# Presentation: 249803

## PANIC05

**POWER CORRECTIONS AND CP PHASES**

**Tsung-Wen Yeh**
**National Taichung University**
**Taiwan, R.O.C.**

## CP Phases

**CP phases are defined through unitarity triangles**

- T.W. Yeh-Power corrections and CP phases

- PANIC05

## CP Phases

**unitarity**

**CP phases are defined through unitarity triangles**

- T.W. Yeh-Power corrections and CP phases

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## CP Phases 

**unitarity**

***W ******-***

***b***

***u***

***d***

**CP phases are defined through unitary triangles**

- T.W. Yeh-Power corrections and CP phases

- PANIC05

## Roadmap for CP Phases in B Physics

- R. Fleischer, PITHA 05 talk

- T.W. Yeh-Power corrections and CP phases

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## CP Phases in present status

- A. Höcker, SLAC 05 talk

- T.W. Yeh-Power corrections and CP phases

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## CP Phases in 

- M. Neubert, **JHEP 9902:014,1999** ;
**Nucl.Phys.Proc.Suppl.86:477-486,2000**

- T.W. Yeh-Power corrections and CP phases

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## CP Phases from Hadronic B Decays

**Existing strategies for extracting CP phases  from hadronic B decays requires knowledge of hadronic mechanisms**

- T.W. Yeh-Power corrections and CP phases

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## CP Phases from Hadronic B Decays

- OPE at weak scale: nonlocal operator factorized into SD Wilson Coeff. and LD local operators

**Existing strategies for extracting CP phases from hadronic B decays requires knowledge of hadronic mechanisms**

- T.W. Yeh-Power corrections and CP phases

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## CP Phases from Hadronic B Decays

- OPE at weak scale: nonlocal operator factorized into SD Wilson Coeff. and LD local operators

- RG equations : evolutions of local operators from high scale to low scale

**Existing strategies for extracting CP phases from hadronic B decays requires knowledge of hadronic mechanisms**

- T.W. Yeh-Power corrections and CP phases

- PANIC05

## CP Phases from Hadronic B Decays

- OPE at weak scale: nonlocal operator factorized into SD Wilson Coeff. and LD local operators
- RG equations : evolutions of local operators from higher scale to lower scale

**Existing strategies for extracting CP phases from hadronic B decays requires knowledge of hadronic mechanisms**

- T.W. Yeh-Power corrections and CP phases

- PANIC05

## Theories

- Theoretical Approaches based on QCD:
- QCD FA : Beneke *et al*, PRL 83, 1914(99);NPB606,245(01); NP B675, 333 (03)
- pQCD : Keum *et al, *PLB 504, 6(01); PRD 67, 054009 (03)
- SCET : Bauer *et al*, PRD 63, 114030 (01)

- Theoretical Approaches based on symmetry
- Strong isospin symmetry SU(2) : Gronau, London, PRL 65:3381(99)
- 1+ SU(3) flavor sysmtery :Buras, Fleisher, PLB360:138(95’);Charles, PRD59:054007(99’)
- Isospin + QCD FA

- T.W. Yeh-Power corrections and CP phases

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## QCD FA

- Heavy quark limit : mb >>
- Energetical final state meson : E >>
- Factorization of m.e. into hard scattering kernel and LC  DAs
- Factorization holds at O(1/ mb) and
- Extension of naive factorization, color transparency
- Automatically including rescattering phase

- T.W. Yeh-Power corrections and CP phases

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## QCD FA - Topology

**QCD FA - Topology**

- vertex

- T.W. Yeh-Power corrections and CP phases

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## QCD FA - Topology

**QCD FA - Topology**

- Penguin

- T.W. Yeh-Power corrections and CP phases

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## QCD FA - Topology

**QCD FA - Topology**

- Spectator

- T.W. Yeh-Power corrections and CP phases

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## QCD FA - Topology

**QCD FA - Topology**

- annihilation

- T.W. Yeh-Power corrections and CP phases

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## Sources of Power Corrections

