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Pion Electroproduction Models

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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


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