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Twist 4 Matrix elements

Twist 4 Matrix elements. Su Houng Lee 1. S. Choi et al, PLB 312 (1993) 351 2. Su Houng Lee, PRD 49 (1994) 2242 3. Su Houng Lee, PRC 57 (1998) 927. Some basics on matrix elements and moments. DIS. e ( E’,k ’). e (E,k). q. X. P. Relation to Polarization Tensors.

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Twist 4 Matrix elements

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  1. Twist 4 Matrix elements Su Houng Lee 1. S. Choi et al, PLB 312 (1993) 351 2. Su Houng Lee, PRD 49 (1994) 2242 3. Su Houng Lee, PRC 57 (1998) 927

  2. Some basics on matrix elements and moments • DIS e (E’,k’) e (E,k) q X P • Relation to Polarization Tensors

  3. Diagrammatic rep of Structure function X P P • Diagrammatic rep of OPE OPE n P P P P

  4. Twist-2 Operators (LO) P P • Twist-4 Operators Politzer (80), Shuryak, Vainshtein (81) , Jaffe, Soldate (81) P P P P

  5. Twist-4 Operators • OPE Politzer (80), Shuryak, Vainshtein (81) , Jaffe, Soldate (81) • Operators • mass Operators Lee (94)

  6. Parameterizing F2 (t=4) • For Cp: BCDMSdata and SLAC data +Virchauz,Milsztajin, PLB274 (92) 221 • We fit to • For Cp-Cn: NMC (combining NMC,SLAC, BCDMSdata) • We fit to

  7. Parameterizing FL (t=4) • Parameterization using transverse basis (Ellis, Furmanski, Petronzio 82) P P • SLAC data analyzed by Sanchex Guillen etal. (91)

  8. Constraints for matrix elements from experiments Note that the matrix elements A’s for the proton and neutron data are independent. data MIT Bag

  9. MIT Bag model calculations (Jaffe-Soldate 81) • Definitions • Calculations • operators • Normalizations by Jaffe (75)

  10. Calculations- cont • calculations involve spin and spatial parts

  11. MIT Bag model vs experimental constraint • F2: Q2=5 GeV2 as = 0.5 Typical numbers • FL: Q2=5 GeV2 as = 0.5 Typical numbers

  12. Need more correlations a) Bag model calculations only measures correlations between valance quarks b) Need much more correlation such as c) Non-trivial test of low energy models of hadrons and QCD

  13. A Parameterization based on flavor structure • Flavor Structure • Unknowns:: 7 • Constraints: F2 (Proton, Neutron),FL,(proton, neutron)  4 • Flavor Assumptions • Unknowns:: 7-3 = 4 • Constraints: F2 (Proton, Neutron),FL,(proton)  3

  14. Typical Result

  15. Summary - i • Twist-4 matrix elements are interesting itself because, • a) First experimental measurements of multiparticle correlation inside proton • b) Old data seems to suggest need much more correlation than • such as

  16. Summary - ii Twist-4 matrix elements are relevant for Vector and Axial vector in medium

  17. Summary - iii 2. Analysis suggests Large cancellation in Twist-4 effect in F2 3. OPE suggests Large Twist-4 effect in FL and proportional to Twist-2

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