Hadronic Form-Factors Robert Edwards Jefferson Lab

1
Hadronic Form-FactorsRobert EdwardsJefferson
Lab

• Abstract
• A TECHNOLOGY TALK!!
• Outline a known but uncommon method in 3-pt
  function calculations that avoids sequential
  sources
• Demonstrate efficacy on some hadronic
  form-factors
• Particularly suitable for overlap quarks

2
Motivation

• Motivation for various electromagnetic
  form-factors why do all of them together??
• Pion -gt Pion transition from perturbative to
  non-perturbative regimes
• Rho -gt Pion isolate isovector meson exchange
  currents within deuterons, etc.
• Rho -gt Rho elucidate dominant exchange
  mechanisms in nuclei
• Nucleon -gt Nucleon fundamental, intensive
  experimental studies
• Delta -gt Nucleon info on shape/deformation of
  nucleon
• Delta -gt Delta allows access to Q20 and
  determine magnetic moments
• Similarly considerations apply to mixed valence
  form-factors and structure functions

3
Anatomy of a Matrix Element Calculation

• Jf,iy Current with desired quantum numbers of
  state A,B
• Normalize
• Compute ratio
• Problem need propagator from t ! t2

Want h 0Jyni2 dn,0 for best plateau
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Method

• How to get the backward propagator in 3-pt
• Sequential inversion through insertion
• Pros can vary source and sink fields
• Cons insertion momenta and operator fixed
• Sequential inversion through sink
• Pros can vary insertion operator momenta
• Cons sink operator momenta fixed. Baryon spin
  projection fixed
• Common problem is one vertex have a definite
  momentum
• Instead, make a sink (or source) propagator at
  definite momentum, but not sequential

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Wall-sink(source) Method

• Put sink(source) quark at definite momentum
  (e.g., 0)
• Build any (accessible) hadron state at
  source/sink
• Avoid sequential inversions computing hB(t2)
  O(t) A(t1)i
• Need to gauge fix
• Known tricks
• Improve statistics with time-reversal in
  anti-periodic BC
• Method does work for Dirichlet boundary
  conditions
• Maintain equal source sink separation from
  Dirichlet wall
• Use time-reversal then do wall source
• Overlap can use multimass inversion both
  source/sink

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Comparisons

• How does a wall sink (or source) method compare
  to say a sequential-through-sink method?
• Examples Electromagnetic form-factors of
• Pion -gt Pion
• Rho -gt Pion
• Nucleon -gt Nucleon
• Rho -gt Rho (not presented)
• Delta -gt Nucleon (not presented)
• Delta -gt Delta (not presented)

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Ratios

• Need new ratio method of correlation functions
  (e.g. for Ds! N)
• where A, B, C are generic smearing labels, L is
  local, Jmygmy
• Similarly, RD N RND where D N . Note, momenta
  and smearing labels not interchanged
• The combination (RD N RND)1/2 cancels all
  wave-function factors and exponentials

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Computational Strategies

• Dynamical (full QCD)
• Nf 2 1
• Asqtad staggered sea quarks
• Domain Wall valence quarks, 616MeV 320MeV
• Use partially quenched chiral perturbation theory
• Low energy Gasser-Leutwyler constants are those
  of QCD!
• Other calculations presented by G. Fleming, D.
  Renner, W. Schroers

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Partially Quenched Chiral Perturbation Theory

• Full QCD expensive!
• Leverage off cheap(er) valence calcs
• Correct low-energy constants, in principle
• Must be in domain of validity
• Extend partially quenched cPT to include O(a)
  terms
• Mixed actions

Bär, Rupak, Shoresh, 2002, 2003
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Asqtad Action O(a2) Perturbatively Improved

• MILC collab computationally tractable full QCD
• Symanzik improved glue
• Smeared staggered fermions Sf(V,U)
• Fat links remove taste changing gluons
• Lepage term 5-link O(a2) correction of flavor
  conserving gluons
• Third-nearest neighbor Naik term (thin links)
• All terms tadpole improved

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Decay in Quenched Approximation

• Dramatic behavior in Isotriplet scalar particle
  a0!hp intermediate state
• Loss of positivity of a0 propagator from missing
  bubble insertions
• Quenched a0 has double pole in cPT
• Also appears in mh0

Bardeen, Duncan, Eichten, Thacker, 2000
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Partially Quenched Singularity

• Non-positivity of a0 correlator
• (Partially) Quenched singularity (still) present
  at mp, valencea mp, seaa .
• Suggests not single staggered pion in chiral
  loops taste breaking not neglible
• Need complete partial cPT
• Vary valence and sea masses
• Theory under development

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Pion Electromagnetic Form Factor Fp(Q2)

• Considered a good observable for studying the
  interplay between perturbative and
  non-perturbative descriptions of QCD
• Large Q2 scaling as predicted by Brodsky-Farrar
• For small Q2 , vector meson dominance gives an
  accurate description Fp(0) 1 by charge
  conservation
• No disconnected diagrams
• Experimental results are coming for Q2 1 GeV2

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Experimental Results

• Existing data fit VMD monopole formulae too well.
  Wheres perturbative QCD?
• Dispersion relation estimates correct
  asymptotics but suggest a slow approach to
  perturbative behavior
• The introduction in many experimental papers
  read
• The valence structore of the pion is relatively
  simple. Hence, it is expected that the value of
  Q2 down to which pQCD can be applied is lower
  than e.g. for the nucleon
• Results from Lattice QCD simulations can shed
  light on the debate

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Comparing techniques for extracting Fp(Q2)

• Form factor definition
• Compare sequential-sink and wall-sink methods
• Forward APE smeared
• Sequential-sink APE smeared
• Wall-sink gauge-fixed wall smeared (zero sink
  momentum)
• Conclusion wall-sink compares favorably

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Partially Quenched DWF Form Factor

• DWF Fp(Q2,t)
• Smaller mass close to experimental VMD.
• Charge radius (crude analysis)
• Exp. h r2i 0.439(8)fm2 , VMD ! 0.405fm2
• Statistical 0.156(5)fm2 mp730MeV, 0.310(
  6)fm2 mp300MeV strong mass dependence

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Proton Electric Form-Factor

• Plateaus and Q2 dependence reasonable limited
  statistics
• All proton spin polarizations computed can
  average

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Proton EM Form-Factors

• Comparison at fixed mass with experiment
  reasonable agreement

GEp
GMp
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Neutron Magnetic Form-Factor

• Comparison at fixed mass with experiment
  reasonable agreement

GMp
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Rho!Pion Transition Form-Factor

• Electro-disintegration of deuteron intensively
  studied
• Isovector exchange currents identified
• Isoscalar exchange currents not clear
• h p(pf)Jmrk(pi)i V(Q2)
• First lattice measurement

Ito-Gross 93
8 GeV2
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Conclusions

• Work in progress!
• D!D
• D! N
• r!r
• Wall-sink method (at least so far) appears
  competitive with sequential-sink method.
• Need tests at non-zero sink momenta
• Should probably use the wall-source method
• Cheaper! greater reuse of propagators
• Well-suited to multi-mass systems (e.g., overlap)