# Hadronic Form Factor Uncertainties J. W. Martin, University of Winnipeg M. Pitt, Virginia Tech.

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Hadronic Form Factor Uncertainties J. W. Martin, University of Winnipeg M. Pitt, Virginia Tech

Physics The usual form factors G E , G M  are “known”. By measuring at very low Q 2 and very forward angles, we attempt to isolate the first term, which to zeroth order in Q 2 is just proportional to Q W p However, there are still corrections due to “unknown” terms: –G E s, G M s, G A e For example, at our experiment’s kinematics, the 2 nd and 3 rd terms (only weakly dependent on Q W p ) contribute about 30%. So, to measure Q W p at the 2% level, these must be controlled at 5% relative level. Also there are EW rad cor: we take these to be “known”.

Procedure to Estimate Uncertainties due to G E s, G M s Use asymmetry data from previous experiments. Assume a reasonable empirical form for G E s, G M s with some unknown parameters (typically the strangeness radius and the strangeness magnetic moment). Use fitting to determine the errors in those parameters. Calculate the error induced on the asymmetry to be measured by the Qweak experiment and hence on the extraction of Q W p.

Example: the empirical model known as “linear” P1=  s ; P2=  s SAMPLE, HAPPEX, PVA4, G0FWD proton included. Relative uncertainty on Q w p is Result:

Example: the empirical model known as “Galster” P1=  s ; P2=  s SAMPLE, HAPPEX, PVA4, G0FWD proton included. Relative uncertainty on Q w p is Result:

Additional studies Tried eight different empirical forms, fitted over all data and over restricted Q2<0.25 range. Tried fixing  s (motivated by Leinweber et al). Tried “three parameter fit”: –Include Qweak as just another experiment –Fit  s,  s, and Q W p directly. –Advantage: Unified description of Q W p from all PV electron experiments. –Disadvantage: statistical and systematic uncertainties of Qweak and all the other experiments are rolled into final answer for Q W p.

Example: three parameter fit with “Galster” P1=  s P2=  s P3=Q W p SAMPLE, HAPPEX, PVA4, G0FWD. and Qweak proton included. TOTAL Relative uncertainty on Q w p is displayed on graph. Result: fair agreement with other method

Results

For PAC Jeopardy results of 2-par fit for “linear” (fit to all data) and “super simple” (fit to Q 2 <0.25). Although fit to all experiments, plot contains experiments which are at roughly the same beam energy (HAPPEX and G0).

Conclusions and Remaining Work For two of the reasonable models considered, the answer is within the error envelope. These models are definitely justifiable. However, uncertainty appears to depend on empirical form assumed for strangeness form factors. Remaining to do: –include more data: G0BACK, PVA4 backward, deuterium, HAPPEX-He. –Q2 binning for Qweak. –effect of lowering average Q2 of Qweak. Mark will now talk more about use of these results and axial piece.