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Decay properties of the heavy-light mesons

Takayuki Matsuki (Tokyo Kasei U.) T. Morii (Kobe U.) K. Seo (Gifu Women’s College). Decay properties of the heavy-light mesons. Based on. Isgur-Wise Function in a semi-relativistic potential model , Prog. Theor. Phys. 118 (2007) . 1087-1114 (hep-ph/0703158)

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Decay properties of the heavy-light mesons

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  1. Takayuki Matsuki (Tokyo Kasei U.) T. Morii (Kobe U.) K. Seo (Gifu Women’s College) Decay properties of the heavy-light mesons Based on • Isgur-Wise Function in a semi-relativistic potential model, • Prog. Theor. Phys. 118 (2007) .1087-1114 (hep-ph/0703158) • Structure of mass gap between two spin multiplets, Phys. Lett. B659 (2007) 593 (hep-ph/0710.0325) • Mixing angle between in HQET, hep-ph/0910.5612 • New Heavy-Light Mesons , • Prog. Theor. Phys. 51 (2007) 1077 (hep-ph/0605019) • Spectroscopy of heavy mesons expanded in1/mQ, • Phys. Rev. D56 (1997) 5646 (hep-ph/9702366) NFQCD10

  2. Motivations • Decays into heavy meson + pion(s)/photon are major decay modes of the heavy-light system • Radiative decay can be described by a vector current (compare this with semileptonic weak decay -> Isgur-Wise function) • Use Georgi-Manohar construction for the interaction between quarks and a chiral multiplet • May support our relativistic potential model expanded in 1/mQ • On the other hand • Effective couplings among heavy mesons, chiral multiplets, and photons can be easily realized (BEH) • pure HQET uses QCD sum rule, which needs a couple of inputs from other fields, e.g., lattice theory, chiral theory, etc. (decay constants, chiral condensates, …) NFQCD10

  3. What we have done so farusing our semirelativistic model • Construct the formulation how to calculate the mass spectra of heavy-light systems • Numerically calculate the mass spectra of these systems and compare them with the experiments • Predicted mass spectra for D_{s0}*(2317), D'_{s1}(2457), D_{0}*(2308), and D_{1}'(2427) agree well with the experiments • Predict that 0+ and 1+ of B_s are also below the threshold BK/B^*K • Refurbish the calculations and fit these with the experimental data, B_1(5720), B_2*(5745), and B_{s2}*(5839), which predicted M(B_{s1}')=5831 MeV while the experiment observes it at 5829 MeV • Fit our calculations with the experimentally observed radial excitations, n=2, D_s*(2715), D_s^0(2860), and, D_s(3040) and to obtain other radial excitations of D/D_s/B/B_s • Explain the superficially recovered global SU(3) invariance among 0+ states of D and D_s (mass gap between multiplets: ) • Calculate the KM matrix elements by first computing the Isgur-Wise functions from the wave functions used in the above mass spectra NFQCD10

  4. Mass Spectraof DsJ • Successful prediction/reproduction of Ds mass spectra using our semi-relativistic potential model • Lowering 0+ and 1+ of Ds0*(2317) and D1’(2427) compared with other potential models Below threshold prediction by our semi-relativisitic potential model (Prog. Theor. Phys.117(2007) 1077) prediction by conventional potential model (Godfrey & Kokski, PRD43, 1679 (1991)) NFQCD10

  5. Other Mass Spectraof Our Model • Successful reproduction of the following spectra • D0*(2308) and D1’(2427) by Belle • Ds0(2860) and Ds*(2715) by BaBar & Belle (n=2; 0+ and 1- states of Ds) • B1(5720) and B2*(5745) by D0 (1+ and 2+ states of B) • Bs2*(5839) by D0 (2+ state of Bs) D Below threshold B Bs NFQCD10

  6. Radial Excitations of Ds n=2 radial excitation : Eur. Phys. J. A 31, 701 (2007) • Predicted in 2007 “1+” with 3082 MeV as a radial excitation of Ds1(2460) (T. Matsuki, T. Morii, and K. Sudoh, Eur. Phys. J.A 31, 701 (2007)) Very recent BaBar data by Palano et. al could be n=1, higher state 3+ nearly two peaks NFQCD10

  7. Our Model Hamiltonian for System Scalar confining potential • Start with an effective Hamiltonian for 2-body bound states • Heavy Meson System (eigenvalue equation): mass of a heavy meson= One gluon exchange Coulomb potential Semi-relativistic approach to heavy meson Foldy-Wouthuysen-Tani (FWT) transformation on the heavy quark ~p/mQ expansion NFQCD10

