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HKNS fragmentation functions and proposal for exotic-hadron search

HKNS fragmentation functions and proposal for exotic-hadron search. Shunzo Kumano High Energy Accelerator Research Organization (KEK) Graduate University for Advanced Studies (GUAS). shunzo.kumano@kek.jp http://research.kek.jp/people/kumanos/.

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HKNS fragmentation functions and proposal for exotic-hadron search

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  1. HKNS fragmentation functions and proposal for exotic-hadron search Shunzo Kumano High Energy Accelerator Research Organization (KEK) Graduate University for Advanced Studies (GUAS) shunzo.kumano@kek.jp http://research.kek.jp/people/kumanos/ with M. Hirai (Juntendo U), T.-H. Nagai (GUAS), M. Oka (Tokyo Tech), K. Sudoh (KEK) Workshop on parton fragmentation processes in the vacuum and in the medium ECT*, Trento, Italy, February 25-29, 2008 February 25, 2008

  2. References on our works Part 1: Determination of fragmentation function and their uncertainties M. Hirai, SK, T.-H. Nagai, K. Sudoh (hep-ph/0702250) Phys. Rev. D75 (2007) 094009, 1-17. Determination of FFs for , K, p in LO and NLO with their uncertainties. Part 2: Proposal for exotic-hadron search by fragmentation functions M. Hirai, S. Kumano, M. Oka, and K. Sudoh (arXiv:0708.1816) Phys. Rev. D77 (2008) 017504, 1-4. Determination of FFs for f0(980) in NLO with their uncertainties  Internal quark structure of f0(980)

  3. Part I HKNS Fragmentation Functions For , K, p/p Ref. M. Hirai, SK, T.-H. Nagai, K. Sudoh Phys. Rev. D75 (2007) 094009, 1-17. Code for calculating the fragmentation functions is available at http://research.kek.jp/people/kumanos/ffs.html .

  4. Contents (1) Introduction to fragmentation functions (FFs)  Definition of FFs  Motivation for determining FFs (2) Determination of FFs  Analysis method  Results  Comparison with other parameterizations (3) Summary for part I

  5. Introduction

  6. e+ , Z q h e– q Fragmentation Function Fragmentation: hadron production from a quark, antiquark, or gluon Fragmentation function is defined by Variable z • Hadron energy / Beam energy • Hadron energy / Primary quark energy A fragmentation process occurs from quarks, antiquarks, and gluons, so that Fh is expressed by their individual contributions: Non-perturbative (determined from experiments) Calculated in perturbative QCD

  7. Momentum (energy) sum rule Favored and disfavored fragmentation functions

  8. Purposes of investigating fragmentation functions Semi-inclusive reactions have been used for investigating ・origin of proton spin Quark, antiquark, and gluon contributions to proton spin (flavor separation, gluon polarization) ・properties of quark-hadron matters Nuclear modification (recombination, energy loss, …)

  9. pT p p Pion production at RHIC: p + p 0 + X S. S. Adler et al. (PHENIX), PRL 91 (2003) 241803  • Consistent with NLO QCD calculation up to 10–8 • Data agree with NLO pQCD + KKP • Large differences between Kretzer and KKP calculations at small pT  Importance of accurate fragmentation functions Blue band indicates the scale uncertainty by taking Q=2pT and pT/2.

  10. Situation of fragmentation functions (before 2007) There are two widely used fragmentation functions by Kretzer and KKP. An updated version of KKP is AKK. See also Bourhis-Fontannaz-Guillet-Werlen (2001) for FFs without hadron separation. (Kretzer) S. Kretzer, PRD 62 (2000) 054001 (KKP) B. A. Kniehl, G. Kramer, B. Pötter, NPB 582 (2000) 514 (AKK) S. Albino, B.A. Kniehl, G. Kramer, NPB 725 (2005) 181 The functions of Kretzer and KKP (AKK) are very different.

  11. Status of determining fragmentation functions (before 2007) Parton Distribution Functions (PDFs), Fragmentation Functions (FFs) Uncertainty ranges of determined fragmentation functions were not estimated, although there are such studies in nucleonic and nuclear PDFs. The large differences indicate that the determined FFs have much ambiguities.

