S. Fajfer

1. Charm meson resonances in D semileptonic decays S. Fajfer based on hep-ph/0412140, Phys. Rev. D 71 (2005) 014020 and hep-ph/0506051 in collaboration with J. Kamenik

2. motivation to investigate D meson semiletponic form factors • recent experimental results on D semileptonic decays (Focus and CLEO) (an indication of two poles form factors) • constraints form factors HQET, SCET (LEET) • framework: HM + Ch. Lagrangian including excited charm meson states • form factors calculation and comparison with the experimental results for and • summary

3. Motivation to investigate D meson semiletponic form factors There are new experimental results on D semileptonic decays (FOCUS and CLEO). form factors. They have studied Usually in D semileptonic decays a simple pole parametrization has been used in the past. However, the results of their studies suggest that the single pole parameters required by the fit of their data, are inconsistent with physical masses of the lowest lying charm meson resonances. In their analysis they utilized a modified pole fit and their results indeed suggest the existence of contributions beyond the lowest lying charm meson resonances.

4. New experimental results on charm meson resonances • BABAR announced a discovery of new narrow state ; • this was confirmed by FOCUS and CLEO ; • CLEO also observed narrow state ; • Belle found both states and also provided first evidence for two new, broad states and with opposite parity; both ca. 350-400 MeV higher above the usual • finally SELEX has announced a new surprisingly narrow state with • spin-parity assignment ; there is a proposal to consider it as a first radial excitation of Both have already been proposed as of the spin doublet chiral partners of the heavy-light pseudoscalar and and vector Ds mesons. The states have been proposed to be chiral partners of the D-meson doublet .

5. Constraints on form factorsin In our study of form factors distribution we follow the analysis of D. Becirevic and A.B. Kaidalov, Phys. Lett. B 478, 417 (2000); hep-ph/9904490. (kinematic condition) In the heavy quark limit and near the zero-recoil point where the pion is soft , the well known Isgur-Wise scaling law gives

6. from the light cone QCD sum rules: This scaling law was derived also in the large energy effective theory (LEET). In LEET , in the rest frame of the heavy meson

7. In order to satisfy one can use

8. and

10. at he leading order in 1/M and chiral expansion

11. experimental studies used:

12. in the limit of static heavy meson limit ( ) At leading order in heavy quark expansion might contain

13. If one uses directly extraction of form factors from the definition one ends up with mixed leading and subleading terms in ! Furthermore, the scalar meson contribution appears in .

14. We fix the parameters a and b by the next-to-nearest resonances and we use physical pole masses of excited charmed mesons we use for scalar resonance - dubious Selex results! instead we used theoretical prediction ( ) We use

15. by fitting PDG data on branching ratios and chiral corrections are not included, but might be important! by varying

16. From equality

25. In order that matrix elements are finite at the form factors must satisfy

26. We use static limit of HQET where the eigenstates of QCD and HQET Lagrangians are related as Matching QCD and HQET at

27. At leading order in HQET scaling laws in the limit of zero recoil In the LEET limit J. Charles et al. Phys. Rev. D 60 014001 (the explicit realization of this scaling law is done within LCSR!)

28. In order to have proper behavior the form factors should be In LEET there is the useful relation

29. It is convenient to introduce helicity amplitudes The model includes Strong interactions Weak interactions

30. Experimentally are known our input: results of our fit (we imposed effectively taking mass of the second pole to be infinite)

33. Summary • we have investigated semileptonic form factors for D P decays within • An approach which combines heavy meson symmetries and chiral symmetry; • the double pole behavior of the form factor is a result of two charm meson resonances; • the obtained dependence of the form factors is in good agreement with recent experimental results and the lattice calculation for ; • we have devised general parametrization of form factors ; • the second pole of form factors are getting contributions of • the radial excitations of ; • the single pole behavior of the form factor is explained by the presence • while in in addition to these states one might also account for their next • radial excitations; • the calculated branching ratios are close to the experimental ones;

35. References

38. we estimate (chiral corrections are small)