Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero 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) ] Ongoing work with F. Zuo QNP’12, April 19 th 2012
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero VVA vertex in QCD Holographic model and Chern-Simons term Longitudinal and transverse GF: LR and VVA correlators: Son-Yamamoto relation [ arXiv: [hep-ph] ] Outline:
VVA Green's function in AdS/QCD J. J. Sanz Cillero VVA Green’s function in QCD
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero This work is focused on the GF, In the soft photon limit k 0, provided by the relation in terms of the VVA correlator The GF is decomposed in T and L Lorentz structures with, JAJA JVJV JAJA JVJV J EM k0k0 qq
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero High-energy OPE for m q =0 High-energy OPE for m q ≠0 with the magnetic susceptibility : [ Vainshtein ‘03 ]
VVA Green's function in AdS/QCD J. J. Sanz Cillero AdS/QCD: Yang-Mills + Chern-Simons
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero Setup: gauge chiral symmetry Dilaton AdS Metric The YM action provides the propagator and 2-point GFs: - SB through the v.e.v. v(z) - Phase-shift induced by the axial source A 0 || (x) Dual operators [ Karch et al. ‘06 ]
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero Equations of Motion: Vector EoM Analytically solvable A 5 =V 5 =0
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero Scalar v.e.v. - Explicit breaking: m q - Spontaneous breaking: [ UV behaviour / short-distance (y 0) ]
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero Contribution to A V (soft k 0) with group factor Chern-Simons action Chiral anomaly - Chern-Simons term with - Invariant under Vector transf. up to a boundary term (which is removed) (relevant part for AVV)
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero This produces the AdS prediction with fixed by for m q =0 All that remains Extract the B-to-b propagators V, A , A ||
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero VVA in AdS/QCD
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero All EoM can be analytically solved ( v(y)=0 ) : In agreemente with exact QCD with m q =0 and no S SB [ just massless pQCD ] We used this to fix k CS
VVA Green's function in AdS/QCD J. J. Sanz Cillero
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero At Q 2 ∞ one has the OPE The OPE requires the presence of a logarithmc ln(Q 2 /m q 2 ) at O(1/Q 4 ) Impossible if the UV-b.c. for is just a constant?
VVA Green's function in AdS/QCD J. J. Sanz Cillero
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero The Parallel component can be still analytically solved: The perp. component [expansion in 1/Q 2 ] PROBLEM: OPE at high-energies Our model produces =0?
VVA Green's function in AdS/QCD J. J. Sanz Cillero
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero The Parallel component exp. in 1/Q 2 The perp. Component [expansion in 1/Q 2 ]? ? ISSUES with the OPE: m q term: no susceptibility, =0 !! m q 2 term: w L : If (Q 2,0 ) Impossible to recover simply a constant the lnQ 2 terms w T : Impossible to recover the lnQ 2 terms
VVA Green's function in AdS/QCD J. J. Sanz Cillero LR-correlator and w T,L (m q =0) : Son-Yamamoto relation
VVA Green's function in AdS/QCD J. J. Sanz Cillero Son-Yamamoto proposed the relation [ 2010 ] SB through IR BC’s [Hirn,Sanz ‘05] SB through v(y) [Sakai,Sugimoto ’04, ‘05] [Son,Stephanov ‘04] [Karch et al. ‘06] [Colangelo et al. ‘08] ? MHA with + a 1 [Knecht,De Rafael ‘98]
VVA Green's function in AdS/QCD J. J. Sanz Cillero Summary andconclusions
VVA Green's function in AdS/QCD J. J. Sanz Cillero For m q =0 one has = A || = 1 [ topological quantity ] Not determined by EoMs but by b.c. Problems for m q =0 in w T : =0 !! More ingredients needed? Problems for m q ≠0 : SY relation (at large N C ) : No 5D-field dual to q q No transition q q Need for the dual field B ? [ Gorsky et al. ‘12 ] (Q,0) ? =0 again from m q !! Are m q corrections understood? Study of AA || Issues in AdS for Q 2 ∞ BUT BUT it seems to work at Q 2 0 Maybe ‘cause the MHA already does well [ Knecht et al. ‘11 ] [Kampf ‘11 ] [ Cappielo et al. ‘10 ]
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero BACKUP
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero Scalar v.e.v. chiral symmetry breaking -Explicit breaking: -Spontaneous breaking: However, in the simplest model [ Colangelo et al. ’08 ] C 1 and C 2 related (unlike QCD) Supossedly solvable by adding a potential V(|X|) We will assume the v.e.v. profile (regardless of its origin)
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero Scalar v.e.v. chiral symmetry breaking -Explicit breaking: -Spontaneous breaking: We will assume the v.e.v. profile (regardless of its origin)
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero For our scalar v.e.v. v(y)= m q y/c Notice the relevance of the UV value of the field !! At Q 2 ∞ one has the OPE The OPE requires the presence of a logarithmc ln(Q 2 /m q 2 ) at O(1/Q 4 ) Impossible if the UV-b.c. for is just a constant?
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero Phenomenology (m q =0)
Anomalous AV*V amplitude in soft-wall models J. J. Sanz Cillero For Q 2 0 the EoM can be analytically solved for v(y) = y 3 /c 3 Experiment [ PDG ’10 ] This work [ Colangelo et al. ‘11] ± For Q 2 ∞ perturbatively solved for g 5 v(y) = y 3 + O(y 4 ) Experiment [ Prades et al. ’10 ] This work [ Colangelo et al. ‘11] -2.2 ± [ Prades et al. ’10 ] -3.9 ± 1.0 [ Friot et al. ’04 ] INPUTS: NOT a fit !!!