  12. Determination of Fragmentation Functions

  13. New aspects in our analysis (compared with Kretzer, KKP, AKK) • Determination of fragmentation functions (FFs) and their uncertainties in LO and NLO. • Discuss NLO improvement in comparison with LO by considering the uncertainties. (Namely, roles of NLO terms in the determination of FFs) • Comparison with other parametrizations • Avoid assumptions on parameters as much as we can, Avoid contradiction to the momentum sum rule • SLD (2004) data are included.

  14. Comparison with other NLO analyses in  comments on DSS later

  15. Initial functions for pion Constraint: 2nd moment should be finite and less than 1

  16. Experimental data for pion Total number of data：264

  17. Analysis Results for the pion Uncertainty estimation: Hessian method

  18. Error estimation Hessian method 2() is expanded around its minimum  0 ( =parameter) where the Hessian matrix is defined by In the2 analysis,1 standard error is The error of a distribution F(x) is given by

  19. Comparison with pion data Our fit is successful to reproduce the pion data. The DELPHI data deviate from our fit at large z. Our NLO fit with uncertainties Rational difference between data and theory

  20. Comparison with pion data: (data-theory)/theory

  21. Determined fragmentation functions for pion • Gluon and light-quark fragmentation functions have large uncertainties. • • Uncertainty bands • become smaller in NLO • in comparison with LO. • The data are sensitive to NLO effects. • The NLO improvement is clear especially in gluon and disfavored functions. • Heavy-quark functions are relatively well determined.

  22. Comparison with kaon data

  23. Determined functions for kaon The situation is similar to the pion functions. • Gluon and light-quark fragmentation functions have large uncertainties, which are larger than the pionic ones. • Uncertainty bands become smaller in NLO in comparison with LO. • Heavy-quark functions are relatively well determined.

  24. Comparison with other parametrizations in pion (KKP) Kniehl, Kramer, Pötter (AKK) Albino, Kniehl, Kramer (HKNS) Hirai, Kumano, Nagai, Sudoh • • Gluon and light-quark disfavored • fragmentation functions have • large differences, but they are • within the uncertainty bands. • The functions of KKP, Kretzer, AKK, and HKNS are consistent with each other. All the parametrizations agree in charm and bottom functions.  DSS (next page)

  25. D. De Florian, R. Sassot, M. Stratmann, Phys. Rev. D 75 (2007) 114010; 76 (2007) 074033. Comparison with DSS in pion DSS functions generally agree well with HKNS in the pion.

  26. Comparison with other parametrizations in kaon and proton kaon proton

  27. Comparison with DSS in kaon DSS functions differ from HKNS in light-quark and gluon functions of the kaon; however, they are within the uncertainties.

  28. Comments on “low-energy” experiments, Belle & BaBar • Gluon fragmentation function is very important for hadron production at small pT at RHIC (heavy ion, spin) and LHC, • (see the next transparency) • and it is “not determined” as shown in this analysis. • Need to determine it accurately. • Gluon function is a NLO effect with the coefficient function and in Q2 evolution. We have precise data such as the SLD ones at Q=Mz, so that accurate small-Q2 data are needed for probing the Q2 evolution, namely the gluon fragmentation functions. (Belle, BaBar ?)

  29. Pion production at RHIC: Subprocesses (from Torii’s talk at Pacific-Spin05) Gluon polarization g at small pT  Gluon fragmentation function plays a major role

  30. Summary on Part I Determination of the optimum fragmentation functions for , K, p in LO and NLO by a global analysis of e++e– h+X data. • This is the first time that uncertainties of the fragmentation functions are estimated. • Gluon and disfavored light-quark functions have large uncertainties.  The uncertainties could be important for discussing physics in  Need accurate data at low energies (Belle and BaBar). •For the pion and kaon, the uncertainties are reduced in NLO in comparison with LO. For the proton, such improvement is not obvious. • Heavy-quark functions are well determined. • Code for calculating the fragmentation functions is available at http://research.kek.jp/people/kumanos/ffs.html .

  31. Part II Fragmentation Functions For Exotic-Hadron Search: f0(980) as an example Ref. M. Hirai, S. Kumano, M. Oka, and K. Sudoh Phys. Rev. D77 (2008) 017504, 1-4.