**HS**-Hard Spectator

**AT**-annihilation topology

**SRG**-soft radiative gluon

**NFCG**-nonfactorizable
-     collinear gluon

**Renor**-renormalon

**CP**-charming penguin

**DG**-dynamical gluon

**FSI-**final state interaction

- T.W. Yeh-Power corrections and CP phases

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## Sources of Power Corrections

**HS**-very small

**AT**-20%

**SRG**-few %

**NFCG**-few to 10 %

**Renor**-very small

**CP**-sizable(model) or very small(LCSR)

**DG**-sinificant

**FSI-sizable(**model)

- T.W. Yeh-Power corrections and CP phases

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## QCD FA

- for i=1-4,8,10

- for i=8,10

- for i=4,6

- for i=5,7

-  Hard spectator functions diverge at end points – regularized by a model
-  twist-3 two parton effects included

- T.W. Yeh-Power corrections and CP phases

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## QCD FA

- for i=1-4,8,10

- for i=8,10

- for i=4,6

- for i=5,7

-  Hard spectator functions has no 3 parton contributions
-  Coefficient functions for O6 and O8 are corrected by 3 parton

- 3 PARTON

- T.W. Yeh-Power corrections and CP phases

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## QCD FA

-  annihilation functions contain end point divergences
- 3 parton effects can be neglected in annihilation functions

- T.W. Yeh-Power corrections and CP phases

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## Amplitudes defined in QCDFA

- T.W. Yeh-Power corrections and CP phases

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## Amplitudes defined in QCDFA

**Amplitudes defined in QCDFA**

- T.W. Yeh-Power corrections and CP phases

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## Amplitudes defined in QCDFA

**Amplitudes defined in QCDFA**

- T.W. Yeh-Power corrections and CP phases

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## Strong Phases in QCDFA

**Strong Phases in QCDFA**

- T.W. Yeh-Power corrections and CP phases

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## Slide 27

- T.W. Yeh-Power corrections and CP phases

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## Slide 28

- T.W. Yeh-Power corrections and CP phases

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- 24.9

- -21.2

- 20.9

- -16.1

- 2.2

- -13.2

- 60.5

- 1.28

- 7.3

- -47.8

- 27.9

- 15.0

- 3pt

- T.W. Yeh-Power corrections and CP phases

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- +

- +

- +

- +

- +

- +

- T.W. Yeh-Power corrections and CP phases

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## Comparison between EXPT and QCD FA

- A. Höcker, SLAC 05 talk

- LO+2PT TW3 contributions for
-  theoretic uncertainty are large due to input parameters and higher order corrections

- T.W. Yeh-Power corrections and CP phases

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## Exploring CKM in QCD FA

- 2 parton

- 3 parton

- R

- R

- T.W. Yeh-Power corrections and CP phases

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## Exploring CKM in QCD FA

- Inputs: R* and εexp

- T.W. Yeh-Power corrections and CP phases

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## 2 parton

- 3 parton

- T.W. Yeh-Power corrections and CP phases

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## Exploring CKM in QCD FA

- Assume

- PDG2004

- BN01

- T.W. Yeh-Power corrections and CP phases

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## 2 parton

- 3 parton

- 3 parton -2 parton

- T.W. Yeh-Power corrections and CP phases

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## 3 parton

- 2 parton

- HFAG 05’

- T.W. Yeh-Power corrections and CP phases

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## 3 parton

- 2 parton

- T.W. Yeh-Power corrections and CP phases

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## 3 parton

- 2 parton

- T.W. Yeh-Power corrections and CP phases

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## 3 parton

- 2 parton

- T.W. Yeh-Power corrections and CP phases

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## 2 parton

- 3 parton

- T.W. Yeh-Power corrections and CP phases

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## 3 parton

- 2 parton

- T.W. Yeh-Power corrections and CP phases

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## 3 parton

- 2 parton

- T.W. Yeh-Power corrections and CP phases

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## I will only discuss power corrections in QCDF

