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 Charm form factors Lin,Ko nucl-th/

Charmonium decays in B factories Liu, Zhang, Zhu, hep-ph/ X (3872)

interactions at FAIR Haidenbauer, Krein, Meissner, Sibirtsev arXiv: [nucl-th]

Form factors in QCD sum rules (data)

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:

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

9) Decompose in tensor structures and choose one of them: 10) Write a double dispersion relation: On both sides: 11) Identify 12) Apply a double Borel transform: double discontinuity

13) Write the sum rule: 14) Numerical analysis: Numbers : Borel masses: Continuum thresholds : or

15) Check Borel stability and OPE convergence: total perturbative gluon condensate off-shell

Exp. 16) Fix M, plot fit and extrapolate to the meson pole:

Correlated extrapolation of the three form factors D* D J/Psi

Varying M and M´ independently: Good stability ! off-shell

Dependence on the continuum threshold off-shell

Couplings

Parametrizations:

Comments Compatibility with HQET relations : = Coupling D*-D-pion compatible with data and with lattice QCD: data lattice 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 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, (2005) M.E. Bracco et al., Phys. Lett. B521, 1 (2001) F.S. Navarra et al., Phys. Rev. D65, (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: [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

Errors Truncation of the OPE Pole + continuum Ansatz Continuum threshold parameters 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:

14 tensor structures Choose

Form factors in different structures :

versus

Couplings with vector mesons not very compatible with VDM estimates : Matinyann, Muller, PRC (1998) Oh, Lee, Song, PRC (2000)

P1

P3

P4

P5

Sergei G. Matinyann, Berndt Muller Phys.Rev.C58: ,1998. nucl-th/ P5

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

Borel stability: off-shell total perturbative quark condensate

bare couplings B) Meson loops with Meson loops

Introduce the : Calculate the loops and compute the vertex function Calculate the form factor of an off-shell D: fitted to adjust QCDSR points

16) Fix M, plot fit and extrapolate to the pion pole: How to reduce the uncertainties ? Exp. CLEO, PRL 87 (2001) Coupling constant:

sum rules off-shell Three different particles off-shell in the vertex !

OPE convergence : off-shell total perturbative gluon condensate

J/Psi D

Parametrizations:

versus

off-shell

Parametrizations:

Borel stability: off-shell

dependence on the continuum threshold parameters

Parametrizations: ( other structure )

structure Borel stability: off-shell total perturbative quark condensate perturbative

Dependence on the continuum threshold parameters

Form factors

Parametrizations:

Borel stability: off-shell perturbative total perturbative quark condensate

Dependence on the continuum threshold parameters:

Parametrizations:

List of form factors

The gluon condensate

The quark condensate

Oh, Song, Lee, Wong, nucl-th/ Charm form factors Oh, Song, Lee, Wong, nucl-th/ Oh, Song, Lee, Wong, nucl-th/ Liu,Ko nucl-th/ Phys.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:... Form factors: simple parametrizations fitted to data Monopole: Coupling constant

Hyperon - nucleon interactions Haidenbauer, Meissner, Nogga, Polinder, nucl-th/

12) Fix M, plot fit and extrapolate to the pion pole: PLB (2000)PRD (2002) Exp.

old 8) Check the pole dominance:

É difícil acreditar...

Compute the Lagrangian, energy-momentum tensor and obtain the EOS : But we can estimate the Laplacian :