YuKuo Hsiao Academia Sinica In collaboration with H

Yu-Kuo Hsiao Academia Sinica In collaboration with H. Y. Cheng, C. Q. Geng and Chun-Hung Chen Feb. 26 , 2008 Outline: • Introduction • Formalism • Results • Summary

The features of the 3 -body baryonic B decays • B meson is heavy enough to create baryon pairs. • 3 -body>2 -body: against three-monks-sharing-no-water principle • Large forward-backward angular distribution asymmetries of more than 40%. • Possible large CP violation around 20% in B→pp. K*. • T-violation can be studied due to their rich spin structures.

3 -body>2 -body in baryonic B decays

• 3 -body>2 -body due to the threshold effect: The spectrum peaks as the dibaryon invariant mass gets close to the threshold (m 1+m 2). It was first conjectured by W. S. Hou and A. Soni in PRL 86, 2732 (2001). This effect manifests in all charmless cases.

• Theoretical calculations: The pole model: using the resonance as the pole around dibaryon rest masses. The p. QCD counting rules: with the expansion of 1/t^n to account for hard gluon propagators, which attach to valence quarks in baryon pairs. There are some other methods, such as the fragmentation and the final state interaction.

The forward-backward angular distribution asymmetry

• As we know, there are no such things as the asymmetries of more than 20% but for 3 -body baryonic cases. Take the example of B-> K ee : the partial decay width is in the form of where To create the b term, it is necessary to have new physics to apply scalar-type currents, since the electron pair only has a vector-type coupling in SM. This is how we test new physics. However, to explain the 3 -body baryonic cases =>a unusual spin structure

Theoretical description for The forward-backward angular distribution asymmetry • • Fragmentation (Rosner) Short-distance picture (H. Y. Cheng and K. C. Yang) Partial wave (Suzuki) p. QCD counting rules (Geng and Hsiao)

Summary for angular distribution Fragmentation Short-distance Partial wave p. QCD counting pp. K (o) (x) (o) ppπ (x) (o) (? ) (o) Λpγ (x) (o) -- Λpπ (x) (x) --

T-violation In 3 -body baryonic B decays, dibaryon’s spin strutures with a meson momentum can create T-odd triple product PRD 72, 037901 (2005) and ar. Xiv: 0801. 0022 [hep-ph] by Geng and Hsiao

Direct CP violation • Direct CP violation: We found B->pp. K* is free of the hadron structure, and this leads to large and stable prediction for direct CP violation. PRL 98, 011801 (2006) by Geng, Hsiao and Ng. the data from Babar [PRD 76, 092004(2007)] is. 32± 0. 13± 0. 05.

Motivation to study charmful 3 -body baryonic B decays • similar behaviors in charmful cases: Threshold effect pp. D* Λp. J/ψ Angular distribution asymmetry The Dalitz plot of B->pp. D and B->pp. D* with asymmetric distributions can be recognized as a nonzero angular distribution asymmetries.

• So, we expect that the method for the charmless cases could also be used for the charmful cases. • The study of the charmful cases may clarify the puzzle of the angular distribution in the charmless cases, because they are supposed to be related by the same baryonic form factors.

Advantages for the charmful cases 1. The charmful 3 -body baryonic B decays are simpler: Tree level dominates Without scalar-type currents 2. Brs are of order 10^{-4} to 10^{-6}, larger than the charmless ones. Easier to measure Easier to trace angular distribution/Dalitz Plot asymmetries

Who have studied the charmful 3 -body baryonic B decays? [with the charm mesons in the final states] • C. K. Chua, W. S. Hou and S. Y. Tsai: PRD 65, 034003 (2002) Tsai’s thesis (2005) • H. Y. Cheng and K. C. Yang: PRD 66, 094009 (2002) • Vincenzo Laporta ar. Xiv: 0707. 2751 • Angular distribution asy • Dalitz plot asy exp’t (x) (o) ther’y (x)

Branching ratios

Branching ratios

Effective quark level Hamiltonian

Amplitudes and decay modes: 1. Current type

Amplitudes and decay modes: 2. Transition type

Amplitudes and decay modes: 3. Hybrid type

Meson decay constants

B to P(V) transition form factors

0 to BB Form Factors

0 to BB Form Factors n Some of them are suppressed.

B to BB transition Form Factors

B to BB transition Form Factors

B to BB transition Form Factors

parameters

a 1 and a 2

Current type Data

transition type with D and D* Data

transition type with J/Ψ Data

Hybrid type

Summary The data for charmful cases can be explained by using the information from the charmless cases. Some modes are predicted to be accessible to the B factories, such as

Thank you!