Aug Hadron Physics in China and opportunities, Lanzhou, China 1 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

Aug 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

Aug 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

Aug 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.

Aug 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

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

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

Aug 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

Aug 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)

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

Aug Hadron Physics in China and opportunities, Lanzhou, China 12 2), Target mass Corrections Moderate momentum transfer region TMCs Resonance language Scaling range (large Q 0 ^2) Same definite Q^2 Simultaneously explained by the two Languages GRSV: Glueck, Reya, Stratmann & Vogelsang AAC : Asymmetry analysis collaboration LSS ： Leader ， Sidorov & Stamenov

Aug 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)

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

Aug Hadron Physics in China and opportunities, Lanzhou, China 16 The target mass corrections to SSF by Piccione & Ridolfi (twist-2) Results

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

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

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

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

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

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

Aug Hadron Physics in China and opportunities, Lanzhou, China 23 TMCs Target mass corrections is of 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).

Aug 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

Aug Hadron Physics in China and opportunities, Lanzhou, China 25 TMCs to g 2 Wandzura-Wilczek relation WW relation for twist-2 With twist-3 High Twist effect

Aug Hadron Physics in China and opportunities, Lanzhou, China 26 E155(2003,1999) g 2 and A 2 Experimental data

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

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

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

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

Aug 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

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

Aug 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

Aug 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

Aug 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 the appearance 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 Melnitchouk proposed a new implementation of the TMCs which has a correct kinematics threshold behavior at finite Q^2 in the limit of x →1

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

Aug 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

Aug 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

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

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

Aug 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

Aug 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.

Aug 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)

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Aug 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)

Aug 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)

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

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