Yu-Kuo Hsiao Academia SinicaIn collaboration with

H.Y. Cheng, C.Q. Geng and Chun-Hung ChenFeb. 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→ppK*.

• 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 The spectrum peaks as the dibaryon invariant mass gets close to the

threshold (m1+m2).threshold (m1+m2).

It was first conjectured by W.S. Hou and A. Soni in PRL86,2732 (2001).It was first conjectured by W.S. Hou and A. Soni in PRL86,2732 (2001).

This effect manifests in all charmless cases.This effect manifests in all charmless cases.

• Theoretical calculations:

The pole model: using the resonance as the pole around dibaryon rest masses.

The pQCD counting rules: with the expansion of 1/t^nto 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 sc

alar-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)• pQCD counting rules (Geng and Hsiao)

Summary for angular distribution

ppK ppπ Λpγ ΛpπFragmentation (o) (x) (x) (x)

Short-distance (x) (o) (o) (x)

Partial wave (o) (?) (o) (x)

pQCD counting (o) (o) -- --

In 3-body baryonic B decays, dibaryon’s spin strutures with a meson momentum can create T-odd triple product

PRD72, 037901 (2005) and arXiv:0801.0022 [hep-ph] by Geng and Hsiao

T-violation

• Direct CP violation: We found B->ppK* is free of the hadron structure, and this leads to large and stable prediction for direct CP violation.

PRL98, 011801 (2006) by Geng, Hsiao and Ng.the data from Babar [PRD76, 092004(2007)] is .32±0.13±0.05.

Direct CP violation

• similar behaviors in charmful cases:Threshold effect

ppD ppD* ΛpJ/ψ

Angular distribution asymmetry The Dalitz plot of B->ppD and B->ppD* with asymmetric distributions

can be recognized as a nonzero angular distribution asymmetries.

Motivation to study charmful 3-body baryonic B decays

• 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.

1. The charmful 3-body baryonic B decays are simpler:Tree level dominatesWithout scalar-type currents

2. Brs are of order 10^{-4} to 10^{-6}, larger than the charmless ones.Easier to measureEasier to trace angular distribution/Dalitz Plot asymmetries

Advantages for the charmful cases

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:

PRD65, 034003 (2002)

Tsai’s thesis (2005)• H.Y. Cheng and K.C. Yang:

PRD66, 094009 (2002)• Vincenzo Laporta

arXiv: 0707.2751

exp’t ther’y • Angular distribution asy (x) (x)• Dalitz plot asy (o) (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 Meson decay constants

B to P(V) transition form factors

0 to BB Form Factors

0 to BB Form Factors0 to BB Form Factors

Some of them are suppressed.Some of them are suppressed.

B to BB transition Form Factors

B to BB transition Form FactorsB to BB transition Form Factors

B to BB transition Form FactorsB to BB transition Form Factors

parametersparameters

a1 and a2

DataData

Current type

DataData

transition type with D and D*

DataData

transition type with J/Ψ

Hybrid typeHybrid 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!