Generalized analysis on B K r within and
Generalized analysis on B K* r within and beyond the Standard Model Sechul OH (Yonsei University) in collaboration with C. S. Kim, C. Sharma, R. Sinha, Y. Yoon (Phys. Rev. D 76, 074019 (2007)) Yong. Pyong, February 26, 2008 1
l B K* r is a vector version (B V V) of B K p (B P P) l The dominant quark level subprocesses are loop (penguin) processes b s penguin is sensitive to NP q q l We expect that NP contribution to B K* r has the same nature as that of B K p ( Prof. C. S. Kim’s talk ) l B K* r (B V V) provides enormously many observables 2
B → V V decays from Angular Momentum Conservation in helicity basis: in the transversity basis: parallel transverse longitudinal 3
Conventional Hierarchy in B K* r Large strong penguin EW penguin Small color-suppressed tree 4
l Parameterization of decay amplitudes Hierarchy relation in the SM: Isospin relations: 5
l Observables for B K p Only 9 observables 6
l Observables Time dependent measurement: 35 independent observables (18 magnitudes + 17 relative phases) 7
Determine all the parameters in terms of observables! 36 parameters (including the weak phase g) only 35 independent observables from measurements It is only possible to solve for the parameters with respect to one parameter (e. g. , g). ( e. g. , The weak phase g can be measured in ) For now, neglect the annihilation contribution which is expected to be very small where & we set 8
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In the SM, Hierarchy relation: (1) (2) (3) 10
(1) (2) (3) The validity of these relations will help in uncovering possible NP contributions. 11
Using angular analysis, one can determine all the parameters ( in terms of ) These determined values include any NP effects that may be present. Consider NP contributing via the EW penguins: Assume that NP contributes with an amplitude (Reparameterization invariance) In this case, only and are modified by NP. 12
In the SM, to a good approximation, using flavor SU(3) symmetry, (SM part) (NP part) 4 relations with only 3 unknowns for each . 13
Therefore, it is easy to determine The NP weak phase can be obtained from the relation In fact, there are enough observables even to solve for . Not only determine NP but also test the SU(3) assumption. 14
Investigate how much sensitive to possible NP effects each observable for decays could be. Assume that NP contributing via the EW penguins. For simplicity, further assume that the SM amplitudes and are known (by additional information from somewhere, e. g. from future theoretical estimates). Thus, the SM amplitude is the only one modified by NP. (SM part) (NP part) 15
Procedure: (i) In order to determine theoretical parameters, adopt the c 2 minimization technique & use the currently available experimental data as constraints on the parameters. (HFAG) : longitudinal polarization fraction 16
(ii) [number of data] < [number of parameters] Try to fit the dominant strong penguins and their phases with , first. (iii) Assume that the SM amplitudes ( the conventional hierarchy as in ) follows within the SM: in PQCD, (iv) Using the parameters determined, calculate all the 35 observables in the SM. (v) To investigate the possible NP effects, consider two different cases. (SM part) (NP part) 17
For illustration: Very sensitive to NP: 18
For illustration: Very sensitive to NP: 19
For illustration: Very sensitive to NP: 20
For illustration: Very sensitive to NP: 21
decays are very interesting: u It is possible to determine theorectical parameters in terms of observables analytic solutions u One can test the validity of the hierarchy relations which must hold within the SM. u Useful for NP study: - NP signals can be isolated “with certain (theoretical) inputs. ” - certain observables are expected to be very sensitive to NP effects. 22
- Slides: 22