Beijing, QNP091 Matthias F.M. Lutz (GSI) and Madeleine Soyeur (Saclay) Irfu/SPhN CEA/ Saclay Irfu/SPhN CEA/ Saclay Dynamics of strong and radiative decays of D s -mesons in the hadrogenesis conjecture Nucl. Phys. A 813 (2008) 14

Beijing, QNP092 Irfu/SPhN CEA/ Saclay Irfu/SPhN CEA/ Saclay 1. D s -mesons: spectrum and decays 2. Dynamical generation of D s -mesons 3. Isospin-violating strong decays 4. Radiative decays 5. Towards the next steps

Beijing, QNP093 Irfu/SPhN CEA/ Saclay 1. D s -mesons: spectrum and decays 143 MeV 144 MeV ││││ ││││ DK MeV Ds±Ds± _ cs _ cs

Beijing, QNP094 Irfu/SPhN CEA/ Saclay The positive parity states appear at lower energies than expected in the simple constituent quark model (by ~160 MeV for the 0 + ) Question: Origin of the additional attraction? Framework: Effective field theory constrained by QCD symmetries (chiral and heavy-quark) M. A. Nowak et al., Phys. Rev. D 48 (1993) 4370; Acta Phys. Polon. B35 (2004) 2377 W.A. Bardeen and C.T. Hill, Phys. Rev. D 49 (1994) 409; D 68 (2003) ● Both symmetries are approximate (m s ≠ 0, m c ≠ ∞) → subleading contributions important ● Spectrum:

Beijing, QNP095 Irfu/SPhN CEA/ Saclay ● Strong decays: Isospin-violating D* s0 (2317) → D s (1968) π 0 (0 + → 0 - π 0 ) D* s1 (2460) → D* s (2112) π 0 (1 + → 1 - π 0 ) Question: Isospin-mixing mechanism? Dominant contribution to the (poorly determined) total widths Γ [D* s0 (2317)] < 3.8 MeV and Γ [D* s1 (2460)] < 3.5 MeV Γ [D* s0 (2317)] and Γ [D* s1 (2460)]: Key quantities to measure (normalizations)

Beijing, QNP → 1 - γ 1 + → → 0 - γ 1 + → 1 - γ 1 + → 0 + γ (BABAR, Belle, CLEO) Irfu/SPhN CEA/ Saclay ● Electromagnetic decays: Question: Mechanisms of the decay processes?

Beijing, QNP097 ● Chiral coupled-channel dynamics applied to the generation of heavy-light meson resonances with J π = 0 + and J π = 1 + S-wave scattering of Goldstone bosons (0 - ) off heavy-light ‘ground’ states Pseudoscalars (0 - ) : {D 0 (1864), -D + (1869), D s + (1968)} → 0 + ¯ ¯ ¯ SU(3) antitriplet cu cd cs Vectors (1 - ) : {D* μ 0 (2007), -D* μ + (2010), D* sμ + (2112)} → 1 + Basic conjecture: Meson resonances not belonging to the large N c ground states of QCD are generated by coupled-channel dynamics E.E. Kolomeitsev and M.F.M. Lutz, Phys. Lett. B 582 (2004) 39 J. Hofmann and M.F.M. Lutz, Nucl. Phys. A 733 (2004) 142 Irfu/SPhN CEA/ Saclay 2. Dynamical generation of D s -mesons « Hadrogenesis »

Beijing, QNP098 Channels for D* s0 -meson: η D s +, π 0 D s +, K 0 D +, K + D 0 Channels for D* s1 -meson: η D* s +, π 0 D* s +, K 0 D* +, K + D* 0 Dynamical assumptions: ● Approximate (spontaneously broken) chiral SU(3) L x SU(3) R symmetry for light quarks (m u, m d, m s ≲ Λ QCD ) → Effective Lagrangian consistent with chiral symmetry (interaction of Goldstone bosons with D-mesons) ● Approximate heavy-quark symmetry m c > Λ QCD Spin–independence of heavy quark interactions → Constraints on couplings involving scalar and vector D-mesons Irfu/SPhN CEA/ Saclay

Beijing, QNP099 Irfu/SPhN CEA/ Saclay Irfu/SPhN CEA/ Saclay Other approaches based on effective Lagrangians F. Guo et al., PLB 666 (2008) 251 ; PLB 647 (2007) 133; PLB 641 (2006) 278. Heavy chiral unitary Lagrangian : Broken SU(4) symmetry : D. Gamermann et al., PRD 76 (2007) ; Eur. Phys. J. A 33 (2007) 119; PRC 76 (2007) Phenomenological Lagrangian : A. Faessler et al., PRD 76 (2007) and

