QUARK TRANSVERSE MOMENTUM IN LONGITUDINAL NUCLEON STRUCTURE By

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

EARLY ATTEMPTS TO INCORPORATE KT IN QPM From the early QPM (Quark Parton Model), for small k. T 2 Generalized QPM, with arbitrary k. T 2 Hwa, Matsuda, Roberts, Z. Phys. C 1, 279(1979) Inconsistent treatment of 1/Q 2 corrections

KINEMATICS Breit Frame:

where is the transverse momentum dependent PDF

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

From factorizable model, Flavor dependence No longer has k. T dependence in the denominator Additional x dependence

RESULTS Comparison of Models with Data on R

Our model matches more closely to Feynman’s

The model favors a small value for the quark mass

X DEPENDENCE AT CONSTANT Q 2 The data suggests a much stronger x dependence than our model

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

Our model suggests a value for between 0. 1 ~ 0. 15 Ge. V 2

CONCLUSIONS k. T dependence is non-negligible <k. T 2> is ~ 0. 1 to 0. 15 Ge. V 2 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

IN PROGRESS… Implement modern PDF sets 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 Q 2

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