# Presentation: 477024

## Charmless Hadronic BPP decays in the context of SU(3) symmetry

**Denis  Suprun**
**Brookhaven National Lab**

## Motivation

**	****	****	****	****sin2β=****0.685±0.032**
**	****from B********K****S**** based upon BaBar’s and Belle’s data (LP05)**
**	****	****           ****era of precision measurement**
**	****	**
**We also want to observe ****direct CPV**** ****in B system**** and to check whether it is consistent with SM expectation**
**	****BaBar and Belle announced first observation of direct CPV:**
**	****   ****	****             ****A****CP****(π****-****K****+****) = -0.114 ******** 0.018   **
**Most branching ratios of charmless B ******** PP and PV are currently measured with errors about 10%, **
**	****	****	****	****	****i.e. ****~5% errors in amplitude**

**Motivation**

## Charmless B decays 

- Relatively rare decays with branching ratios of the order 10-5
- Wealth of new increasingly precise measurements
- Many of them involve interference of a tree and a penguin amplitude with a weak phase ***γ*** between them
- Nonzero (mod ***π***) strong phases are required for *CP* Violation
- 	Are well suited to
- constrain ***γ***
- determine the magnitude of penguin contributions
- get information on strong phases

## CKM Matrix and Unitarity Triangle

## CKM Matrix and B Physics

** ****The ultimate goal of studies in B physics is not only to achieve precision measurements of the above parameters, but to discover New Physics**
** ****One way to detect New Physics is to perform consistency checks for the sizes and phases of the CKM elements**

**CKM Matrix and B Physics**

## CKM Fitter and UT Fit results

**CKM Fitter, indirect: **
***	******γ=(59+7-13)******o***

**UT Fit, indirect: **
***	******γ=(57.9****±****7.3)******o***

**Direct measurements: **
***	******γ=(63+15-12)******o***

## B PP decays

## Dominant types of amplitudes

## Assumptions

- Neglect E, A, PA
- SU(3) flavor symmetry
- 	The only deviation from SU(3) is through decay constants in tree diagrams
- SU(3) is implied when we assume
- the same phases for ***T*** and ***T*********
- that QCD and EW penguins ***P******* and ***P****  *and*  *color-suppressed amplitudes* ****C******* and ***C**** *are related to each other as the ratio of the involved CKM parameters
- that a penguin in which a gluon couples to      has the same amplitude as those that couple to       and

## Approach

- Take all available information on charmless *B* decays to a *PP* final state and fit it with a simple model of interference between appropriate tree and penguin diagrams
- Extract magnitudes and relative phases of tree and penguin amplitudes
- Predict branching ratios and *CP* asymmetries for observed and as-yet-unseen modes
- Considerable sensitivity to *γ*.

## Data, Parameters and Results of ππ, KK, Kπ Fit

- 19 branching ratios and *CP* asymmetries in
- strangeness-preserving ***ππ******, ******KK*** decays  (***ΔS=0***)
- strangeness-changing ***K******π****** ***decays (***ΔS=1***)
- direct and mixing-induced asymmetries in ***π******+******π******- ***and ***π******0******K******S ***decays
- 8 fit parameters:
- weak phase ***γ***
- amplitudes: ***|T|, |C|, |P************|, |P******tu******|***
- strong phases: ***δ******T ******, ******δ******C ******, ******δ******P******tu ***
- RESULTS:
- Fit :      χ2=15.5/11;    ***γ=(43±12±2)******o***
- Reasonable |C/T|=0.45±0.13±0.01
- Large *δC*=-66o , indication of final state interactions

## Data and Parameters and Results of the Full PP Fit

- 30 data points:
- branching ratios and *CP* asymmetries in
- strangeness-preserving ***ππ******, KK, ******πη,****** ******πη********* decays  (***ΔS=0***)
- strangeness-changing ***K******π******, K******η,****** K******η************ ***decays (***ΔS=1***)
- direct and mixing-induced asymmetries in ***π******+******π******-***, ***π******0******K******S ***and ***η************K******S*** decays
- 12 fit parameters:
- weak phase ***γ***
- amplitudes: ***|T|, |C|, |P************|, |P******tu******|, |S************|, |S******tu******|***
- strong phases: ***δ******T ******, ******δ******C ******, ******δ******P******tu ******, ******δ******S ******, ******δ******S******tu ***
- RESULTS:
- Fit : 	χ2=26.2/18;   	***γ=(60±9±2)******o***

## Comments on SU(3) and other assumptions 

- In the last year new and more precise PP measurements shifted closer to our predictions.
**Used to say:**
- Despite smaller errors the quality of the fit improved from 32% to 41% to 51%. Fit parameters remained stable.
- We can not yet see significant SU(3) breaking effects or the presence of the E, A, or PA amplitudes in the current *PP* data.
**Now:**
- No longer true. SU(3) fit quality after LP’05 is 16%.
- Perhaps, our assumptions of SU(3) or negligible E,A,PA are close to being inadequate for the current precision of the experimental data.

## Flavor symmetry is employed to analyze B decays into PP final states; symmetry breaking effect is partially taken into account through the ratio of tree amplitudes.

Flavor SU(3) generally fits data well, with some exceptions.  Predictions are made based upon current measurements.

Our preferred γ=(60±9±2)o fit in PP modes favors a weak phase  within the range 51o-69o at 1 level.  It is also compatible with the indirect constraints on : 46o<γ<66o

Indications of substantial A, E, PA amplitudes – or SU(3) breaking effects 

- Flavor SU(3) generally fits data well, with some exceptions.  Predictions are made based upon current measurements.
- Our preferred γ=(60±9±2)o fit in PP modes favors a weak phase  within the range 51o-69o at 1 level.  It is also compatible with the indirect constraints on : ***46******o******<γ<66******o***
- Indications of substantial A, E, PA amplitudes – or SU(3) breaking effects

**Summary of SU(3) fits**