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Radiative M1-transitions of heavy mesons in light-front quark model. Ho-Meoyng Choi(KNU) Ref: PRD 75, 073016(07). Outline. Motivation Why Light-Front? 3. Model Description -Light-front(LF) quark model(LFQM)
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Radiative M1-transitions of heavy mesons in light-front quark model Ho-Meoyng Choi(KNU) Ref: PRD 75, 073016(07) Outline • Motivation • Why Light-Front? • 3. Model Description • -Light-front(LF) quark model(LFQM) • 4. Radiative V(3S1) P(1S0)g decays of heavy-flavored mesons • 5. Conclusion The 4th international Conference of Flavor Physics, Beijing(Sep. 24~28, 2007) 1
Our Light-Front Quark Model(LFQM) based on the QCD-motivated effective Hamiltonian has been successful in describing various exclusive heavy meson decays : (I) Leptonic P ln decays (II) Semileptonic P Pln decays, (III) Rare B Kl+l- decays, [Refs: Choi and Ji: PLB 460,461(99), PLB513,330(01); Choi, Ji, and Kisslinger: PRD 65, 074032(02)] decay constants, weak form factors VCKM 1. Motivation Exclusive heavy meson decays has provided useful testing ground of SM and QCD dynamics: Experiment: easy to access Theory: difficult to understand due to the nonperturbative QCD dynamics Phenomenological approache to NPQCD • To extend the applicability of our LFQM, we thus investigate (I) vector meson decays constants (II) magnetic dipole V(3S1) P(1S0)g decays of heavy-flavored mesons such as (D,D*,Ds,D*s,hc,J/y) and (B,B*,Bs,B*s,hb,U) 2
Equal t Equal t k·q=(k+q-+k-q+)/2-k^·q^ k·q=k0q0-k·q k0=Ök2+m2 k-=(k2^+m2)/k+ (k+=k0+k3) Equal t Equal t k1+ k1 k2+ k2 k3+ k3 k1+ + k2+ + k3+=0 k1+k2+k3=0 2. Why Light-Front? Not allowed ! since k+>0
Covariant vs. time-ordered diagram LF nonvalence LF valence
z t Boost in equal t and equalt Y(x,k^) :Boost invariant! v t’= eft g= coshf bg= sinhf ct’=g(ct+bz) z’=g(z+bct) b=v/c and g=1/(1-b2)1/2
Linear (br2) HO 3. Model DescriptionPRD59, 074015(99); PLB460, 461(99) by Choi and Ji Key idea of our LFQM: Using the variational principle to the QCD-motivated effective Hamiltonian, we fix the model parameters! Variational Principle Input parameters for the linear confining potential : mu=md=220 MeV b=0.18 GeV2 Relativistic spin-orbit w.f. 3
Experiment Linear potential M1 transition Harmonic oscillator (HO)potential Input masses Optimized model parameters(in unit of GeV) and meson mass spectra Current theoretical estimates for hb mass (from PQCD and lattice NRQCD): Dm(=MU-Mhb)=34~141 MeV 4
Heavy meson decay constants (fDs/fD)=1.18[1.20](Exp. 1.23+0.11+0.04); (fJ/y/fhc)=0.91[0.90](Exp. 0.81+0.19) 5
g* Transition form factor: q2=-Q2 V P x,k^ Decay width for real photon(g): x,k^+(1-x)q^ G(V Pg) = (a/3)F(0)2 (M2V-M2P)3/(2MV)3 yP yV LF in Drell-Yan-West q+(=q0+q3)=0 frame Hadronic matrix element with ‘+’-current: <P’|J+|P,h=+> =Sjeejò[dx][d2k^] y*P(x,k^+(1-x)q^) yV(x,k^) analytic continuation F(Q2) F(q2) (in spacelike) (in timelike) 4. Magnetic dipole(M1) transition V(13S1) P(11S0) g* 6
D*0D0 B*+B+ J/y hc Destructive c-quark contribution Uhb D*+sD+s B*0sB0s Restoration of SU(3) symmetry D*+D+ B*0B0 Transition form factors F(q2) (going beyond the static results at q2=0) 7
NRQCD Predictions for charmonium[Brambilla,Jia, Vairo, PRD73, 054005(06)] G(J/yhcg) = 2.83 keV G(J/yhcg) = (1.50+1.0) keV (in leading order of v) (up to v4) Decay widths and Br for V Pg. Br(D*+ D+g) Br(D*0 D0g) G(D*+ D+g) Gtot(D*0) Gth(D*0 D0g)Gtot(D*+) (relativistic corrections) = Prediction of the unmeasured full widths for D*0 and D*+s Gtot(D*0) = (55 + 6) keV [Gexp(D*0)<2.1 MeV] Gtot(D*+s)=(0.19 + 0.01)keV[Gexp(D*+s)<1.9MeV] 8
Dependence ofG(Uhbg) on Dm(=MU-Mhb) May help to determine the hb mass! G(V Pg) = (a/3)F(0)2 (M2V-M2P)3/(2MV)3 ~ (Dm)3 Current theoretical estimates for hb mass (from PQCD and lattice NRQCD): Dm(=MU-Mhb)=34~141 MeV 9
Our LFQM constrained by the variational principle has been successful in describing various exclusive heavy meson decays: • (1) Leptonic P ln decays(i.e. decay constants of pseudoscalar mesons) • (2) Semileptonic P Pln decays, • (3) Rare B Kl+l- decays, • Future works for other exclusive process: • Semileptonic P V transitions • Rare B decays such as B K* • Other hadronic decays Our LFQM is quite useful to calculate the hadronic matrix elements ! 5. Conclusions • In this work, we extend our LFQM to (4) Decay constants of vector mesons (5) Decay rates for magnetic dipole(M1) transitions V Pg • -G(J/yhcg ) and G(D*+ D+g) fall within the experimental error bars. • Unmeasured full widths for D*0 and D*+s was estimated. • G(Uhbg ) is very sensitive to the value of Dm=MU-Mhb, which may help to • determine the mass of hb experimentally. 10