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Arie Bodek, Univ. of Rochester1 New form factor parametrization Focus on Neutron ARIE BODEK University of Rochester http://www.pas.rochester.edu/~bodek/New-form-factors.ppt

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Arie Bodek, Univ. of Rochester2 Gep and Gmp fits by others will always be better then ours and will improve with time as more date in space-like and time-like region accumulate. For example, dispersion relation fits include both time like and space for Gmp and Gep data. Also there is a fit for Gmn. This kind of fit cannot be done for neutron Gen, since no time-like neutron Gen has been measured. There is some Gmn time-like data (not too much) Therefore, use the world’s best Gep and Gmp for now and only fit neutron form factors as a ratio to proton form factors. This means that as proton form factors improve (at high Q2), our ratio fits still hold since they were fit to low Q2 data with duality constraints at high Q2. For the region where the neutron data exist, the Kelly parametrization works very well, so we fit ratio of Gmn-data/Gmp (Kelly) and ( Gen-data/Gmn(Kelly)) /Gep (Kelly)/Gmp(Kelly). We should compare Kelly Gmp, Gep and Gmn to the dispersion relations fits and to the duality fits. Motivation

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Arie Bodek, Univ. of Rochester3 New Kelly Parameterization – J. Kelly, PRC 70 068202 (2004) Fit to sanitized dataset favoring polarization data. Employs the following form (Satisfies power behavior of form factors at high Q 2 ): --> introduces some theory constraints G ep, G mp, and G mn We will only use Kelly for Gmp and Gep

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Arie Bodek, Univ. of Rochester4 Kelly Parameterization Gep crosses zero at Q2 = 10. Source: J.J. Kelly, PRC 70 068202 (2004).

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Arie Bodek, Univ. of Rochester5 Dispersion Relations Simone Pacetti http://microtron.iasa.gr/pavi06/ http://microtron.iasa.gr/PAVI06/Talks/Pacetti_IIIb.pdf 1) What can we learn about the ratio |G(p)(E)(q**2)/G(p)(M)(q**2)| by using space-like, time-like data and dispersion relations? R. Baldini, M. Mirazita, S. Pacetti (Enrico Fermi Ctr., Rome & Frascati & INFN, Perugia), C. Bini, P. Gauzzi (Rome U. & INFN, Rome), M. Negrini (Ferrara U. & INFN, Ferrara). 2005. 4pp. Prepared for 10th International Conference on Structure of Baryons Â(Baryons 2004), Palaiseau, France, 25-29 Oct 2004. Published in Nucl.Phys.A755:286-289,2005 2) A Description of the ratio between electric and magnetic proton form-factors by using space-like, time-like data and dispersion relations. R. Baldini (Chicago U., EFI & Frascati), C. Bini, P. Gauzzi (INFN, Rome), M. Mirazita (Frascati), M. Negrini (INFN, Ferrara), S. Pacetti (Frascati). Jul 2005. 12pp. Published in Eur.Phys.J.C46:421-428,2006 e-Print Archive: hep-ph/0507085 3) Determination of nucleon and pion form-factors via dispersion relations. R. Baldini, E. Pasqualucci (Frascati), S. Dubnicka (Bratislava, Inst. Phys.), P. Gauzzi (Rome U. & INFN, Rome), S. Pacetti, Y. Srivastava (Perugia U. & INFN, Perugia & Northeastern U.). 2000. Prepared for Workshop on the Structure of the Nucleon (Nucleon 99), Frascati, Italy, 7-9 Jun 1999. âPublished in Nucl.Phys.A666:38-43,2000

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Arie Bodek, Univ. of Rochester6 Dispersion Relation --> Gep crosses zero at Q2=10 agrees with Kelly - Yellow band

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Arie Bodek, Univ. of Rochester7 Dispersion fits to Gmp and Gmn

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Arie Bodek, Univ. of Rochester8 Constraint 1: Rp=Rn (from QCD) From local duality R for inelastic, and R for elastic should be the same at high Q2: We assume that G en > 0 continues on to high Q 2. This constraint assumes that the QCD Rp=Rn for inelastic scattering, carries over to the elastic scattering case. This constraint is may be approximate. Extended local duality would imply that this applies only to the sum of the elastic form factor and the form factor of the first resonance. (First resonance is investigated by the JUPITER Hall C program) at high Q 2.

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Arie Bodek, Univ. of Rochester9 Constraint 2: From local duality: F 2n /F 2p for Inelastic and Elastic scattering should be the same at high Q 2 In the limit of →∞, Q 2 →∞, and fixed x: In the elastic limit: (F 2n /F 2p ) 2 →(G mn /G mp ) 2 We do fits with d/u=0,.2

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Arie Bodek, Univ. of Rochester10 Constraint 2 In the elastic limit: (F 2n /F 2p ) 2 →(G mn /G mp ) 2. We use d/u=0, 0.2 This constraint assumes that the F2n/F2p for inelastic scattering, carries over to the elastic scattering case. This constraint is may be approximate. Extended local duality would imply that this applies only to the sum of the elastic form factor and the form factor of the first resonance. (First resonance is investigated by the JUPITER Hall C program)

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Arie Bodek, Univ. of Rochester11 Constraints: R1 = (G mn /G mp ) 2 0.42875 (d/u=0.2) 0.25 (d/u=0.0) We should fit R1= (G mn /G mp ) 2 (Kelly) –One for each value of (d/u)=0, 0.2 (at high x) Use a new variable y= 1/(1+Q 2 /A) n Where A and n are optimized R1(y) = e.g. polynomial (Cubic or higher) Depends on A and n y= 0 is Q 2 = infinity R1(y=0) = 0.42875 or 0.25 y=1 is Q 2 = 0 R1(y=1) = 0.46912445 = (1.913/2.793) 2 (1-y) What do dispersion fits say? Is it 0.25 or 0.43 ? R1(y)

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Arie Bodek, Univ. of Rochester12 Fit to R2= (G en /G mn ) 2` / (G ep /G mp ) 2 Use a new variable y= 1/(1+Q 2 /A) n Where A and n are optimized R2(y) = e.g. polynomial (Cubic or higher) depends on A and n. Or some other form. y= 0 is Q 2 = infinity R2(y=0) = 1 y=1 is Q 2 = 0 R2(y=1) = 0 Kelly would be better Since it goes to 0 Q2=10 (1-y) R2(y) What do dispersion fits say? Is Gep/Gmp agree with DIS QCD?

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Arie Bodek, Univ. of Rochester13 Comparison with Kelly Parameterization Kelly (our fits for Gep do not agree with Kelly or with dispersion fits. Kelly BBBA

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Arie Bodek, Univ. of Rochester14 Would like to see Email sent to simone.pacetti@pg.infn.it He is redoing all the fits with most recent data (lost old analysis results) Arie will meet with him in Italy Sept 8-17 in Perugia (he is INFN/U of Perugia, while attending the annual Perugia Science Conference Does Gep, Gmp and Gep/Gmp for Kelly agree with Dispersion fits. Does Gmn/Gmp for dispersion fits agree with local duality fits with d/u=0 or d/u=0.2 ? Or neither (which may mean that local duality needs to include first resonance). Does Gep/Gmp Kelly and/or Dispersion agree with DIS QCD plus target mass calculation,ala local duality?

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