluons G, and their orbital angular momenta hl Z i. In these years, a great deal of efforts have been made for extrating those omponents from polarized struture funtions of nuleons[1]. Based on the next to leading order QCD analyses on the polarized struture funtions g 1 (x), the ontribution of quarks to the proton spin is well known. However, knowledge on polarized gluons in the proton is still poor. o understand the origin of the nuleon spin, it is very important to know how gluons polarize in the nuleon. So far, several interesting proesses have been proposed for extrating G. Here we also propose a different proess to obtain more detailed information on polarized gluons, expeting the forthoming RHIC experiment. he proesses whih we propose here are the polarized harmed hadron prodution, i.e. p~p! ~ Λ + X and p~p! ~ D Λ X,in the polarized proton unpolarized proton ollision, 1 whih will be observed at the RHIC experiment. We study whih observables are useful for extrating information about polarized gluons in the proton and also disuss its sensitivity. 1 hough we have alulated even for D Λ prodution, we fous only on the Λ + beause the main point of the result remain unhanged. prodution in this report,
Λ + C BARYON PRODUCION IN PROON PROON COLLISION In the proess on whih we fous here, the Λ + baryon is expeted to have some advantageous properties for probing behavior of polarized gluons in the proton. hose properties are as follows; 1. A harm quark whih is one of onstituents of the Λ + baryon is dominantly produed via gluon-gluon fusion in pp reation, beause harm quarks are tiny ontents in the proton. hus, the ross setion of this proess is diretly proportional to the gluon distribution in the proton. 2. Sine the Λ + baryon is omposed of a harm quark and antisymmetrially ombined light up and down quarks, the spin of Λ + baryon is expeted to be almost equal to the spin of its onstituent harm quark. 3. Sine a harm quark is heavy, it must be very rare for the harm quark to hange its spin arrangement during its fragmentation into a Λ + baryon. In other words, the spin diretion of the harm quark produed in the subproess is expeted to be kept in the Λ + baryon produed in the final state. After all, the spin of the Λ + is in strong orrelation to the polarization of gluons in the proton. herefore, by observing the spin orrelation between the polarized proton in the initial state and the polarized Λ + in the final state, we an get, rather learly, information on the polarized gluon in the proton. SPIN CORRELAION ASYMMERY AND IS SAISICAL SENSIIVIY o study the polarized gluon distribution in the proton, we introdued the spin orrelation asymmetry of the target polarized-proton and produed Λ + baryon [2]; = dσ ++ dσ + + dσ dσ + dσ ++ + dσ + + dσ + dσ + d σ =dx dσ =dx ; (X = p or η); (1) 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. and η, whih are represented by X in Eq.(1), are transverse momentum and pseudo-rapidity of produed Λ +, respetively. Aording to the quark-parton model, d σ =dx an be expressed as d σ dx =Z Y max Y min Z 1 x min a Z 1 x min b G pa!g a (x a ;Q 2 ) G ~pb!~g b (x b ;Q 2 ) D ~! ~ Λ + d ˆσ Jdx a dx dˆt b dy; (z) X ;Y = η or (X 6= Y) ; (2)
with 2sβ p 2 J q oshη zŝ m 2 + p 2 ; β osh2 η s 1 4m2 p s where G pa!g a (x a ;Q 2 ), G ~pb!~g (x b b ;Q 2 ) and D ~! (z) ~ Λ + represent the unpolarized gluon distribution funtion, the polarized gluon distribution funtion and the spindependent fragmentation funtion of the outgoing harm quark deaying into a polarized ~ Λ +, respetively. d ˆσ =dˆt is the spin-dependent differential ross setion of the subproess and J is the Jaobian whih transforms the variables z and ˆt into and η. In the expression of Eq.(2), and η are desribed as X or Y. Statistial sensitivities of for the and η distribution are estimated by using the following formula; δ ' 1 1 P ε Lσ : (3) q bλ + o numerially estimate the value of δ, here we use following parameters: operating time; -day, the beam polarization; P =7%, a luminosity; L = 8 1 31 (2 1 32 )m 2 se 1 for p s = 2 (5) GeV, the trigger effiieny; ε = 1% for deteting produed Λ + events and a branhing ratio; b Λ + Br(Λ +! pk π + ) ' 5% [3]. he purely harged deay mode is needed to measure the polarization of produed Λ +. σ denotes the unpolarized ross setion integrated over suitable or η region. NUMERICAL CALCULAIONS o arry out the numerial alulation of, we used, as input parameters, m = 1:2 GeV, m p = :938 GeV and m Λ + = 2:28 GeV[3]. We limited the integration region of η and of produed Λ + as 1:3» η» 1:3 and 3 GeV»» 15(4) GeV, respetively, for p s = 2(5) GeV. he range of η