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Institute of High Energy Physics (IHEP) Beijing

Polarized nucleon structure functions, target mass corrections and the high twist by Dong Yu-Bing （董宇兵）. Institute of High Energy Physics (IHEP) Beijing. Outline. 1), Polarized nucleon structure functions at some Quark-hadron duality High twist effect

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Institute of High Energy Physics (IHEP) Beijing

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  1. Polarized nucleon structure functions, target masscorrections and the high twistby Dong Yu-Bing （董宇兵） Institute of High Energy Physics (IHEP) Beijing Hadron Physics in China and opportunities, Lanzhou, China

  2. Outline 1),Polarized nucleon structure functions at some Quark-hadron duality High twist effect 2), Target mass corrections to structure functions to high-twist effects: 3), Summary Hadron Physics in China and opportunities, Lanzhou, China

  3. 1，Nucleon structure functions DIS region • DIS provided rich information on quark-gluon structure of the nucleon and the strong interaction(QCD) • High energy:asymptotic freedom perturbative QCD calculation works, QCD well tested parton distributions functions (PDFs) extracted from DIS data Hadron Physics in China and opportunities, Lanzhou, China

  4. Nucleon structure functions In the resonance region: Resonance transitions properties Confinement, Resonance peaks Resonance structures, quark structure Strong interaction: Two end points 1), non-pQCD, Confinements : Resonance bumps 2), pQCD, Asymptotic freedom 3), Connection of pQCD and non-pQCD. Hadron Physics in China and opportunities, Lanzhou, China

  5. Duality(BG) for the structure functions Observable can be explained by two different kinds of Languages (Resonance, Scaling) Bloom-Gilman Duality( ,1970) Resonance region data oscillate around the scaling curve. Smooth scaling curve seen at high Q**2 was an accurate average over the resonance bumps at a low Q**2 Hadron Physics in China and opportunities, Lanzhou, China

  6. Hadron Physics in China and opportunities, Lanzhou, China

  7. Hadron Physics in China and opportunities, Lanzhou, China

  8. Other experiment(II) • Hermes, by Fantoni, Bianchi, Liuti(EJPA05) for g1 Onset ~1.7GeV^2 Hadron Physics in China and opportunities, Lanzhou, China

  9. Interpretation • Close and Isgur (PLB01)evolution from a coherent resonance region to incoherent inelastic scattering region Hadron Physics in China and opportunities, Lanzhou, China

  10. Duality and OPE（operator production expansion) • The resonance strengths average to a global scaling curve resembling the curve of DIS, as the higher-twist effect is not large, if averaged over a large kinematics region.(CN moment) Hadron Physics in China and opportunities, Lanzhou, China

  11. Twist effect pure kinematical origin Of dynamical origin Hadron Physics in China and opportunities, Lanzhou, China

  12. 2), Target mass Corrections • Moderate momentum transfer region • TMCs • Resonance language • Scaling range (large Q0^2) • Same definite Q^2 • Simultaneously explained by the two • Languages GRSV: Glueck, Reya, Stratmann & Vogelsang AAC : Asymmetry analysis collaboration LSS： Leader，Sidorov & Stamenov Hadron Physics in China and opportunities, Lanzhou, China

  13. Target mass corrections(TMCs) • Literature: Georgi and Polizter(PRD76); • Nachtmann (NPB75); Wandzura and Uematsu(NPB77); Matsuda(NPB80), Kawamura(PLB95). • Piccone and Ridolfi(NPB98); • Blumlein & Tkabladze (NPB99), • Sidorov & Stamenov(MPLA06); • Steffens & Melnitchouk(PRC06) Hadron Physics in China and opportunities, Lanzhou, China

  14. Hadron Physics in China and opportunities, Lanzhou, China

  15. The target mass corrections to SSFby Piccione & Ridolfi • Twist-2(Georgi-Politzer (GP) implementation) • The Cornwall-Norton moment(CN) Hadron Physics in China and opportunities, Lanzhou, China

  16. The target mass corrections to SSFby Piccione & Ridolfi (twist-2) • Results Hadron Physics in China and opportunities, Lanzhou, China

  17. TMCs to nucleon SSFs • define Hadron Physics in China and opportunities, Lanzhou, China

  18. TMCs to the Cornwall-Norton moments • CN-moment • Expansion in order Hadron Physics in China and opportunities, Lanzhou, China

  19. TMCs to the Nachtmann moments Hadron Physics in China and opportunities, Lanzhou, China

  20. TMCs to higher-twist (CN) Twist-3, spin-2 Twist-2 Hadron Physics in China and opportunities, Lanzhou, China

  21. TMCs to higher-twist (CN) • Without TMCs Twist-3, spin-2 Twist-2 Hadron Physics in China and opportunities, Lanzhou, China

  22. TMCs to higher-twist (CN) With TMCs (CN moments) Hadron Physics in China and opportunities, Lanzhou, China

  23. TMCs • Target mass corrections isof purely kinematics origin Before one can reliably extract the information of the higher-twist contributions, it is important to remove from the data the corrections arising from purely kinematics effects (TMCs). Hadron Physics in China and opportunities, Lanzhou, China

