New form factor parametrization Focus on Neutron

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New form factor parametrizationFocus on Neutron

• ARIE BODEK
• University of Rochester
• http//www.pas.rochester.edu/bodek/New-form-facto
  rs.ppt

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Motivation

• Gep and Gmp fits by others will always be better
  then ours and will improve with time as more date
  in space-like and timelike 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 not timelike
  neutron Gen has been measured. There is some Gmn
  timelike data (not too much)
• Therefore, use the worlds 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.

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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 Q2) --gt
  introduces some theory constraints

Gep, Gmp, and Gmn
We will only use Kelly for Gmp and Gep
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Kelly Parameterization

• Gep crosses zero at Q2 10.

Source J.J. Kelly, PRC 70 068202 (2004).
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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)(q2)/G(p)(M)(q2) 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.A755286-289,2005
• 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.C46421-428,2006
• e-Print Archive hep-ph/0507085

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Dispersion Relation --gt Gep crosses zero at
Q210agrees with Kelly - Yellow band
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Dispersion fits to Gmp and Gmn
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Constraint 1 RpRn (from QCD)

• From local duality R for inelastic, and R for
  elastic should be the same at high Q2
• We assume that Gen gt 0 continues on to high Q2.
• This constraint assumes that the QCD RpRn 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 Q2.
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Constraint 2 From local dualityF2n/F2p for
Inelastic and Elastic scattering should be the
same at high Q2

• In the limit of ??8, Q2?8, and fixed x
• In the elastic limit (F2n/F2p)2?(Gmn/Gmp)2

We ran with d/u0, .2, and .5.
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Constraint 2

• In the elastic limit (F2n/F2p)2?(Gmn/Gmp)2

.
We use d/u0, 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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Constraints R1 (Gmn/Gmp )2

• We should fit R1 (Gmn/Gmp )2 (Kelly)
• One for each value of (d/u)0, 0.2 (at high x)

Use a new variable y 1/(1Q2/A)n Where A and n
are optimized R1(y) e.g. polynomial (Cubic or
higher) Depends on A and n
y 0 is Q2 infinity R1(y0) 0.42875 or 0.25
y1 is Q2 0 R1(y1) 0.46912445
(1.913/2.793) 2
(1-y)
What do dispersion fits say?
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Fit to R2 (Gen/Gmn)2 / (Gep/Gmp)2
Use a new variable y 1/(1Q2/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.
Kelly would be better Since it goes to 0 Q210
y 0 is Q2 infinity R2(y0) 1
y1 is Q2 0 R2(y1) 0
(1-y)
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Comparison with Kelly ParameterizationKelly (our
fits for Gep do not agree with Kelly or with
dispersion fits.
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Would like to see

• Email sent to simone.pacetti_at_pg.infn.it
• 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/u0 or d/u0.2 ? Or neither
  (which may mean that local duality needs to
  include first resonance).