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Hadronic Form Factor Uncertainties

This study evaluates the uncertainties in hadronic form factors affecting the QWeak experiment's measurement of the weak charge of the proton, QWp. By focusing on very low Q² and forward angles, we isolate corrections from unknown terms in electromagnetic form factors. We utilize asymmetry data from prior experiments and empirical fitting to estimate errors in strangeness parameters and their impact on QWp measurements. Various fitting methods were tested, including a unified three-parameter fit, demonstrating that the choice of empirical models significantly influences uncertainty estimates.

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Hadronic Form Factor Uncertainties

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

  2. Physics • The usual form factors GE, GM are “known”. • By measuring at very low Q2 and very forward angles, we attempt to isolate the first term, which to zeroth order in Q2 is just proportional to QWp • However, there are still corrections due to “unknown” terms: • GEs, GMs, GAe • For example, at our experiment’s kinematics, the 2nd and 3rd terms (only weakly dependent on QWp) contribute about 30%. So, to measure QWp at the 2% level, these must be controlled at 5% relative level. • Also there are EW rad cor: we take these to be “known”.

  3. Procedure to Estimate Uncertainties due to GEs, GMs • Use asymmetry data from previous experiments. • Assume a reasonable empirical form for GEs, GMs 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 QWp.

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

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

  6. 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 QWp directly. • Advantage: Unified description of QWp from all PV electron experiments. • Disadvantage: statistical and systematic uncertainties of Qweak and all the other experiments are rolled into final answer for QWp.

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

  8. Results

  9. For PAC Jeopardy • results of 2-par fit for “linear” (fit to all data) and “super simple” (fit to Q2<0.25). • Although fit to all experiments, plot contains experiments which are at roughly the same beam energy (HAPPEX and G0).

  10. 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.

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