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)

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

Polarization Fractions Belle Collab, PRL 91 (03) 201801 PRL 91 (03) 221801 hep-ex/0408141 BaBar Collab., PRL 91 (03) 171802 PRD 69 (04) 031102 hep-ex/0408017 Logitudinal polarization seems to be dominant in B VV modes, except for

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

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

The decay rate is: and the three polarization fractions:

Effective weak hamiltonian inducing transitions QCD penguins EW penguins Dipole operators

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

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

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

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

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

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

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

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

Resulting matrix elements for kaon vertices

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

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

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:

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

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?

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

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