QUARK TRANSVERSE MOMENTUM IN LONGITUDINAL NUCLEON STRUCTURE

By Daniel Koch

With Wally MelnitchoukRolf EntPedro 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

kT , the primordial transverse momentum

Expected that R, , is particularly sensitive to quark transverse momentum

1972, Feynman model

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)

KINEMATICS Breit Frame:

is the transverse momentum dependent PDFwhere

TMD PDF

Eg. Gaussian form

Normalization of TMD PDF

In general, x and kT dependence may be coupled

Usually one assumes factorizable distribution

From factorizable model,

Flavor dependence

No longer has kT 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 Q2

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 GeV2

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

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 Q2

THANK YOU