Fragmentation Function studied with e+-e- data and its impact on the nucleon spin structure analysis

Transcription

1 Fragmentation Function studied with e+-e- data and its impact on the nucleon spin structure analysis Yoshiyuki Miyachi, Tokyo Tech

2 Contents Fragmentation and parton distribution function Resent fragmentation function analysis Impact on the proton spin structure analysis Strange quark component and kaon fragmentation Quark transversity and Collins fragmentation function Fragmentation function analysis in Belle Summary

3 Parton distribution and Fragmentation functions q(x) Dqh(z) Probability of finding a parton with momentum fraction x of a parent proton q Probability of fragmenting to a hadron h with energy fraction z of a parent parton q Deep inelastic scattering (DIS) Single inclusive anihiration (SIA) 1 q 0 dx x q x =1 1 h 0 dz z D q z =1 h

4 Semi-inclusive DIS 3 l N l ' h X Structure Function h d h e q x, Q D z, Q q q i dx dz dq d 3 h h e q x, Q D z, Q q i q dx dz dq F i x,q, g i x, Q Parton Distribution q x,q, q x,q z= P ph E h = P q FF and PDF are equally important to analyze high energy process with hadron production Flavor Tagging: P= M,0 Fragmentation Dhq z, Q p h= E h, p h Hadron carries information on quark flavor through fragmentation function

5 Fragmentation function parametrization Parametrize functional form: D z N i z 1 z [ 1 1 z Constraint: ] N: nd moment of D(z) no sensitivity on quark and anti-quark separation weak quark flavor sensitivity ( especially for light quarsk: u, d, s ) Favored dis-favored fragmentation D disfav = 1 z D fav Fit the available data from the experiments: Determine the parameters ( and possibly their uncertainty ) - S. Kretzer - B.A. Kniehl, G. Kramer and B. Pötter - M. Hirai, S. Kumano, T.-H. Nagai, K. Sudoh. - D. de Florian, R. Sassot, M. Stratmann Phys. Rev. D 6, (000) Nucl. Phys. B58, 514 (000) Phys. Rev. D75, (007) Phys. Rev. D75, (007) Phys. Rev. Lett. 76, (007) Including Hadron multiplicity in SIDIS and hadron cross-section in p-p (allow to loose some constraint)

6 Available data for FF analysis DSS, Phys. Rev. D75, (007), pion 9GeV Phys. Rev. Lett. 76, (007) kaon 9GeV

7 Pion Fragmentation Analysis DSS, Phys. Rev. D75, (007) TPC (9GeV) SLD (Mz) ALEPH (Mz) HERMES DELPHI (Mz) OPAL (Mz) HERMES + charged and neutral pions in pp

8 Data used for kaon fragmentation DSS, Phys. Rev. D75, (007) TPC (9GeV) SLD (Mz) ALEPH (Mz) HERMES DELPHI (Mz) HERMES + charged kaon produciton in pp scattering

9 Extracted kaon fragmentation function DSS, Phys. Rev. D75, (007) DSS: e+e-, SIDIS, pp Kretzer: e+e- AKK: e+e-

10 Impact on the nucleon spin analysis - strange quark spin component Δs

11 Helicity distribution function Δq q x q x 1 F 1 x = q e q x q 1 g 1 x = q eq q x q x =q x q x q x =q x q x 1 Spin sum rule: q 0 q x = 1

12 Proton spin problem Nucl. Phys. B38 (1989) 1, Phys. Lett. B06 (1988) 364 Polarized DIS: ' X N Structure Function F i x,q, g i x,q µ Parton Distribution q x, Q, q x,q dx g x = 9 a0 1 a3 36 a8 =0.16±0.01± P= M,0 X p 1 SU(3) flavor symmetry a 3=1.6, a 8=0.58 q q~0.1 s~ 0.19 G 0

13 Updated results on g1 and Δs Phys. Rev. D 75 (007) Procedure and assumption: Q evolution to 5GeV with NLO pqcd High x contribution = 0 Saturation in the lower x region SU(3) flavor symmetry: g 1 x,5 GeV dx= d ±0.001±0.018±0.0008±0.006 s 5 GeV = 0.085±0.013±0.008±0.009 Phys. Lett. B 647 (007) 8: Assuming SU(3) flavor symmetry s = 0.08±0.01±0.0 No Fragmentation function involved.

