Quark Transverse Momentum in Longitudinal Nucleon Structure

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