- T.W. Yeh-Power corrections and CP phases

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## Hard Spectator Gluons

- Radiative gluons connecting the spectator quark and the partons of  the emitted meson
- Gluons carry momentum of scale
- except        and           ,  other 8 effective operators participate
- Amplitudes  are of                            ~ few %  of Tree

- T.W. Yeh-Power corrections and CP phases

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## Annihilation Topology

- Radiative gluons  involve in annihilation diagrams
- Gluons carry momentum of scale
- except          ,  other 10 effective operators participate
- Amplitudes  are of                            ~ few -- 20% of Tree
- Uncertainty ~30-40% due to a regularization for end-point divergence

- T.W. Yeh-Power corrections and CP phases

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## Nonfactorizable soft Gluons

- soft gluons  involve in vertex diagrams
- Gluons carry momentum of scale
- except          ,  other 10 effective operators participate
- Significant for some PP and VP with
- Require Sum Rule assumptions (optical theorem for correlators)

- K.W. Yang,PRD69 (2004) 054025

- T.W. Yeh-Power corrections and CP phases

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## Collinear Expansion

- QCD factorization, LO partons can carry only collinear momenta into hard scattering center
- systematical expansion of parton momenta w.r.t. coll. momenta
- non-collinear parts of parton momenta as higher order effects [EFP, 82,83]
- parton model + Feynman diagram calculation techniques [J. Qui,  90,92]
- only dynamical gluon contributions included
- exclusive process applicable [T.W. Yeh, 00,02,]

- S'

- v

- v=0

- +

- T.W. Yeh-Power corrections and CP phases

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## Dynamical Gluons

- Collinear gluons of the emitted light meson enter into the hard scattering center
- Scale analysis indicate that collinear partons dominate
- FDG ~                     ,  while NFDG ~
- FDG corrections enhanced by their hard kernel ~ 50 %  of two parton twist-3 contributions

- T.W. Yeh-Power corrections and CP phases

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## Vertex Diagrams

- Adding Collinear gluon to the vertex diagrams in QCD FA:
- 112  diagrams
- Up to            , only 8 factorizable DG diagrams remain
- Only            participate and collinear (soft) div.’s cancelled out
- About 20 % of two parton twist-3 vertex corrections

- T.W. Yeh-Power corrections and CP phases

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## Hard Spectator Diagrams

- Adding Collinear gluon to the vertex diagrams in QCD FA:
- 40  diagrams, NFDG ~ FDG/mb
- Up to            , only 4 FDG diagrams remain
- Only            participate at twist-3 and pair cancellations lead to a vanishing result

- T.W. Yeh-Power corrections and CP phases

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## Annihilation Diagrams

- Adding Collinear gluon to the annihilation diagrams in QCD FA:
- 96  diagrams, NFDG ~ FDG/mb
- Up to            , only 16 FDG diagrams remain
- Only            participate at twist-3
- about 1.5% of 2 parton twist annihilation contributions

- T.W. Yeh-Power corrections and CP phases

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## Penguin Diagrams

- Adding Collinear gluon to the penguin diagrams in QCD FA:
- 42  diagrams, NFDG ~ FDG/mb
- Up to            , only 4 FDG diagrams remain
- Only            participate

- T.W. Yeh-Power corrections and CP phases

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## Summary

**We have calculated the        twist-3 contributions to**                    **up to one loop order**
**The effects of 3 parton on strong rescattering phases are small**
**The effects of 3 parton on extracting the CP phases are small in QCD FA approach**
**The effects of 3 parton on enhancement of branching ratios are significant**
**Only dynamical gluon corrections are investigated**
**Other power suppressed corrections may exist, but still lack useful theoretical tools**
**More detailed analysis are undertaken**
**Applying and extending present calculations to other processes may clearly classify how much power corrections can contribute**
**More future works are necessary**

- T.W. Yeh-Power corrections and CP phases

- PANIC05