  24. TMCs to twist-3 • The Nachtmann moments do not contain TMCs 2,spin-n 3,spin-(n-1) • The Nachtmann moment is a right one for d2 Hadron Physics in China and opportunities, Lanzhou, China

  25. TMCs to g2Wandzura-Wilczek relation • WW relation for twist-2 • With twist-3 High Twist effect Hadron Physics in China and opportunities, Lanzhou, China

  26. E155(2003,1999) g2 and A2 • Experimental data Hadron Physics in China and opportunities, Lanzhou, China

  27. TMCs to twist-3 • Consider the Nachtmann moment Hadron Physics in China and opportunities, Lanzhou, China

  28. TMCs to other matrix elements Hadron Physics in China and opportunities, Lanzhou, China

  29. Recent experiment analysis RSS RSS data provide a support • By Slifer(RSS), arXiv:0906.4766, 0812.0031 Hadron Physics in China and opportunities, Lanzhou, China

  30. 3), Summary 1), Structure functions 2), Target mass corrections are important to structure functions at large x, to the higher-twist: d2 3), More precise data are required to get d2 From RSS. ------------------------------- The End---------------------------------- Hadron Physics in China and opportunities, Lanzhou, China

  31. The Nachtmann variable • In general case • When the target mass corrections are considered, one should consider the Nachtmann variable Hadron Physics in China and opportunities, Lanzhou, China

  32. TMCs to SSFs Hadron Physics in China and opportunities, Lanzhou, China

  33. Duality and OPE（operator production expansion) • In QCD framework: •  1/Q expansion (twist expansion) twist is related to (mass dimension – spin) it contains twist-t matrix elements Hadron Physics in China and opportunities, Lanzhou, China

  34. Discussions of x ~ 1 GP implementation for TMCs • X>1(TMCs) SF does not vanishing ≠ Dynamical reasons at x=1 • Threshold problem （ξ-dependent) ξ_0= ξ(x=1)<1, the parton distribution isn’t well defined in the unphysical region between elastic limit ξ_0 and ξ= 1 Hadron Physics in China and opportunities, Lanzhou, China

  35. Discussions of x ~ 1 GP implementation for TMCs Higher-twist operators There is a non-uniformity in the limits as n→∞& ^2 →∞, and theappearance of the higher-twist effects proportional to nM^2/Q^2 for the n-th moment signals the breakdown of the entire approach at low W.Higher-twist is no longer suppressed by 1/Q^2 • Steffens and Melnitchoukproposed a new implementation of the TMCs which has a correct kinematics threshold behavior at finite Q^2 in the limit of x→1 Hadron Physics in China and opportunities, Lanzhou, China

  36. Duality in the elastic local region • Form factors and duality (elastic region) Hadron Physics in China and opportunities, Lanzhou, China

  37. The other higher-twist terms result from the reduced matrix elements. They are of dynamical origin, since they show the correlation among the partons Hadron Physics in China and opportunities, Lanzhou, China

  38. Sum rules and their generalized versions Magnetic moment: GDH Sum Rule Axial charge Bjorken Sum Rule Polarizabilities Hadron Physics in China and opportunities, Lanzhou, China

  39. Hadron Physics in China and opportunities, Lanzhou, China

  40. Hadron Physics in China and opportunities, Lanzhou, China

  41. Duality and OPE（operator production expansion) • In QCD framework: •  1/Q expansion (twist expansion) twist is related to (mass dimension – spin) it contains twist-tau matrix elements Hadron Physics in China and opportunities, Lanzhou, China

  42. Nucleon structure functions Strong interaction: Two end points 1), non-pQCD, Confinements : Resonance bumps 2), pQCD, Asymptotic freedom 3), Connection of pQCD and non-pQCD. Hadron Physics in China and opportunities, Lanzhou, China

  43. Studies of quark-hadron duality • Rujula，Georgi and Politzer (PLB76) OPE • Carlson, Mukhopadhyay(PRD93), Stoler, Sterman resonance transition properties • Simula (Italy group), (parameterizations of SFs) • Melnitchouk (Jefferson Lab., Phys. Report 05) • Isgur,Jechonnek, Melnitchouk and Van Orden (PRD01) confinement plus Dirac equation • Matsui, Sato and Lee(PRC05) (Isobar model) • Paris et al.，(PRC02) • Fiore et al.,(PRD04) (Regge-dual model) Hadron Physics in China and opportunities, Lanzhou, China

  44. Hadron Physics in China and opportunities, Lanzhou, China

  45. High twist from TMCs • 1), twist-2 (sizable) • 2), twist-3 (sizable) • 3), twist-4 (smaller) • 4), To other observables: • Color polarizabilities (smaller) Hadron Physics in China and opportunities, Lanzhou, China

  46. Cornwall-Norton moments contain TMCs (one SF, mix) • Nachtmann Moments contains no TMCs (two SSFs, pure) Hadron Physics in China and opportunities, Lanzhou, China

  47. TMCs to the duality • To study quark-hadron duality and TMCs • Without TMCs Hadron Physics in China and opportunities, Lanzhou, China

  48. Global duality in the resonance region Hadron Physics in China and opportunities, Lanzhou, China

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