14 Semi-inclusive DIS 3 l N l ' h X Structure Function F i x,q, g i x, Q Parton Distribution q x,q, q x,q h d h e q x, Q D z, Q i q q dx dz dq d 3 h h e q x, Q D z, Q q i q dx dz dq P ph E h z= P q FF and PDF are equally important to analyze high energy process with hadron production Flavor Tagging: P= M,0 Fragmentation Dhq z, Q p h= E h, p h = Hadron carries information on quark flavor through fragmentation function

15 Helicity distribution with SIDIS data - LO extraction e' h X e N s x =0 assumed Phys. Rev D 71 (005) assuming Δq(x)=0 0.6 q= 0.03 dx q x Q =.5 GeV u=0.601±0.039±0.049 d =.6±0.039±0.050 u =.00±0.036±0.03 d =.054±0.033±0.011 s=0.08±0.033± without SU(3) symmetry assumption - only partial moments are available - LO extraction - String model based MC for FF (<Q> ~.5GeV)

16 Helicity distribution from QCD fit D. de Florian, R. Sassot, M. Stratmann, and W. Vogelsang, Phys. Rev. Lett. 101, (008) Data FF DSSV DIS, SIDIS DSS pp DNS DIS SIDIS Kretzer GRSV DIS

17 Belle and Fragmentation function Fragmentation function at Belle (on going) sqrt(s) ~ 10.5 GeV Cover the lowest scale Gluon FF from scale violation Similar scale to pol. DIS Light quarks: u, d, s pion, kaon

18 Fragmentation function analysis in Belle Collins Fragmentation Function Belle collaboration, Phys. Rev. D78 (008) Transverse momentum dependence: kt Vector meson Di-hadron fragmentation function Unpolarized Fragmentation function - published - on-going - plan/idea Charged pion, charged kaon, proton sqrt(s) = 10.8 GeV: cover lower Q ( for gluon ), similar Q with SIDIS and p-p Other mesons: pi0, eta, f0, phi, Ks,... Barions: Lambda,...

19 Contents Fragmentation Function has been analyzed with e+e- data, SIDIS, and pp data together Fragmentation function is important for analysis of high energy scattering with hadron production With DSS kaon FF, Δs > 0 was obtained in the middle x Neutral pion FF is also important for ΔG. (especially gluon part) Fragmentation function analysis at Belle Collins fragmentation ( published ) Normal fragmentation function analysis (on-going) sqrt(s) = 10.5 GeV, pion, kaon

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21 Quark Transversity and Collins Fragmentation

22 Transverse momentum dependent parton distribution function Unpolarized Long. polarized Trans. polarized Nucleon Unpol. f 1 =q Number density Nucleon Parton These survive after integration over k. Sivers naïve T-odd Helicity Chira-odd Trans. polarized Parton Long. pol. g 1L = q h 1 f 1T requires chiral-odd partner Boer-Mulders h 1L g 1T h 1T = q Transversity h 1T naïve T-odd

23 Collins asymmetry in SIDIS Unpol Target d UU 1 q D 1 cos Long. Pol. Target d UL sin SL Trans. Pol. Target ST d UT sin S f D 1T 1 sin S h H sin 3 S 1 1T Siverse Collins

24 Collins mechanism Quark Transversity h1 Collins Fragmentation H1 L=1 + 1 H 0 sin S 0

25 Collins Asymmetry at HERMES HERMES Collaboration, arxiv:0706.4

26 Collins asymmetry at Belle Belle collaboration, Phys. Rev. D78 (008) 03011

27 Extracted transversity and Collins FF Alexei SPIN008 Quark tarnsversity Collins fragmentation function

28 END

29 HERMES Multiplicity: pion DSS, Phys. Rev. D75, (007)

30 Charged pion production in p-p DSS, Phys. Rev. D75, (007)

31 Neutral pion production in p-p DSS, Phys. Rev. D75, (007)

32 Extracted pion fragmentation function DSS, Phys. Rev. D75, (007)

33 Kaon production in pp scattering DSS, Phys. Rev. D75, (007)

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35 Helicity distribution function LO extraction HERMES Collaboration, Phys. Lett. B666 (008)

36 FF choice in Siverse function analysis

37 Data used in helicity distribution D. de Florian, R. Sassot, M. Stratmann, and W. Vogelsang, Phys. Rev. Lett. 101, (008)

38 Double spin asymmetry in p-p D. de Florian, R. Sassot, M. Stratmann, and W. Vogelsang, Phys. Rev. Lett. 101, (008)

39 Gluon polarization in polarized protonproton scattering DSSV results...

40 Quark flavor sensitivity Belle collaboration, Phys. Rev. D78 (008) u,d,s-pair c-pair B-pair

41 SU(3) violation and impact on s J. Lichtenstadt and H. J. Lipkin, Phys. Lett. B353 (1995) 119 E. Leader et. al., Phys. Lett. B488 (000) 83 SU(3): symmetry violation χqm calculation: (X. Song et. al, Phys. Rev. D55 (1997) 64-69) SU(3) symmetry: s = -0.1 SU(3) breaking: s = -0.05

42 Extracted Transversity and models Alexei SPIN008