  32. Contents (1) Introduction to exotic hadrons  Recent discoveries  Exotic hadrons at M~1 GeV, especially f0(980)  FFs in heavy-ion collisions (2) Criteria for determining quark configurations by fragmentation functions  Functional forms, Second moments (3) Analysis of e++e– f0 +X data for determining fragmentation functions for f0(980)  Analysis method, Results, Discussions (4) Summary for part II

  33. Introduction

  34. qq Meson q3 Baryon q2q2 Tetraquark q4q Pentaquark q6 Dibaryon … q10q e.g. Strange tribaryon … gg Glueball … Recent progress in exotic hadrons (Japanese ?) Exotics • Q+(1540)?: LEPS Pentaquark? • S0(3115), S+(3140): KEK-PS • Strange tribaryons? X (3872), Y(3940): Belle Tetraquark, DD molecule • DsJ(2317), DsJ(2460): BaBar, CLEO, Belle Tetraquark, DK molecule • Z(4430): Belle Tetraquark, …

  35. 1.0 GeV 0.5 GeV Scalar mesons JP=0+ at M~1 GeV Naïve quark-model Strong-decay issue: The experimental widths (f0 , a0) = 40 – 100 MeV are too small to be predicted by a typical quark model. R. Kokoski and N. Isgur, Phys. Rev. D35 (1987) 907; SK and V. R. Pandharipande, Phys. Rev. D38 (1988) 146.

  36. Electric dipole:er (distance!) KK moleculeor qqqq:  = large Experimental results of VEPP-2M and DANE suggest that f0 is a tetraquark state (or a KK molecule?). qq model: = small Determination of f0(980) structureby electromagnetic decays F. E. Close, N. Isgur, and SK, Nucl. Phys. B389 (1993) 513. Radiative decay:S S=f0(980), a0(980) Jp=1–  0+ E1 transition For recent discussions, N. N. Achasov and A. V. Kiselev, PRD 73 (2006) 054029; D74 (2006) 059902(E); D76 (2007) 077501; Y. S. Kalashnikova et al., Eur. Phys. J. A24 (2005) 437.

  37. f0(980) in heavy-ion collisions L. Maiani, A. D. Polosa, V. Riquer, and C.A. Salgado, Phys. Lett. B645 (2007) 138. (See also C. Nonaka et al., Phys. Rev. C69 (2004) 031902. ) Recombination / Fragmentation

  38. x 1/3 1 gluon x 1/3 1 Parton distribution functions (PDFs) Momentum distribution is spread. Sea quark Valence- and sea-quark distributionsare different.  Internal quark configurationHowever, PDFs of exotic hadrons could not bemeasured because lifetimes are too short.  Possible in fragmentation functions ?! Valence quark

  39. Criteria for determining internal structure of f0(980) by fragmentation functions

  40. Criteria for determining f0 structure by its fragmentation functions Discuss 2nd moments and functional forms (peak positions)of the fragmentation functions for f0 by assumingthe above configurations, (1), (2), (3), and (4).

  41. ss picture for f0(980) + one O (g3) term of gluon radiation from the antiquark O (g2) O (g3) + one O (g3) term of gluon radiation from the antiquark O (g3) + one O (g2) term of gluon radiation from the quark O (g2) O (g3) + two O (g3) terms of gluon radiation from the quark or antiquark u (disfavored) s (favored) g

  42. nnss picture for f0(980) KK picture for f0(980) O (g4) O (g4) O (g4) + six O (g4) terms of gluon radiation from other quarks O (g4) O (g4) u, s (favored) g

  43. nn picture for f0(980) O (g3) O (g3) O (g2) O (g3) + four O (g3) terms of gluon radiation from other quarks O (g3) O (g3) O (g2) + Two O (g2) terms of gluon radiation from other quarks + two O (g3) terms of gluon radiation from other quarks O (g2) u (favored) s (disfavored) g

  44. O (g2) O (g1) gg picture for f0(980) u, s (disfavored) g (favored)

  45. Judgment

  46. Global analysis for fragmentation functions of f0(980)

  47. e+ , Z q h e– q Fragmentation functions for f0(980)

  48. Experimental data for f0 One could foresee the difficulty in getting reliable FFs for f0 at this stage. Total number of data：only 23 f0 pion Total number of data：264 

  49. Analysis results: Comparison with data Rational difference between data and theory • Uncertainties of determined FFs are very large! • Only a few data at small Q2  difficult to determine the FFs (f0) especially at small Q2  difficult to find scaling violation = gluon FF cannot be fixed = quark FFs should have extra uncertainties due to error correlation with the gluon HRS, PRL 57, 1990 (1986) OPAL, EPJ C4,19 (1998) DELPHI, PL 449B, 364 (1999), ZP C65, 587 (1995)

  50. Results on the fragmentation functions

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