1. Pion Electroproduction Models
MAID and MAID2000
Only useful for W<2 GeV – not appropriate for most pionCT kinematics
VGL Regge Model
Appropriate for W>2 GeV
Seems to under-predict sT
Parameterizations
“sigBlok” in SIMC – fit to Brauel and Bebek data
Jochen Volmer’s parameterization from Fp-1 (JV)
PARAM04 from Henk – improvement on JV to work better at higher Q2

2. Pion Electroproduction Cross Section
Virtual photon cross section
In forward kinematics, average over f so interference terms go to zero
Count rate dominated by sT+esL, but interference terms can influence shapes within acceptance
Discussions here will deal just with sT+esL

3. H(e,e’p+) Data Fpi-1 Brauel DESY data Bebek Cornell data
Extracted sL, sT, sTT, and sLT at W=1.95 GeV, Q2 = 0.6, 0.75, 1.0, 1.6 GeV2
Brauel DESY data
Z. Phys. C3, p. 101 (1979)
L-T separation at W=2.19 GeV, Q2=0.7 GeV2
Unseparated cross sections (plus interference terms) at Q2=0.28,1.35 GeV2
Bebek Cornell data
PRD13, p. 25 (1976); PRD17, p (1978)
Unseparated cross sections at t=tmin, Q2= GeV2, W= GeV

4. Fp-1 Data vs. VGL
W=1.95 GeV
Red curve= VGL model with L2p=0.45 GeV2, L2r=0.6 GeV2
Blue curve= VGL model with L2p=0.54 GeV2, L2r=1.5 GeV2

5. VGL Model at Q2=2.5 GeV2
Garth Huber compared to large –t test data taken during Fp-2 -> -t dependence was too steep
By tweaking r trajectory cutoff parameter (Lr), found better agreement in –t dependence

6. Brauel Data vs. VGL
W=2.19 GeV

7. Bebek Data vs. VGL t=tmin Low e (0.33-0.47) High e (0.8-0.95) W=3.09
Other 4 points W~2.65
Other 3 points W=2.14

8. VGL Summary VGL model describes Fp-1 and Brauel sL ok (either option)
Transverse cross section consistently low
Low transverse cross sections results in poor agreement with Bebek unseparated data
For L2p=0.54 GeV2, L2r=1.5 GeV2, multiplying sT by 2.5 gives decent agreement for all the data I’ve looked at here

9. Fp-1 Data vs. Parameterizations
Red = original Blok/Huber param.
Green = Volmer param.
Blue = updated PARAM04
Note that I’ve multiplied Henk’s
sL by a factor of 2 in this and all
following figures

10. Brauel Data vs. Parameterizations

11. Bebek Data vs. Parameterizations
Low e ( )
High e ( )
W=3.09
W=2.66
W=2.11
Other 4 points W~2.65
Other 3 points W=2.14

12. Parameterization Summary
Original Blok-Huber fit does a decent job for Brauel and Fpi-1 separated data – also does pretty well with Bebek data
Can probably be tweaked pretty easily to give better agreement
J. Volmer’s parameterization only intended for use with Fpi-1 data – pathological at larger Q2
PARAM04 intended to extend Q2 range, but still not intended for arbitrarily large Q2
Also relatively easy to do-it-yourself.

13. E91003 Model Iteration and Ratio Extraction
E91003 goal: A(e,e’p+)/H(e,e’p+) (longitudinal cross sections)
Ideally, I would have used a single H(e,e’p+) cross section model + nuclear wave function
This did not work – I needed to iterate the model for each target separately
siterated = smodel F(f) W(n) Q(Q2)
No common model in the end

14. E91003 Ratio Extraction
In the end, I had to break my results into 2 parts:
Experimental ratios: Rexp= (sA/sH)exp
No (or little) model dependence
Well defined over certain missing mass range, DMx
Do not need to re-analyze data if cross section models change
Calculated ratios: Rquasifree=(sA/sH)quasifree
Totally dependent on hydrogen model and “quasifree” implementation
In my case, not too sensitive to starting H model
Final result was super-ratio: Rexp/Rquasifree
The above procedure is implicit in A(e,e’p) transparency measurements (T= YAexp/YAsimc)
Expressing model dependence explicitly allows easier comparisons with theory