1. Polarization in charmless B VV decays
EURIDICE Midterm Collaboration Meeting
Frascati, February 2005
Polarization in charmless B VV decays
Fulvia De Fazio, INFN BARI
Experimental situation
Polarization fractions in the HQ limit
Rescattering effects
Perspectives
Based on work in collaboration with
P. Colangelo (INFN Bari) and T.N. Pham (Ecole Polythecnique)

2. + annihilation in the charged modes
Experimental data
Branching ratios
Different topologies s b b u
+ annihilation in the charged modes

3. Polarization Fractions
Belle Collab, PRL 91 (03)
PRL 91 (03)
hep-ex/
BaBar Collab., PRL 91 (03)
PRD 69 (04)
hep-ex/
Logitudinal polarization seems to be dominant in B VV modes,
except for

4. Polarization in factorization-based approaches
Since the B meson is spinless, the two vector mesons
share the same helicity.
Example
S-wave
D-wave
P-wave transition

5. The three helicity amplitudes can be written in terms of
In the transversity basis, one uses the following combinations of

6. The decay rate is:
and the three polarization fractions:

7. Effective weak hamiltonian inducing transitions
QCD penguins
EW penguins
Dipole operators

8. The factorized amplitude can be written as:
Combination of
Wilson coefficients
f decay constant
B to K* form factors

9. Behaviour of the polarization fractions for large values of MB:
In the limit and for
giving
J. Charles et al, PRD (99)

10. Present experimental data indicate effects beyond factorization
Use of generalized factorization does not modify the polarization fractions,
since it amounts to perform the substitution
of the parameters ai with effective ones, which cancel out in the ratios
Which effects can explain the small fraction fL in
Finite mass corrections
Effects beyond factorization
Effects beyond the Standard Model

11. Ratios of B to K* form factors in different theoretical frameworks
1,2 and 3 s
regions using
Belle data
Average of
Belle and
BaBar data
QCDSR Quark Model BSW LCSR

12. Rescattering effects
The process can take contribution from rescattering
of charmed intermediate states, induced by the process
Such a contribution should be sizable, since
it involves current-current operators with Wilson coefficients of O(1),
while coefficients of penguin operators are of 0(10-2)
there is no CKM suppression since

13. f
Typical diagram B K*
Different intermediate states contribute
to different polarization amplitudes
Considering only pseudoscalar and vector charmed mesons,
intermediate states comprising
1 vector + 1 pseudoscalar mesons contribute to P-wave transition
2 pseudoscalar mesons contribute to
2 vector mesons contribute to

14. Weak vertex B
For this transition factorization is not expected to hold
(B M1M2 heavy mesons)
However, there is experimental evidence that the calculation of the amplitude
using factorization reproduces the main features of the modes
Luo, Rosner 2001
Isgur-Wise
Form factor

15. In the heavy quark mass limit, interactions of heavy mesons with
Strong vertices
In the heavy quark mass limit, interactions of heavy mesons with
light vector mesons can be described thorugh the effective lagrangian
All the couplings can be expressed in terms of two constants:
QCD sum rules +
Vector meson dominance

16. Resulting matrix elements for kaon vertices

17. Off-shellness of the exchanged charmed mesons
can be taken into account by writing the various couplings as
functions of the variable t
L unknown parameter
Also the sign between the factorized amplitude and
the rescattering contribution is unknown.
One can therefore fix L=2.3 GeV and analyse the sum:
and include the uncertainty on L in the variation of the parameter r

18. Results Exp data Using the B K* form factors
P. Colangelo, T.N. Pham,FDF,
PLB 04
Exp data
Using the B K* form factors
obtained using light cone QCDSR
Using the B K* form factors
obtained using three point QCDSR

19. Transverse polarization fractions:
A contribution of the rescattering amplitude
is necessary to obtain the measured BR
For: r=0.08 a small longitudinal fraction
is obtained:
Transverse polarization fractions:
P. Colangelo, T.N. Pham, FDF
PLB 597 (04) 291
The estimated polarization fractions are compatible with data.
Notice however the hierarchy:

20. Rescattering effects can modify the helicity amplitudes
in penguin dominated decays
The numerical results depend on the interplay between
Wilson coefficients, form factors and rescattering amplitude
What do we expect for polarization fractions in other modes?
Rescattering effects are too small to affect the observed B rr decays:
but the Wilson coefficients for
current-current operators are O(1)
FSI could contribute to Cabibbo or colour-suppressed decays
and other penguin-induced B VV modes

21. Explicit calculation of rescattering contribution gives
smaller than the 2003 data
Rescattering effects can reproduce a small fL for
at the price of having a small value for the longitudinal
polarization fraction in as well
A small longitudinal fraction in
and a large longitudinal fraction in
cannot be simultaneously reproduced including
a rescattering mechanism.
Are new effects required?

22. BABAR BELLE More recent data (August 2004)
New data seem to indicate lower values for the longitudinal
polarization fraction in as well

23. Conclusions
Experimental data indicate that the longitudinal
polarization fraction in is
suggesting deviations from factorization-based
approaches in the HQ limit.
Effects beyond factorization can be due to rescattering
through intermediate charmed resonances,
which differentiate among the three polarization fractions
Such effects can reproduce a small fL in
predicting an analogously small fL in
Recent data seem to support this indication
More precise data would be able to understand whether
B VV decays can be accomodated within the SM or
whether NP effects are required