Scaling behavior of quark propagator in full QCD

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Scaling behavior of quark propagator in full QCD
Maria B Parappilly CSSM, University of Adelaide
PANIC 05, October 24-28, Santa Fe, USA
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Collaborators

• Patrick Bowman (Indiana University)
• Urs. M. Heller (American Physical Society)
• Derek B Leinweber (CSSM)
• Anthony G Williams (CSSM)
• Jianbo Zhang (CSSM)

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Outline

• Lattice QCD
• Unquenched simulations
• Quark Propagator
• Results role of sea quarks
• Scaling
• Conclusions

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Lattice QCD

• Lattice QCD is the nonperturbative calculational
  method based on the principles of QCD .
• QCD is a gauge theory where the elementary
  matter fields are quarks.
• In an asymptotically free theory, there is no
  barrier using perturbation theory at large
  momenta.
• At high momenta, quarks are asymptotically free
  and the quark propagator approaches its
  tree-level behavior.

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Lattice Calculations

• Lattice QCD allows a direct probe of the
  nonperturbative quark propagator.

• To carry out simulations, we must select
• Coupling parameter lattice
  spacing (a)
• Grid size (Ns3xNt)
• Quark masses (mu, md, ms)
• The number of configurations to average over ,
  governing statistical errors.
• To eliminate systematic errors , we must
• Take the continuum limit a ? 0

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Quark Propagator

• The infrared structure gives insight to the
  dynamical mass generation.
• The quark propagator is an input in DSE based
  model calculations.
• Operationally SF Inverse of Dirac Operator,
• The quark propagator is a gauge dependent
  quantity.
• Landau gauge is selected.

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Quark Propagator
The most general expression for full quark
propagator can be written as
M(p2) is the mass function and Z(p2) is the quark
renormalization function.
Asymptotic freedom implies that as p2?8
reduces towards the tree-level propagator
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Ensemble of Configurations

• The configurations we use in this study were
  generated by MILC collaboration.

• We use AsqTad or A2tad fermion action (an
  improved staggered action).
• AsqTad action Removes lattice
  artifacts up to errors of O(a4) and O(a2g2).
• Staggered quarks are fast to simulate.

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Unquenched Simulations

• Quenched approximation
• (Dynamics of sea quarks ignored)
• Dynamical QCD
• Computationally expensive. Computing
  resources now available are powerful enough to
  begin treating up, down and strange quarks
  dynamically.

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Full QCD

• Motivation
• 1. Nature is full QCD
• 2. Shed light on the properties of QCD.
• Most insight is based on quenched approximation.
• Sea quark mass may be thought of as infinite in
  quenched approximation.
• 3. For the first time well learn about the
  sea-quark mass dependence of the quark
  propagator.

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MotivationUnquenched gluon propagator
Enhancement for intermediate momenta . At tree
level, q2 D(q2) constant
Gluon dressing function - quenched dynamical
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Lattice Parameters
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Results (Partially Quenched)
Full QCD
The unquenched M(q2) for a variety of valence
quark masses.
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Results (Partially Quenched)
Full QCD
The unquenched Z(q2) for a variety of valence
quark masses.
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Sea Quark Mass Dependence
? light sea 14.0 MeV ? heavy sea
27.1 MeV
Valence quark mass 14.0 MeV
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Sea Quark Mass Dependence
? light sea 14.0 MeV ? heavy sea
27.1 MeV
Valence quark mass 135.6 MeV
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Sea Quark Mass Dependence
Valence quark mass 14.0 MeV
? light sea 14.0 MeV ? heavy sea
27.1 MeV
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Sea quark Mass Dependence
? light sea 14.0 MeV ? heavy sea
27.1 MeV
Valence quark mass 135.6 MeV
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Comparison of Results
musea 15.7 MeV mdsea 15.7 MeV mssea 78.9 MeV
Degree of mass generation diminished by the
presence of the loops .
Comparison of full QCD and quenched mass function
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Scaling behavior
Comparison of unquenched M(q2) for two
different lattices. Bare masses adjusted so
that M(q2) agrees at renormalization point of q
3.0 GeV
a 0.090 fm
a 0.125 fm
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Scaling behavior
Comparison of unquenched Z(q2) for two
different lattices. Bare masses obtained
by matching M(q2)at renormalization point of q
3.0 GeV.
a 0.090 fm
a 0.125 fm
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Light quark Scaling behavior
Same as previous case except that sea quark
masses are lighter, i.e., near chiral
limit. Bare masses adjusted so that M(q2)
agrees at renormalization point of q 3.0 GeV
a 0.090 fm
a 0.125 fm
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Light Quark Scaling behavior
Same as previous case except that sea quark
masses are lighter, i.e., near chiral
limit. Bare masses obtained by matching M(q2) a
at renormalization point of q 3.0 GeV.
a 0.090 fm
a 0.125 fm
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Conclusions

• The addition of sea-quark loops screens the
• interactions of QCD.
• Dynamical Mass Generation suppressed.
• Renormalization function reduction is suppressed.
• In accord with perturbative prediction that
  adding
• fermion loops suppresses nonabelian effects.
• Adding quark loops moves the result toward the
• tree-level form (IR behavior of M and Z
  more abelian-like).
• But the effect is subtle.
• We find good scaling behavior for a 0.125 fm
  with
• AsqTad fermions.

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Scaling behavior of quark propagator in full QCD
Maria B Parappilly CSSM, University of Adelaide
PANIC 05, October 24-28, Santa Fe, USA
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Asymptotic Freedom
Theoretical prediction for the coupling
Quarks behave as approximately free particles
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Lattice Quark Propagator

• Each configuration from the ensemble of lattice
  gauge configuration is rotated to desired gauge
  (Landau gauge).
• On each configuration, quark propagator is
  calculated by
• K is the fermion
  matrix
• for
  AsqTad action
• The propagator is Fourier transformed to momentum
  space.
• The result is averaged over all configurations in
  the ensemble.
• Extract the mass function M(q2) and the quark
  renormalization function Z(q2).
• M(q2) and Z(q2) contain all the non-perturbative
  behaviour of the propagator.