Spin Transfer Studies for Λ c+ c+ Production at RHIC

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1 Spin Transfer Studies for Λ c+ c+ Production at RHIC Kazutaka SUDOH (KEK) SPIN25, TITech 8 July 25 In collaboration with V. L. Rykov (RIKEN/RBRC) I. Introduction & Motivation II. III. IV. Polarized Λ c+ Production at RHIC p + p Λ + X + c Numerical Results Conclusion

2 I. Introduction Polarized Gluon Distribution: g(x) A key for understanding the nucleon s spin Theoretical and experimental uncertainties are large. Prompt photon, Heavy flavor production observing cross section asymmetry A LL Polarized Fragmentation function: D h (z) Our knowledge are very poor. Spin transfer : A correlation between the spins of initial and final particles Connected to above objects for hadron production in polarized proton collisions. Page-2

3 Spin Transfer Studies Experiments Studied only for Λ hyperon Significantly non-zero spin transfers have been observed. Theory E74 Collab., PRL 78, 43 (1997). E665 Collab., EPJ C17, 263 (2). HERMES Collab., PRD 64, 1125, (25). Λ D. de Florian et al., PRL81, 53 (1998); PLB439, 176 (1998). Many by J. Soffer, W. Vogelsang, Bo-Q. Ma, M. Strarmann. Σ + Xu Qing-Hua and Liang Zuo-Tang, PRD7, 3415 (24). Λ c + K. Ohkuma, K.S., T. Morii, PLB491, 117 (2). We extend this analysis to helicity-to-general spin correlations. Page-3

4 Why Λ c+? Λ c+ baryon consists of heavy c quark and antisymmetrically combined light u and d quarks. Polarization of Λ c+ baryon ~ Polarization of c quark u c d c quark is not main constituent of proton c quark is produced in hard processes mainly through gluon-gluon fusion There is a correlation between the gluon polarization and the produced c quark polarization Measurement of Λ c+ polarization gives us information about g(x) and/or D(z) of Λ c+. Page-4

5 What can be measured at RHIC ξ 3 ξ 1 ξ2 Unpolarized cross-section dσ dω ( p, p ; p, p ) ξ 4 Only initial particles polarized dσ dω ( p ) 1, p2, ξ1, ξ2; p3, p4 All particles polarized dσ dω ( p ) 1, p2, ξ1, ξ2; p3, p4, ξ3, ξ4 Spin Asymmetries (examples): Cross-section asymmetry: σξ ( 1 ξ2 = 1) σξ ( 1 ξ2 = 1) A = σξ ( ξ = 1) + σξ ( ξ = 1) D Spin transfer: ( 1 3 = 1) ( 1 3 = 1) ( = 1) + ( = 1) σξ ξ σξ ξ = σξ ξ σξ ξ Page-5

6 Notation X S L Spin transfer from initial L (Π=L, S, Z, X) N L ϕ θ N σ σ + σ σ σ σ σ σ ; + ; ; + ; LΠ LΠ LΠ LΠ ; + ; ; + ; LΠ + LΠ + LΠ + LΠ = D LΠ Y Z D dˆ f ( x f ( x ) D ( z) ab cx ) L L a a b b a, bc, = pqcd framework is available in high energy Π Π c gluon fusion gg qq Page-6

7 Spin Transfer D LΠ Spin transfer from initial L (Π = L, S, Z, X): D σ σ + σ σ + ; + + ; ; ; + LΠ LΠ LΠ LΠ LΠ + ; + + ; ; ; + σl Π + σlπ + σl Π + σl Π In addition, following observables are introduced: D D σ σ + σ σ ; + ; ; ; + LΠ LΠ LΠ LΠ LΠ ; + ; ; ; + σl Π + σl Π + σl Π + σl Π σ σ + σ σ + ; + + ; + ; + ; + + LΠ LΠ LΠ LΠ LΠ + ; + + ; + ; + ; + σl Π + σl Π + σl Π + σl Π D LΠ is a weighted average of these parameters + + DLΠσ + DLΠσ 1 + DL Π = = DL Π(1 + ALL) + DLΠ(1 ALL) + σ + σ where ALL ( σ σ )/( σ + σ ) Page-7

8 Relation with A LL Relation between A LL and spin transfer D LΠ A LL + + σ 2D L Π D L Π D L Π σ DLΠ DL Π σ = σ Free from systematic errors due to relative luminosity monitoring Statistical Error δ A LL α PD 2 6 LΠ N α : hyperon decay asymmetry parameter P : beam polarization N : combined statistics in 3 measurements This error is larger than that of direct A LL measurement. If the systematic due to relative luminosity monitoring rather than statistics is a key issue, these measurements could be an option. Page-8

9 LO spin transfer in p +p Λ c+ +X at s=2 GeV AAC ; C=1 AAC ; C=z GRSV ; C=1 GRSV ; C=z Polarized PDFs: G(x, Q 2 ) AAC: Y. Goto, et al., PR D62 (2) 3417 GRSV: M. Glück, et al., PR. D63 (21) 945 Polarized fragmentation function: D = C(z) D(z) D(z) unpolarized fragmentation func. o Only the dominant gg cc o 2 < P T < 5 GeV/c o L = 32 pb -1 o Λ c+ Λ π + pπ - π + Br =.9%, α = -.98 ε = 1% Page-9

10 Model Dependence at s=2 GeV AAC ; C=1 GRSV ; C=1 BB ; C= D LZ D LX D LZ D LX AAC ; C=1 GRSV ; C=1 BB ; C= D LZ D LX g(x) AAC: Y. Goto, et al., Phys. Rev. D62, 3417 (2). GRSV: M. Gl uck, et al., Phys. Rev. D63, 945 (21). BB: J. Bl umlein, et al., Nucl. Phys. B636, 225 (22). Page-1

11 LO spin transfer in p +p Λ c+ +X at s=5 GeV 2 GeV p T 5 GeV Behavior is similar to cases at s=2 GeV AAC ; C=1 AAC ; C=z GRSV ; C=1 GRSV ; C=z Page-11

12 Model Dependence at s=5 GeV 2 GeV p T 1 GeV 2 GeV p T 1 GeV AAC ; C=1 GRSV ; C=1 BB ; C= D LZ D LX D LZ D LX AAC ; C=1 GRSV ; C=1 BB ; C= D LZ D LX g(x) AAC: Y. Goto, et al., Phys. Rev. D62, 3417 (2). GRSV: M. Gl uck, et al., Phys. Rev. D63, 945 (21). BB: J. Bl umlein, et al., Nucl. Phys. B636, 225 (22). Page-12

13 VII. Summary Spin transfers for pp Λ c+ + X at RHIC are studied. Not only helicity correlation, but also, D LZ, D LX. Relation with asymmetry A LL is derived. Significantly non-zero spin transfers are predicted. In the central region at s=2 GeV, the effect is expected ~5-15%, while RHIC statistical errors ~1%. The larger spin transfers, up to 2-5%, are expected at ~2 and beyond. Information about g(x) and/or D(z) can be alternatively extracted. Spin transfers strongly depend on g(x) and D(z). Spin structure of Λ c+ is also interesting. Page-13