Beijing, QNP0910 Chiral Lagrangian (Weinberg-Tomozawa) at leading order (0 - ) with χ 0 : Goldstone boson mass matrix M 0- 2 : 0 - D-meson mass matrix f : pion decay constant (90 MeV) [chiral symmetry breaking scale] Irfu/SPhN CEA/ Saclay

Beijing, QNP0911 Chiral Lagrangian at leading order (1 - ) Important technical point: Use the tensor field representation of massive vector fields to arrive at manifestly gauge-invariant expressions for radiative processes E. Kyriakopoulos, Phys. Rev. D4 (1971) 2002, D6 (1972) 2207 G. Ecker et al., Nucl. Phys. B 321 (1989) 311 Generation of D s * states D* s0 (2317) and D* s1 (2460) _ _ _ Chiral SU(3) multiplicities: 8 x 3 = Strong attraction in antitriplet (0 +, 1 + ) and sextet states Irfu/SPhN CEA/ Saclay

Beijing, QNP0912 Chiral correction terms at order Q χ 2 s- and u-channel exchange of D-mesons Vertices constrained by experiment (D*→Dπ) and heavy quark symmetry Local counter terms Parameters constrained by the ( ) mass gap, heavy quark symmetry and large N c QCD → 1 free parameter left (tuned to reproduce the 0 + and 1 + masses) Irfu/SPhN CEA/ Saclay

Beijing, QNP0913 Irfu/SPhN CEA/ Saclay Irfu/SPhN CEA/ Saclay Numerical results for the masses: Heavy-quark and large N c limits: D* s0 (2317) → 2330 MeV D* s1 (2460) → 2448 MeV

Beijing, QNP0914 Physical origin: m u ≠ m d J. Gasser and H. Leutwyler, Nucl. Phys. B 250 (1985) 465 Induced isospin mixing transitions: ● π 0 - η mixing G.-L. → ε = 0.01 ● K 0 D + - K + D 0 mixing Both effects act constructively A. Faessler et al., PRD 76 (2007) Irfu/SPhN CEA/ Saclay 3. Isospin-violating strong decays

Beijing, QNP0915 Strong decay widths of the D* s0 (2317) and D* s1 (2460) Numerical results : Probe coupled-channel dynamics and ε parameter Γ{D* s0 (2317) → π 0 D s } ≈ Γ{D* s1 (2460) → π 0 D * s } ≈ 0.14 MeV (Exp: < MeV) Factor 20! Similar to F..K. Guo et al., PLB 666 (2008) 251: Γ{D* s0 (2317) → π 0 D s }= 0.18 ± 0.11 MeV Irfu/SPhN CEA/ Saclay

Beijing, QNP0916 Lagrangian for electromagnetic interactions at chiral order Q χ 2 ● Gauging of Lagrangian for hadronic interactions (3-point vertices in chiral correction terms essential) ● Correction terms of chiral order Q χ 2 proportional to F μν corresponding to 4-point vertices (D * Dπγ) ● Correction terms of chiral order Q χ 2 proportional to F μν describing anomalous processes coresponding to 3-point vertices (D * Dγ) + magnetic moments of charmed vector mesons ● Investigate dynamical role of terms involving light vector mesons (K*, φ) in the decays Irfu/SPhN CEA/ Saclay 4. Radiative decays

Beijing, QNP0917 = photon ■ = sum of buble diagrams coupled - channel states D* s0 (2317) and D* s1 (2460) Irfu/SPhN CEA/ Saclay

Beijing, QNP0918 ● Specific dynamical effects - Full relativistic loop computations induce significant deviations from heavy quark symmetry (expected from m c ) - ηD s (ηD s * ) channel important - Large cancellations between ηD s and KD channels - Dynamical role of the light vector mesons in the radiative decay processes important Irfu/SPhN CEA/ Saclay

Beijing, QNP0919 Range of predictions for ‘natural’ sets of parameters Irfu/SPhN CEA/ Saclay

Beijing, QNP0920 Summary of the present work: ● A consistent description of the D* s0 (2317) and D* s1 (2460) mesons (masses, isospin-violating and radiative decays) can be achieved in the hadrogenesis conjecture with reasonable values of the parameters once light vector mesons are included in the radiative decay dynamics. 5. Towards the next steps Spectrum: Linked to chiral and heavy quark symmetries and to coupled –channel dynamics Strong isospin-violating decays : reflect largely KD component Radiative decays: sensitive to ηD s and KD

Beijing, QNP0921 Next steps: ● Improve data on isospin violating and radiative widths of the D* s0 (2317) and D* s1 (2460) Strong widths: Theory: keV Experiment: < 3-4 MeV Panda? ● Improve knowledge on the couplings Data: D * → Dπγ decay Theory: unquenched lattice QCD calculations