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Anomalous AVV* amplitude in soft-wall AdS /QCD

Anomalous AVV* amplitude in soft-wall AdS /QCD. J.J. Sanz -Cillero ( Bari - INFN ) P. Colangelo , F. De Fazio, F. Giannuzzi , S. Nicotri , J.J. SC [PRD 85 (2012) 035013] Ongoing work with F. Zuo. QNP’12, April 19 th 2012. Outline :. VVA vertex in QCD

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Anomalous AVV* amplitude in soft-wall AdS /QCD

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  1. Anomalous AVV* amplitude in soft-wall AdS/QCD J.J.Sanz-Cillero ( Bari - INFN) P. Colangelo, F. De Fazio, F. Giannuzzi, S. Nicotri, J.J. SC [PRD 85 (2012) 035013] Ongoing work with F. Zuo QNP’12, April 19th 2012

  2. Outline: • VVA vertex in QCD • Holographicmodel and Chern-Simonsterm • Longitudinal and transverse GF: • LR and VVA correlators: Son-Yamamotorelation[arXiv:1010.0718 [hep-ph] ]

  3. VVA Green’sfunction in QCD

  4. Thisworkisfocusedonthe GF, • In thesoftphotonlimit k0, providedbytherelation • in terms of the VVA correlator • The GF isdecomposed in T and L Lorentzstructures • with , g JA JA JV JV k0 JEM q q

  5. High-energy OPE formq=0 • High-energy OPE formq≠0 [ Vainshtein ‘03 ] withthemagneticsusceptibilityc: [ Vainshtein ‘03 ]

  6. AdS/QCD: Yang-Mills+Chern-Simons

  7. Setup:  gauge chiralsymmetry •  Dilaton •  AdSMetric •  • The YM actionprovidesthepropagator and 2-point GFs: Dual operators [ Karch et al. ‘06 ] • cSBthroughthev.e.v.v(z) • Phase-shiftp inducedbythe axial source A0||(x)m

  8. A5=V5=0 • Equations of Motion: • Vector EoM Analyticallysolvable

  9. Scalarv.e.v. -Explicitbreaking:mq • - Spontaneousbreaking: s [ UV behaviour / short-distance (y0) ]

  10. Chern-Simonsaction Chiralanomaly • - Chern-Simonsterm • with • - Invariantunder Vector transf. up to a boundaryterm(whichis removed) • (relevantpartfor AVV) • ContributiontoAgV (soft kg0) • withgroup factor

  11. This produces theAdSprediction • withfixedbyformq=0 • AllthatremainsExtractthe B-to-b propagators V, A , A||

  12. VVA in AdS/QCD

  13. AllEoM can beanalyticallysolved (v(y)=0) : Weusedthis tofixkCS In agreementewithexact QCD withmq=0 and no ScSB [ justmasslesspQCD ]

  14. At Q2∞one has the OPE • The OPE requiresthepresence of a logarithmcln(Q2/mq2) at O(1/Q4) •  Impossibleifthe UV-b.c.forpisjust a constant ?

  15. TheParallelcomponentcan bestillanalyticallysolved: • Theperp. component[expansion in 1/Q2 ] • PROBLEM: OPE at high-energies • Ourmodel produces c=0 ?

  16. TheParallelcomponent exp. in 1/Q2 • Theperp. Component[expansion in 1/Q2 ] ? ? • ISSUESwiththe OPE: mqsterm: no susceptibility, c=0 !!  mq2term: wL:Ifp(Q2,0) Impossibletorecover simply a constantthe lnQ2terms wT:Impossibletorecoverthe lnQ2terms

  17. LR-correlator and wT,L(mq=0): Son-Yamamotorelation

  18. Son-Yamamotoproposedtherelation [ 2010 ] cSBthrough IR BC’s [Sakai,Sugimoto ’04, ‘05] [Hirn,Sanz ‘05] ? cSBthroughv(y) [Son,Stephanov ‘04] [Karch et al. ‘06] [Colangelo et al. ‘08] MHA withr + a1 [Knecht,De Rafael ‘98] [Knecht,De Rafael ‘98]

  19. Summary and conclusions

  20. Formq=0one has p = A|| = 1[ topologicalquantity ] • NotdeterminedbyEoMsbutbyb.c. • Problemsformq=0 in wT : c=0 !! • More ingredientsneeded? • Problemsfor mq≠0 : • SY relation(at large NC) : •  No 5D-field dual toqsabq •  No transitionqsabq g •  Needforthe dual fieldBab ? [ Cappielo et al. ‘10 ] [ Gorsky et al. ‘12 ] •  p(Q,0) ? •  c=0againfrommqs !! •  Are mqcorrectionsunderstood? • Study of PAA|| •  Issues in AdSfor Q2∞ • BUTitseemstowork at Q20 • Maybe ‘cause the MHA alreadydoeswell [ Knecht et al. ‘11 ] [Kampf ‘11 ]

  21. BACKUP

  22. Scalarv.e.v. chiralsymmetrybreaking • -Explicitbreaking: • -Spontaneousbreaking: • However, in thesimplestmodel[ Colangelo et al. ’08 ] •  C1 and C2related (unlike QCD) •  Supossedlysolvablebyadding a potentialV(|X|) • Wewillassumethev.e.v.profile(regardless of itsorigin)

  23. Scalarv.e.v. chiralsymmetrybreaking • -Explicitbreaking: • -Spontaneousbreaking: • Wewillassumethev.e.v.profile(regardless of itsorigin)

  24. Forourscalarv.e.v. • v(y)= mq y/c • Noticetherelevance of the UV value of thepfield !! • At Q2∞ one has the OPE • The OPE requiresthepresence of a logarithmcln(Q2/mq2) at O(1/Q4) •  Impossibleifthe UV-b.c.forpisjust a constant ?

  25. Phenomenology(mq=0)

  26. For Q20 theEoM can beanalyticallysolvedforv(y) = sy3/c3 INPUTS: NOT a fit !!!  Experiment [ PDG ’10 ] Thiswork [ Colangelo et al. ‘11] 86.5 92.2 8.3 ±1.3 6.3 • For Q2∞perturbativelysolvedforg5v(y) = Sy3 + O(y4) Thiswork [ Colangelo et al. ‘11] Experiment [ Prades et al. ’10 ] [ Prades et al. ’10 ] -2.2 ±0.4 - 4.0 [ Friot et al. ’04 ] -3.9 ± 1.0

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