Radiative m1 transitions of heavy mesons in light front quark model
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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

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Radiative m1 transitions of heavy mesons in light front quark model

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


Radiative m1 transitions of heavy mesons in light front quark model

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


Radiative m1 transitions of heavy mesons in light front quark model

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

Covariant vs. time-ordered diagram

LF nonvalence

LF valence


Boost in equal t and equal t

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


3 model description prd59 074015 99 plb460 461 99 by choi and ji

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


Radiative m1 transitions of heavy mesons in light front quark model

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


Radiative m1 transitions of heavy mesons in light front quark model

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


Radiative m1 transitions of heavy mesons in light front quark model

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


Radiative m1 transitions of heavy mesons in light front quark model

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


Radiative m1 transitions of heavy mesons in light front quark model

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


Radiative m1 transitions of heavy mesons in light front quark model

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


Radiative m1 transitions of heavy mesons in light front quark model

  • 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.

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