1. Semi-Inclusive DIS measurements at Jefferson Lab
P. Bosted for the E Collaboration
(presented by B. Sawatzky)
Note mes
DNP, October 2009

2. Semi-inclusive DIS orbital motion of quarks (pt, f dependence)
pion
Main focus of SIDIS studies: MX
orbital motion of quarks (pt, f dependence)
parton distributions (separate valence, sea)
X.Ji
Where region I/II boundary?
Can useful information come from Region II?

3. SIDIS kinematic plane and relevant variables
pion MX
Pt is transverse momentum relative to virtual photon
W2=M2+Q2(1/x-1) is invariant mass of total hadronic final state

4. Hall C experiment E00-108 Electron beam with E=5.5 GeV
Proton and Deuteron targets
SIDIS measurements of both p+ and p-
Electrons scattered at 24 to 36 degrees into SOS
Pions detected in the HMS spectrometer
Scan of z at fixed Pt=0, x=0.3
Scan of x at fixed Pt=0, z=0.55
Scan of Pt at fixed x=0.3, Pt=0
Rather low W: 2<W<3 GeV
Rather low Mx: will description in terms of scattering of single quarks hold?

5. Z-Dependence of cross sections
Good agreement with prediction using CTEQ5M PDFs and Binnewies fragmentation functions, except for z>0.7, or Mx<1.4 GeV.
D or D+,D-
Jlab Hall C
X=0.3, Q2=2.5 GeV2, W=2.5 GeV

6. How Can We Verify Factorization?
Neglect sea quarks and assume no pt dependence to parton distribution functions
Fragmentation function dependence drops out in Leading Order
[sp(p+) + sp(p-)]/[sd(p+) + sd(p-)]
= [4u(x) + d(x)]/[5(u(x) + d(x))]
~ sp/sd independent of z and pt
[sp(p+) - sp(p-)]/[sd(p+) - sd(p-)]
= [4u(x) - d(x)]/[3(u(x) + d(x))]
independent of z and pt,
but more sensitive to assumptions

7. Duality in Pion Electroproduction
... or Why does factorization appear to work well at low energies …
GRV & CTEQ,
@ LO or NLO
“Works” better
(recall, z = 0.65 ~
Mx2 = 2.5 GeV2)
“Works” worse
Closed (open) symbols reflect data after (before) events from coherent r production are subtracted

8. More general (e,e’h) “SIDIS” framework
General formalism for (e,e’h) coincidence reaction:
Factorized formalism for SIDIS (e,e’h):
In general, A and B are functions of (x,Q2,z,pT,f).
Note: typical assumption is that that sL/sT = RDIS
Determination of the pT and f dependencies are interesting in their own right  potential to determine the transverse momentum distributions of quarks.

9. kT-dependent SIDIS pt = Pt – z kt + O(kt2/Q2) TMDu(x,kT)
Schematic diagram of semi-inclusive pion electroproduction with a factorized QCD quark parton model at lowest order in as. Final transverse momentum of the detected pion Pt arises from convolution of the struck quark transverse momentum kt with the transverse momentum generated during the fragmentation pt.
pt = Pt – z kt + O(kt2/Q2)
Linked to framework of Transverse Momentum Dependent Parton Distributions
TMDu(x,kT)
f1,g1,f1T ,g1T
h1, h1T ,h1L ,h1 p m x
TMD

10. Transverse momentum dependence of SIDIS
Pt dependence very similar for proton and deuterium targets, but deuterium slopes systematically smaller?

11. Transverse momentum dependence of SIDIS
Fit to updated version of data of previous slide
With severn parameter fit: important four are:
(m+)2 ~ width of D+(z,pt), (m-)2 ~ width of D-(z,pt), (mu)2 ~ width of u(x,kt), (md)2 ~ width of d(x,kt)
Assumptions:
Factorization valid
Fragmentation functions do not depend on quark flavor,
Transverse momentum widths of quark and fragmentation functions are gaussian and can be added in quadrature
Sea quarks are negligible
Particular function form for the Cahn effect
No additional higher twist effects
NLO corrections can be ignored

12. Transverse momentum dependence of SIDIS
+ vs u
- vs d
d vs u
- vs +
Ellipses are fits with different systematic assumptions
Black dot is from a particular di-quark model
Dashed lines have equal (u,d) or (+,-) widths

13. Summary and Outlook
All widths of expected order-or-magnitude (I.e. 0.1 to 0.2 GeV2)
d-quark width may be smaller than u-quark width
Technique seems promising for future studies.
Huge increase in kinematic reach and statistical accuracy expected with JLab upgrade to 11 GeV.
Proposal E plans to continue these studies at higher W, Q2 and Mx over a wide region of x and z.