Fragmentation Function studied with e+-e- data and its impact on the nucleon spin structure analysis Yoshiyuki Miyachi, Tokyo Tech
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
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
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
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, 054001 (000) Nucl. Phys. B58, 514 (000) Phys. Rev. D75, 094009 (007) Phys. Rev. D75, 114010 (007) Phys. Rev. Lett. 76, 074033 (007) Including Hadron multiplicity in SIDIS and hadron cross-section in p-p (allow to loose some constraint)
Available data for FF analysis DSS, Phys. Rev. D75, 114010 (007), pion 9GeV Phys. Rev. Lett. 76, 074033 (007) kaon 9GeV
Pion Fragmentation Analysis DSS, Phys. Rev. D75, 114010 (007) TPC (9GeV) SLD (Mz) ALEPH (Mz) HERMES DELPHI (Mz) OPAL (Mz) HERMES + charged and neutral pions in pp
Data used for kaon fragmentation DSS, Phys. Rev. D75, 114010 (007) TPC (9GeV) SLD (Mz) ALEPH (Mz) HERMES DELPHI (Mz) HERMES + charged kaon produciton in pp scattering
Extracted kaon fragmentation function DSS, Phys. Rev. D75, 114010 (007) DSS: e+e-, SIDIS, pp Kretzer: e+e- AKK: e+e-
Impact on the nucleon spin analysis - strange quark spin component Δs
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
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 1 1 1 0 dx g x = 9 a0 1 a3 36 a8 =0.16±0.01±0.015 1 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
Updated results on g1 and Δs Phys. Rev. D 75 (007) 01007 Procedure and assumption: Q evolution to 5GeV with NLO pqcd High x contribution = 0 Saturation in the lower x region SU(3) flavor symmetry: 0.9 0.01 g 1 x,5 GeV dx= d 0.0436±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.
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
Helicity distribution with SIDIS data - LO extraction e' h X e N s x =0 assumed Phys. Rev D 71 (005) 01003 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±0.009 - without SU(3) symmetry assumption - only partial moments are available - LO extraction - String model based MC for FF (<Q> ~.5GeV)
Helicity distribution from QCD fit D. de Florian, R. Sassot, M. Stratmann, and W. Vogelsang, Phys. Rev. Lett. 101, 07001 (008) Data FF DSSV DIS, SIDIS DSS pp DNS DIS SIDIS Kretzer GRSV DIS -------
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
Fragmentation function analysis in Belle Collins Fragmentation Function Belle collaboration, Phys. Rev. D78 (008) 03011 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,...
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
Quark Transversity and Collins Fragmentation
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
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
Collins mechanism Quark Transversity h1 Collins Fragmentation H1 L=1 + 1 H 0 sin S 0
Collins Asymmetry at HERMES HERMES Collaboration, arxiv:0706.4
Collins asymmetry at Belle Belle collaboration, Phys. Rev. D78 (008) 03011
Extracted transversity and Collins FF Alexei Prokudin @ SPIN008 Quark tarnsversity Collins fragmentation function
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HERMES Multiplicity: pion DSS, Phys. Rev. D75, 114010 (007)
Charged pion production in p-p DSS, Phys. Rev. D75, 114010 (007)
Neutral pion production in p-p DSS, Phys. Rev. D75, 114010 (007)
Extracted pion fragmentation function DSS, Phys. Rev. D75, 114010 (007)
Kaon production in pp scattering DSS, Phys. Rev. D75, 114010 (007)
Helicity distribution function LO extraction HERMES Collaboration, Phys. Lett. B666 (008) 446-450
FF choice in Siverse function analysis
Data used in helicity distribution D. de Florian, R. Sassot, M. Stratmann, and W. Vogelsang, Phys. Rev. Lett. 101, 07001 (008)
Double spin asymmetry in p-p D. de Florian, R. Sassot, M. Stratmann, and W. Vogelsang, Phys. Rev. Lett. 101, 07001 (008)
Gluon polarization in polarized protonproton scattering DSSV results...
Quark flavor sensitivity Belle collaboration, Phys. Rev. D78 (008) 03011 u,d,s-pair c-pair B-pair
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
Extracted Transversity and models Alexei Prokudin @ SPIN008