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Chiral-Odd Twist-3 Distribution Function e(x)

chiral-odd. Why is it interesting ?. M.Burkardt and Y.Koike (2002). What is the physical origin of this delta-function singularity ?. Chiral-Odd Twist-3 Distribution Function e(x). 1. Introduction. M.Wakamatsu and Y.Ohnishi (Osaka Univ.). The purpose of talk is twofold.

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Chiral-Odd Twist-3 Distribution Function e(x)

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  1. chiral-odd Why is it interesting ? M.Burkardt and Y.Koike (2002) What is the physical origin of this delta-function singularity ? Chiral-Odd Twist-3 Distribution Function e(x) 1. Introduction M.Wakamatsu and Y.Ohnishi(Osaka Univ.)

  2. The purpose of talk is twofold (1) Physical Origin of -singularity in Nontrivial structure of QCD vacuum (2) Theoretical predictions for e(x) in the Chiral Quark Soliton Model (CQSM) CLAS measurement of semi-inclusive DIS processes

  3. Measures light-cone correlation of scalar type Existence of delta-function singularity in indicates Long-range (infinite range) correlation 2. Origin of delta-function singularity in e(x) General definition of e(x) with

  4. Why vacuum property comes into hadron obervable ? Due to extraordinary nature of the scalar quark density in the nucleon Within the CQSM, we analytically confirmed this behavior M.W. and Y.Ohnishi, Phys. Rev. D67 (2003) 114011 Existence of this infinite-range correlation is inseparably connected with nontrivial vacuum structure of QCD Spontaneous cSB and nonvanishing vacuum quark condensate

  5. valence Dirac sea Nucleon scalar quark density in the CQSM total

  6. This also dictates that We thus conclude that Nonvanishing quark condensate as a signal of the spontaneous cSB of the QCD vacuum is the physical origin of d(x)-type singularity in e(x)

  7. 3. Numerical study of e(x) in CQSM General structure of e(x) in CQSM Isoscalar part in hedgehog M.F. Isovector part more complicated : (double sum over levels)

  8. Sophisticated numerical method to treat d(x) contained in Y,Ohnishi and M.W., Phys. Rev D69 (2004) 114002 We find that where with

  9. dominant with this gives Favors fairly large pN sigma term 1st moment sum rule for isoscalar e(x) numerically

  10. Isovector part of e(x) total valence Dirac sea regular behavior at x = 0

  11. Combining isoscalar- and isovector-part of e(x), we can get any of Comparison with CLAS data extracted by Efremov and Schweitzer

  12. 4. Summary and Conclusion (1) delta-function singularity in chiral-odd twist-3 distribution e(x) is Manifestation of nontrivial vacuum structure of QCD in hadron observable (2) Existence of this singularity will be observed as Violation of pN sigma-term sum rule of need more precise experimental information on this quantity in wider range of x

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