f. s. n., m. nielsen ifusp (são paulo) brazil charm hadronic form factors with qcd sum rules...
TRANSCRIPT
F. S. N. , M. Nielsen
IFUSP (São Paulo) BRAZIL
Charm hadronic form factors with QCD sum rules
Motivation
Conclusion
Results on form factors
Application: charmonium production
QCDSR
interactions at RHIC and LHC/J
Charm form factors Lin,Ko nucl-th/0210014
Charmonium decays in B factories
Liu, Zhang, Zhu, hep-ph/0610278
X (3872)
X (3872)
interactions at FAIRD
Haidenbauer, Krein, Meissner, Sibirtsev arXiv:0704.3668 [nucl-th]
Form factors in QCD sum rules
DD* /* JDD(data)
/JDD DD
/** JDD **DD
**DD DD*
2) Choose the currents:
1) Write the three-point correlation function:
The QCD side (Operator Product Expansion side):
3) Insert the currents in and make the contractions:
][ duQOPE SSSTr
DD*
4) Perform the OPE:
The hadronic side (phenomenological side):
+ higher resonances
5) Insert hadronic states in
7) Use an effective Lagrangian to compute the amplitude:
6) Use the matrix elements:
8) Write)( phen
qqgpHqpH HH )(),(*)(|´)( 2
*
9) Decompose in tensor structures and choose one of them:
10) Write a double dispersion relation:
On both sides:
11) IdentifyOPEphen
12) Apply a double Borel transform:
222 MPp 222 ´)(´)(´)( MPp
double discontinuity
13) Write the sum rule:
14) Numerical analysis:
Numbers :
Borel masses:
Continuum thresholds :GeVs 5.0 GeVu 5.0
or
15) Check Borel stability and OPE convergence:
total
perturbative
gluoncondensate
),( 22 MQg
off-shell
D
off-shell
off-shell
Exp.
16) Fix M , plot fit and extrapolate to the meson pole:)( 2Qg
)()( 2222* D
DDD mQgmQgg
Correlated extrapolation of the three form factors
D*
D
J/Psi
/* JDD
Varying M and M´ independently:
Good stability !
*D off-shell
/* JDD
Dependence on the continuum threshold
0.6
0.5
0.4
0.6
0.5
0.4
D off-shell
Couplings
3.03.4 DDg
Parametrizations:
Comments
Compatibility with HQET relations :
/**/ JDDJDD gg =
Coupling D*-D-pion compatible with data and with lattice QCD:
data
lattice
**DDDD gg 3.03.4 DDg
Oh, Lee, Song, PRC (2000)
Becirevic, Charles, Le Yaouanc, L.Olivier, Pene, Raynal, (2003)
Oh, Lee, Song, PRC (2000)
Application
Charmonium production and absorption in nuclear matter
Application
Charmonium production and absorption in nuclear matter
“Charmonium regeneration”
withwithout
without with
Conclusion
Charm form factors are still very usefull for phenomenology
We can calculate them with QCDSR (finished the first round)
The obtained coupling constants are of the same order of magnitude
The numbers roughly agree with previous phenomenological estimates
The form factors were used in one phenomenological application
Charm form factors change calculations by one order of magnitude
References
F. Carvalho et al., Phys. Rev. C72, 024902 (2005)
M.E. Bracco et al., Phys. Lett. B521, 1 (2001)
F.S. Navarra et al., Phys. Rev. D65, 037502 (2002)
M.E. Bracco et al., Phys. Lett. B605, 326 (2005)
M.E. Bracco et al., Phys. Lett. B659, 559 (2008)
B. Osorio Rodrigues et al., arXiv:1003.2604 [hep-ph]
R.D. Matheus et al., Int. J. Mod. Phys. E14, 555 (2005)
R.D. Matheus et al., Phys. Lett. B541, 265 (2002)
D*
D
J/Psi
Three different particles off-shell in the vertex
Pole versus continuum
off-shell*D off-shell
** DD
Errors
Truncation of the OPE
Pole + continuum Ansatz
Continuum threshold parameters s u
s corrections
Values of masses and condensates
Choice of Borel mass
Choice of tensor structure
Extrapolation to the mass shell
~ 20 %
?