and the lower limit of were seleted in order to get rid of the ontribution from the diffrative Λ + prodution. As for the upper limit of, we took it as desribed above, for simpliity, though the kinematial maximum of of produed Λ + is slightly larger than 15 GeV and 4 Gev for p s =2 GeV and 5 GeV, respetively. In addition, we took the [4] and GRSV1 [5] parameterization models for the polarized gluon distribution funtion and the GRV98 [6] model for the unpolarized one. hough both of and GRSV1 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 semiinlusive, the fragmentation funtion of a harm quark to Λ + is neessary to arry out numerial alulations. For the unpolarized fragmentation funtion, we used Peterson fragmentation funtion, D!Λ + (z) [3, 7]. However, sine we have no data, at present, about polarized fragmentation funtions for the polarized Λ + prodution, we took the
-.5 -.1 -.15 -.2 -.25 GRSV1-1.3 η 1.3 -.3 3 4 6 8 1 12 14 15 [GeV].2.1 -.1 GRSV1 3GeV 15GeV -.2-1.3-1. -.5.5 1. 1.3 η FIGURE 1. as a funtion of (left panel) and η (right panel) at p s =2 GeV following ansatz for the polarized fragmentation funtion D ~! ~ Λ + (x), D ~! ~ Λ + (z)=c!λ + D!Λ + ; (4) where C!Λ + is a sale-independent spin transfer oeffiient. In this analysis, we studied two ases: (A) C!Λ + = 1 (non-relativisti quark model) and (B) C!Λ + = z (Jet fragmentation model [8]). As we disussed before, if the spin of Λ + is same as the spin of harm quark produed in subproess, the model (A) might be a reasonable senario. Numerial results of are shown in Fig. 1 and Fig. 2. In those figures, statistial sensitivities, δ, are also attahed to the solid line of whih is alulated for the ase of the GRSV1 parametrization model of polarized gluon and the non-relativisti fragmentation model. 2 From these results, we see that the η distributions of are more effetive observables than the distributions at p s =2 GeV and 5 GeV. As shown in the right panel of Fig. 2 given at p s =5 GeV, we ould distinguish the parametrization models of polarized gluon as well as the models of the spin-dependent fragmentation funtion though the magnitude of is rather small. At p s =2 GeV, the magnitude of for η distribution beomes larger, though statistial sensitivities are not so small. If the integrated luminosity at p s =2 GeV ould be large and the detetion effiieny, ε, is improved, this observable ould be promising to distinguish not only the models of G(x) but also the models of D(z). For the distribution of, δ beome rapidly larger with inreasing and we annot say anything from those region. However, if we onfine the kinematial region in rather small range like = 3 ο5(1) GeV at p s = 2(5) GeV, it might be still effetive. 2 Note that as shown from Eq.(4), δ does not depend on both of the model of polarized gluons and the model of fragmentation funtions.
-.1 -.2 -.3 -.4 GRSV1-1.3 η 1.3.2 -.2 -.4 3GeV 4GeV GRSV1 -.5 3 5 1 15 2 25 3 35 4 [GeV] -.6-1.3-1. -.5.5 1. 1.3 η FIGURE 2. he same as in Fig. 1, but for p s =5 GeV CONCLUDING REMARK o extrat information on the polarized gluon distribution in the proton, the harmed hadron prodution proesses at RHIC experiments have been proposed. (Atually, only Λ + proess was disussed in this report.) he spin orrelation asymmetry between the initial proton and the produed Λ + was alulated for p and η distributions with statistial sensitivities whih were estimated using RHIC parameters. We found that is rather sensitive to the model of G(x) and D(z). he η distribution of ould be promising for distinguishing the parametrization model of polarized gluons as well as the model of spin-dependent fragmentation of a harm quark into Λ +. ACKNOWLEDGMENS One of the authors, (K.O), would like to thank the organizers and fellowship ommittee of SPIN22 for giving a hane to present this ontribution at the symposium. REFERENCES 1. For a review see: H. Y. Cheng, Int. J. Mod. Phys. A11, 519, (1996); B. Lampe and E. Reya, Phys. Rep. 332, 1,(2); H. Y. Cheng, Chin. J. Phys. 38, 753, (2) [hep-ph/2157]; B. W. Filippone and X. Ji, hep-ph/11224. 2. K. Ohkuma, K. Sudoh and. Morii, Phys. Lett. B491,117, (2) [Erratum-ibid. B543, 323, (22)]; K. Ohkuma,. Morii and S. Oyama, hep-ph/21144. 3. K. Hagiwara et al, Phys. Rev. D66, 11,(22). 4. Y. Goto et al. [Asymmetry Analysis Collaboration], Phys. Rev. D 62, 3417, (21). 5. M Glük, E. Reya, M. Stratmann and W. Vogelsang, Phys. Rev. D 63, 945, (21). 6. M. Glük, E. Reya and A. Vogt, Eur. Phys. J. C 5, 461, (1998) 7. C. Peterson, D. Shlatter, I. Shmitt and P. M. Zerwas, Phys. Rev. D 27, 15, (1983). 8. A. Bartl, H. Fraas and W. Majerotto, Z. Phys. C 6, 335, (198).