Revealing Treacherous Points for Successful LightFront Phenomenological Applications

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Revealing Treacherous Points for Successful
Light-Front Phenomenological Applications

• LC2005, Cairns, July 14, 2005

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Motivation

• LFD Applications to Hadron Phenomenology
• -GPD,SSA,(JLAB,Hermes,)
• -B Physics (Babar,Belle,BTeV,LHCB,)
• -QGP,Quark R F (RHIC,LHC ALICE,)
• Significance of Zero-Mode Contributions
• -Even in J (G00 in Vector Anomaly)
• -Angular Condition(Spin-1 Form Factors,)
• -Equivalence to Manifestly Covariant
  Formulation

How do we find where they are?
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Outline

• Common Belief of Equivalence
• - Exactly Solvable Model
• - Heuristic Regularization Arc Contribution
  
• Vector Anomaly in W Form Factors
• - Brief History
• - Manifestly Covariant Calculation
• Pinning Down Which Form Factors
• - Dependence on Formulations
• Direct Power-Counting Method
• Conclusions

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Common Belief of Equivalence
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Exactly Solvable Model of Bound-States
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Electromagnetic Form Factor
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Equivalent Result in LFD

Valence Nonvalence
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Heuristic Regularizationto recover the
equivalence
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Arc Contribution in LF-Energy Contour
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Form Factor Results
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Standard Model

• Utility of Light-Front Dynamics (LFD)
• Bottom-Up Fitness Test of Model Theories
• B.Bakker and C.Ji, PRD71,053005(2005)

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CP-Even Electromagnetic Form Factors of W? Gauge
Bosons
At tree level, for any q2,
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One-loop Contributions in S.M.
W.A.Bardeen,R.Gastmans and B.Lautrup,
NPB46,319(1972) G.Couture and J.N.Ng,
Z.Phys.C35,65(1987) E.N.Argyres et
al.,NPB391,23(1993) J.Papavassiliou and
K.Philippidas,PRD48,4255(1993)
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One-loop Contributions in S.M.
W.A.Bardeen,R.Gastmans and B.Lautrup,
NPB46,319(1972) G.Couture and J.N.Ng,
Z.Phys.C35,65(1987) E.N.Argyres et
al.,NPB391,23(1993) J.Papavassiliou and
K.Philippidas,PRD48,4255(1993)
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One-loop Contributions in S.M.
W.A.Bardeen,R.Gastmans and B.Lautrup,
NPB46,319(1972) G.Couture and J.N.Ng,
Z.Phys.C35,65(1987) E.N.Argyres et
al.,NPB391,23(1993) J.Papavassiliou and
K.Philippidas,PRD48,4255(1993)
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One-loop Contributions in S.M.
W.A.Bardeen,R.Gastmans and B.Lautrup,
NPB46,319(1972) G.Couture and J.N.Ng,
Z.Phys.C35,65(1987) E.N.Argyres et
al.,NPB391,23(1993) J.Papavassiliou and
K.Philippidas,PRD48,4255(1993)
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Vector Anomaly in Fermion Triangle Loop
Sidewise channel
Direct channel
L.DeRaad, K.Milton and W.Tsai, PRD9, 2847(1974)
PRD12, 3972(1975)
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Vector Anomaly Revisited
Smearing of charge (SMR)
Dimensional Regularization (DR4,DR2)
Pauli-Villars Regulation (PV1, PV2)
B.Bakker and C.Ji, PRD71,053005(2005)
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Manifestly Covariant Calculation
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Manifestly Covariant Results
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LFD Results
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LFD Results
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LFD Results
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LFD Results for Other Regularizations
?

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Pinning Down Which Form Factors

• Jauss ?-dependent formulation yields
• zero-mode contributions both in G00 and G01.
• W.Jaus, PRD60,054026(1999)PRD67,094010(2003)
• However, we find only G00 gets zm-contribution.
• B.Bakker,H.Choi and C.Ji,PRD67,113007(2003)
• H.Choi and C.Ji,PRD70, 053015(2004)
• Also,discrepancy exists in weak transition form
  factor A1(q2)f(q2)/(MPMV).
• Power Counting Method
• H.Choi and C.Ji, PRD, in press.

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Electroweak Transition Form Factors
where
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where
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Power Counting Method
where
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Conclusions

• The common belief of equivalence between
  manifestly covariant and LF Hamiltonian
  formulations is quite treacherous unless the
  amplitude is absolutely convergent.
• The equivalence can be restored by using
  regularizations with a cutoff parameter L, even
  for the point interactions taking
• ?????L?? limit.
• The vector anomaly in the fermion-triangle-loop
  is real and shows non-zero zero-mode contribution
  to helicity zero-to zero amplitude for the good
  current.
• In LFD, the helicity dependence of vector anomaly
  is also seen as a violation of Lorentz symmetry.
• For the good phenomenology, it is significant to
  pin down which physical observables receive
  non-zero zero-mode contribution.
• Power counting method provides a good way to pin
  down this.