Medium effects
Borel stability in different structures:
D
D
´p
´p
p
p
DD
/** JDD
14 tensor structures
Choose
Form factors in different structures :
*D
/J
*D
/J*D
/J
*D
versus
*D *D *D
** DD /** JDD
Couplings with vector mesons not very compatible with VDM estimates :
3.03.4 DDg
Matinyann, Muller, PRC (1998)
Oh, Lee, Song, PRC (2000)
P1
P3
P3
P4
P4
P4
P5
P5
Sergei G. Matinyann, Berndt Muller Phys.Rev.C58:2994-2997,1998. nucl-th/9806027
P5
P6
P6
Kodjamirian
P7
P8
P10
Frequent questions
Higher dimension condensates ?
Infinities ? Killed by Imaginary Corr + Cutkosky + Borel + s0 / QHD
Differences between on and off-shell ? Only Borel ?
Compatible with SU(4) ? HQET ? VMD?
Pole versus continuum (well defined ?) changes with Q2 ?
Extension to quartic couplings ?Why the restrictions in the Q2 region ?
Observable applications ?
Why not smaller Q2 ?Final errors ?
Back ups
** DD
Borel stability:*D off-shell
total
perturbative
quarkcondensate
bare couplings
B) Meson loops with
*D D Meson loops
Introduce the :
)( 2pCalculate the loops and compute the vertex function
Calculate the form factor of an off-shell D: )()( 22 pGqp
CCK fitted to adjust QCDSR points
16) Fix M , plot fit and extrapolate to the pion pole:)( 2Qg
How to reduce the uncertainties ?
Exp.
CLEO, PRL 87 (2001)
Coupling constant: )( 22* mQgg DD
/* JDD
sum rules
*D off-shell
/J off-shell
Three different particles off-shell in the vertex !
OPE convergence :
*D off-shell
total
perturbative
gluoncondensate
/* JDD
J/Psi
D
/JDD
/J
Parametrizations:
/JDD
DD
D
/J
/J
D
D D D
versus
/J
D
D D D
versus
off-shell
/J
D
DD
Parametrizations:
DD
Borel stability:
off-shell*D off-shell/J
/** JDD
dependence on the continuum threshold parameters
/** JDD
Parametrizations:
( other structure )
/** JDD
** DD
structure
Borel stability:
off-shell*D off-shell
total
perturbative
quark condensate
perturbative
Dependence on the continuum threshold parameters
** DD
Form factors
*D
Parametrizations:
** DD
*D
** DD
Parametrizations:
** DD
DD*
Borel stability:
off-shellD off-shell
perturbative
total
perturbative
quark condensate
Dependence on the continuum threshold parameters:
DD*
D
DD*
Parametrizations:
DD*
/** JDD ** DD
** DD
*D
/J*D
*D
*
List of form factors
The gluon condensate
The quark condensate
Oh, Song, Lee, Wong, nucl-th/0205065
Charm form factors
Oh, Song, Lee, Wong, nucl-th/0205065
Oh, Song, Lee, Wong, nucl-th/0010064
Liu,Ko nucl-th/070277Phys.Rev.C75,064903
Conclusion
Motivação
D* D pi : dados, rede, mais calculos feitos, mais leve!
D* D Psi: mais pesado!
D D Psi e D D rho: comparação de sondas diferente !
D* D* Psi e D* D* rho: comparação de sondas diferente !
D* D rho
D* D* pi
Table...
Motivation
Understand final state interactions in B decays and X(3872) decays
Understand J/psi and D interactions in hadronic and nuclear matter
In the strange sector: KN *KN ...Form factors: simple parametrizations fitted to data
Monopole:22
222 )(
Q
MgQF
22 qQ
gMF )( 2Coupling constant
Hyperon - nucleon interactions
Haidenbauer, Meissner, Nogga, Polinder, nucl-th/0702015
12) Fix M , plot fit and extrapolate to the pion pole:)( 2Qg
PLB (2000) PRD (2002)
Exp.
/JDDold
8) Check the pole dominance:
2
0
2
4
4
)(
)(
c
c
m
s
m
ssd
ssd
Pole
DDDDDDDDccX **00*00* ||||
É difícil acreditar...
BV
V
m
gV 2
202
Compute the Lagrangian, energy-momentum tensor and obtain the EOS :
But we can estimate the Laplacian :