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Revealing Treacherous Points for Successful Light-Front Phenomenological Applications

Revealing Treacherous Points for Successful Light-Front Phenomenological Applications. LC2005, Cairns, July 14, 2005. Motivation. LFD Applications to Hadron Phenomenology -GPD,SSA,… (JLAB,Hermes,…) -B Physics (Babar,Belle,BTeV,LHCB,…) -QGP,Quark R & F (RHIC,LHC ALICE,…)

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Revealing Treacherous Points for Successful Light-Front Phenomenological Applications

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  1. Revealing Treacherous Points for Successful Light-Front Phenomenological Applications LC2005, Cairns, July 14, 2005

  2. 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?

  3. 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

  4. Manifestly Covariant Formulation Equal t Formulation Equal t = t + z/c Formulation S (Time Ordered Amps) However, the proof of equivalence is treacherous. B.Bakker and C.Ji, PRD62,074014 (2000) Heuristic regularization to recover the equivalence. B.Bakker, H.Choi and C.Ji, PRD63,074014 (2001) Common Belief of Equivalence

  5. S.Glazek and M.Sawicki, PRD41,2563 (1990) Exactly Solvable Model of Bound-States

  6. H.Choi and C.Ji, NPA679, 735 (2001) Electromagnetic Form Factor

  7. However, the end-point singularity exists in F-(q2). B.Bakker and C.Ji, PRD62, 074014 (2000) Equivalent Result in LFD + Valence Nonvalence

  8. Heuristic Regularizationto recover the equivalence

  9.  With the arc contribution, we find Arc Contribution in LF-Energy Contour

  10. Form Factor Results

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

  12. Beyond tree level, CP-Even Electromagnetic Form Factors of W Gauge Bosons At tree level, for any q2,

  13. 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)

  14. 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)

  15. 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)

  16. 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)

  17. Vector Anomaly in Fermion Triangle Loop “Sidewise” channel “Direct” channel L.DeRaad, K.Milton and W.Tsai, PRD9, 2847(1974); PRD12, 3972(1975)

  18. Vector Anomaly Revisited Dimensional Regularization(DR4,DR2) Smearing of charge (SMR) Pauli-Villars Regulation (PV1, PV2) B.Bakker and C.Ji, PRD71,053005(2005)

  19. Manifestly Covariant Calculation

  20. Manifestly Covariant Results

  21. J+ LFD Results

  22. J+ q+=0 LFD Results

  23. LFD Results

  24. LFD Results for Other Regularizations ? =

  25. Pinning Down Which Form Factors • Jaus’s -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)/(MP+MV). Power Counting Method H.Choi and C.Ji, PRD, in press.

  26. Electroweak Transition Form Factors where

  27. and where

  28. Power Counting Method where

  29. Conclusions • The common belief of equivalence between manifestly covariant and LF Hamiltonian formulations is quite treacherous unless the amplitude isabsolutely 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.

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