anomalous avv* amplitude in soft-wall ads /qcd
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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) 035013]
Ongoing work with F. Zuo
QNP’12, April 19th 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:1010.0718 [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 k0, provided by the relation
in terms of the VVA correlator
•The GF is decomposed in T and L Lorentz structures
with ,
JA JV
JA JV
g
JEM
k0
q q
Anomalous AV*V amplitude in soft-wall models
J. J. Sanz Cillero
•High-energy OPE for mq=0
•High-energy OPE for mq≠0
with the magnetic susceptibility c:
[ Vainshtein ‘03 ]
[ 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:
- cSB through the v.e.v. v(z)
- Phase-shift p induced by the axial source A0||(x)m
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
A5=V5=0
Anomalous AV*V amplitude in soft-wall models
J. J. Sanz Cillero
•Scalar v.e.v. - Explicit breaking: mq
- Spontaneous breaking: s
[ UV behaviour / short-distance (y0) ]
Anomalous AV*V amplitude in soft-wall models
J. J. Sanz Cillero
•Contribution to AgV (soft kg0)
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 mq=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 mq=0 and no ScSB
[ just massless pQCD ]
We used this to fix kCS
VVA Green's function in AdS/QCD J. J. Sanz Cillero
Anomalous AV*V amplitude in soft-wall models
J. J. Sanz Cillero
•At Q2∞ one has the OPE
The OPE requires the presence of a logarithmc ln(Q2/mq2) at O(1/Q4)
Impossible if the UV-b.c. for p 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/Q2 ]
•PROBLEM: OPE at high-energies
Our model produces c=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/Q2
•The perp. Component [expansion in 1/Q2 ]
?
?
•ISSUES with the OPE:
mqs term: no susceptibility, c=0 !!
mq2 term: wL: If p(Q2,0) Impossible to recover
simply a constant the lnQ2 terms
wT: Impossible to recover the lnQ2 terms
VVA Green's function in AdS/QCD J. J. Sanz Cillero
LR-correlator and wT,L (mq=0)
:
Son-Yamamoto relation
VVA Green's function in AdS/QCD J. J. Sanz Cillero
•Son-Yamamoto proposed the relation [ 2010 ]
cSB through IR BC’s
[Hirn,Sanz ‘05]
cSB through v(y)
[Sakai,Sugimoto ’04, ‘05]
[Son,Stephanov ‘04]
[Karch et al. ‘06]
[Colangelo et al. ‘08]
?
MHA with r + a1 [Knecht,De Rafael ‘98]
[Knecht,De Rafael ‘98]
VVA Green's function in AdS/QCD J. J. Sanz Cillero
Summary and
conclusions
VVA Green's function in AdS/QCD J. J. Sanz Cillero
•For mq=0 one has p = A|| = 1 [ topological quantity ]
Not determined by EoMs but by b.c.
•Problems for mq=0 in wT : c=0 !!
More ingredients needed?
•Problems for mq≠0 :
•SY relation (at large NC) :
• No 5D-field dual to qsabq• No transition qsabq g• Need for the dual field Bab ? [ Gorsky et al. ‘12 ]
• p(Q,0) ?• c=0 again from mqs !!
• Are mq corrections understood?
Study of PAA||
• Issues in AdS for Q2∞
• BUT it seems to work at Q20
• 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 ]
C1 and C2 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)= mq y/c
Notice the relevance of the UV value of the p field !!
•At Q2∞ one has the OPE
The OPE requires the presence of a logarithmc ln(Q2/mq2) at O(1/Q4)
Impossible if the UV-b.c. for p is just a constant
?
Anomalous AV*V amplitude in soft-wall models
J. J. Sanz Cillero
Phenomenology (mq=0)
Anomalous AV*V amplitude in soft-wall models
J. J. Sanz Cillero
•For Q20 the EoM can be analytically solved for v(y) = sy3/c3
Experiment[ PDG ’10 ]
This work[ Colangelo et al. ‘11]
92.2
8.3 ±1.3 6.3
86.5
•For Q2∞ perturbatively solved for g5v(y) = Sy3 + O(y4)
Experiment[ Prades et al. ’10 ]
This work[ Colangelo et al. ‘11]
-2.2 ±0.4 - 4.0 [ Prades et al. ’10 ]
-3.9 ± 1.0 [ Friot et al. ’04 ]
INPUTS:
NOT a fit !!!