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Quark Transverse Momentum in Longitudinal Nucleon Structure

Quark Transverse Momentum in Longitudinal Nucleon Structure. By Daniel Koch. With Wally Melnitchouk Rolf Ent Pedro Jimenez-Delgado. Outline. Motivation Past Models Current Theoretical Models Comparison With Data Future Work. Motivation.

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Quark Transverse Momentum in Longitudinal Nucleon Structure

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  1. Quark Transverse Momentum in Longitudinal Nucleon Structure By Daniel Koch With Wally Melnitchouk Rolf Ent Pedro Jimenez-Delgado

  2. Outline • Motivation • Past Models • Current Theoretical Models • Comparison With Data • Future Work

  3. Motivation • Understand the 3-D structure of the nucleon • Longitudinal momentum fraction x • kT , the primordial transverse momentum • Expected that R, , is particularly sensitive to quark transverse momentum • 1972, Feynman model

  4. Early Attempts to Incorporate kT in QPM • From the early QPM (Quark Parton Model), for small kT2 • Generalized QPM, with arbitrary kT2 • Inconsistent treatment of 1/Q2 corrections Hwa, Matsuda, Roberts, Z.Phys.C1,279(1979)

  5. Kinematics • Breit Frame:

  6. where is the transverse momentum dependent PDF

  7. TMD PDF Normalization of TMD PDF In general, x and kT dependence may be coupled Usually one assumes factorizable distribution Eg. Gaussian form

  8. From factorizable model, • Flavor dependence • No longer has kT dependence in the denominator • Additional x dependence

  9. Results • Comparison of Models with Data on R

  10. Our model matches more closely to Feynman’s

  11. The model favors a small value for the quark mass

  12. X Dependence at constant Q2 The data suggests a much stronger x dependence than our model

  13. Our model shows some correct x dependence , unlike Hwa et al. and Feynman

  14. Our model suggests a value for between 0.1 ~ 0.15 GeV2

  15. Conclusions • kT dependence is non-negligible • <kT2> is ~ 0.1 to 0.15 GeV2 based on our model • Hwa et al. model happens to accommodates larger values of <K> • x dependence from the data suggests need for flavor dependent <K> or a need for a non-factorizable form for the PDF

  16. In Progress… • Implement modern PDFsets • Perform (chi) ^2 fit for complete set of world’s data on R • Explore longitudinal structure function in SIDIS • Explore Models of R at low Q2

  17. Thank You

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