  8. Effective Hamiltonian Expanded in 1/mQ Recoil term spin-spin interaction vector interaction Free kinetic term LS force second order NFQCD10

  9. Results of Heavy Quark Symmetry • Isgur-Wise function • Spin multiplet. e.g., (0-, 1-), (0+, 1+), … • Effective Lagrangian with HQS • Heavy quark effective field theory • Heavy quark effective potential model • Mixing of 3P1 and 1P1 • Mass spectrum • What is left behind (do we miss something?) • There could be lots more which are the results of HQS NFQCD10

  10. de Rujura, Georgi, and Glashow Americans would like to trace back to their paper of Phys. Rev. Lett. 37, 785 (1976) well before Isgur-Wise’paper in 1989 light degrees of freedom NFQCD10

  11. Isgur and Wise heavy quark symmetry NFQCD10

  12. spin doublet Chiral symmetry is broken. Heavy quark symmetry is broken. Heavy Quark Symmetry • mass gap between degenerate masses • In the heavy quark limit, masses for 0- and 1-, and also 0+ and 1+ are degenerate • In the chiral limit, all these four states are degenerate (S has mass dimension) NFQCD10

  13. Decay of heavy-light mesons 1 Various decay modes (D mesons) NFQCD10

  14. Decay of heavy-light mesons 2 Various decay modes (D mesons) NFQCD10

  15. Decay of heavy-light mesons 3 Various decay modes (Ds mesons) NFQCD10

  16. Decay of heavy-light mesons 4 Various decay modes (B mesons) NFQCD10

  17. Decay of heavy-light mesons There are two major approaches to decay calculation • Excited heavy-light systems and hadronic transitions by Di Perro and Eichten, PRD 64, 114004 ‘01 which adopted that of Goity and Roberts PRD 60, 034001 ’99 (couple quarks with chiral multiplets/photon through Georgi-Manohar interaction) • Chiral multiplets of heavy-light mesons by Bardeen, Eichten, and Hill, PRD 68, 054024 ’03 (couple heavy mesons with chiral multiplets/photon through effective Lagrangian) NFQCD10

  18. Method2 – Bardeen, Eichten, Hill – 1 PRD68, 054024 (2003) • Make degenerate meson multiplet • Introduce a chiral multiplet to couple it with • Using and , construct the effective Lagrangian from the Nambu-Jona-Lasinio four-quark model NFQCD10

  19. Method2 – Bardeen, Eichten, Hill – 2Their numerical results MeV 42 196 • Decay width of open charmed mesons NFQCD10

  20. Method2 – Bardeen, Eichten, Hill – 3 0+ 0- • Intermultiplet transitions between • Approximation • Amplitude is given by • hence (eta-pi mixing is expressed in current quark) NFQCD10

  21. Method2 – Bardeen, Eichten, Hill – 4 0- 1- • Intramultiplet transitions between member in • Approximation • Width is given by (phase space gives one more factor ) • For Ds mesons, should be multiplied NFQCD10

  22. Effects of wave function 0+ 0- • Intermultiplet transitions between • Approximation • Amplitude is given by • hence (eta-pi mixing is expressed in current quark) NFQCD10

  23. Method2 – Bardeen, Eichten, Hill – 5 • Radiative decays • Intermultiplet transitions: E1 transitions • Intramultiplet transitions: M1 transitions NFQCD10

  24. Method1 – Di Pierro, Eichten – 1 • Effective interaction NFQCD10

  25. Method1 – Di Pierro, Eichten - 2 Free pion field approximation • Transition matrix element • which is obtained by expanding exponential function: • This is proportional to the spherical Bessel function No phase factor NFQCD10

  26. Our Method – 1 • Effective interaction for a coupling with a chiral multiplet NFQCD10

  27. Our Method – 2 • Wave functions at the lowest order • These depend on the quantum number k NFQCD10

  28. Our Method – 3 • Results of radiative decay for the processes • New sum rule using HQS NFQCD10

  29. Our Method – 4 • Similar sum rule also holds for one pion decay • But it gives vanishing results • May be non-vanishing by Lorentz-boosting the wave function NFQCD10

  30. Summary • Formulate heavy-light meson decay into another heavy-light+pion/photon • Different from Bardeen, Eichten, and Hill and from Di Pierro and Eichten • Find a new sum rule based on heavy quark symmetry • May be applied to other systems which include at least one heavy quark NFQCD10

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