# Presentation: 808591

##       Hadronic rare B-decays

**Sanjay K Swain**

**Belle collaboration**

**B****- ****-> D****cp****K****(*)-**
**B****-**** -> D(K****S********+********-)****K****-**** Dalitz analysis**
**B -> ******
**B -> ********K****(*)**
**Conclusion**

**V****ud****V****ub**

**V****cd****V****cb**

**V****td****V****tb**

*****

*****

*****

******3****(********)**

******2****(********)**

******1****(********)**

## Using B-DCPK-  mode (GLW method)

**B****-**** ******** D****CP****K****-****    where  D****CP**** =     (D****0 ******** D****0**** )**
**A(B****-********D****CP****K****-****) ********|A(B****-********D****0****K****-****)|+|A(B****-********D****0****K****-****)|****e****i******** ****   ****e****i******
**A(B****+********D****CP****K****+****) ********|A(B****+********D****0****K****+****)|+|A(B****+********D****0****K****+****)|****e****-i********    ****e****i******
**When   D****0 ****                                                          D****0**** **
**CP-even states (D****1****): K****+****K****-**** , ********+ ********-****                        **
**CP-odd states   (D****2****): K****S ********0****, K****S ********,****  ****K****S ********, **** ****K****S ********, K****S ********’**** ****                           **

** ̄**

**3**

**3**

** ****common**
**final state**

** ̄**

** ̄**

**PLB 253(1991)483**
**PLB 265(1991)172**

**}**

**Color-favored**

**b**

**u**

**u**

**c**

**u**

**K**

**D**

**B**

**-**

**-**

**-**

**-**

**-**

**o**

**}**

**u**

**u**

**c**

**K**

**D**

**B**

**-**

**-**

**-**

**-**

**Color-suppressed**

**V****cb**

**V****ub**

**-**

**s**

**}**

**s**

**o**

**}**

******3****=arg(V****ub****)**

**u**

**-**

*****

**b**

## GLW method cont.....

******3**

****

****

**A(B****+******** D****0****K****+****)**

**A(B****-******** D****0****K****-****)**

**A(B****+******** D****0****K****+****)**

**A(B****-******** D****0****K****-****)**

**A(B****+******** D****CP****K****+****)**

**A(B****-******** D****CP****K****-****)**** **

**=**

**Reconstruct the two triangles   ********    ********3**

**—**

**-********3**

**One can measure ********3**** even if ********=0( without strong phase)**

**Non vanishing strong phase (******** ******** 0) ******** Direct CP violation**

## GLW method cont...

**Solution:   One can instead measure**

***R*****1,2**** = **

**R    /R**

**D****CP**

**D****non-CP**

**= 1 + r****2 ******** 2r cos(********)cos(********3****)**

**where R **

**D****CP**

** ***B*** (B****- ******** D****1,2****K****-****) + C.C**

*B*** (B****- ******** D****1,2********-****) + C.C**

**=**

***A*****1,2**** = **

*B*** (B****- ******** D****1,2****K****-****)**

*B*** (B****+ ******** D****1,2****K****+****)**

*B*** (B****- ******** D****1,2****K****-****)**

**-**

**+**

******2r sin(********)sin(********3****)**

**3 independent measurements ******** 3 unknowns  ****r , ********, ********3**** ****(solve it)**

**But *****A*****1*****R*****1 ****= - *****A*****2*****R*****2****  **

**1 + r****2 ******** 2r cos(********)cos(********3****)**

*B*** (B****+ ******** D****1,2****K****+****)**

**= **

** **

**Amp(B****-**** ******** D****0****K****-****)**

****** ****0.1 x Amp(B****-**** ******** D****0****K****-****)**

**Also B****- ********  D****0****[K****+********-****]K****-**** has same final state as B****- ********  D****0****[K****+********-****]K****- ****(DCSD)**** **

**But**

**_**

**_**

**r =  |B********KD|/|B********KD|**

**_**

## Kinematics to identify signal

**Candidates are identified by two kinematic variables**
** ****Beam constrained mass ****(M****bc****)= ********(E****2****beam****-p****B****2****)**
** ****Energy difference ****( ********E) = E****B**** - E****beam**
**But @********(4S) peak energy:  24% BB**
**                                              ****76% Continuum (qq,  q =u, d, c or s)**

**        ****KEKB **
**   ****operates here**

****

**–**

**We use continuum suppression variables -> LR( Cos********B**** , Fisher)**

**-**

## Results (78 fb-1) 

**B******** D ******

**B******** D K**

**Flavor**
**specific**

**CP**
**even**

**CP **
**odd**

**6052 ******** 88**

**683.4********32.8**

**648.3********31**

**347.5********21**

**47.3********8.9**

**52.4********9**

**134.4********14.7**

**15.6********6.4**

**6.3********5.0**

******E**

******E**

## Double ratios(R1,2) and asymmetries(A1,2)

***R*****1**** ****= 1.21 ******** 0.25 ******** 0.14   and      *****R*****2**** = 1.41 ******** 0.27 ******** 0.15 **

***A*****0 ****=   0.04 ******** 0.06(stat) ******** 0.03 (sys)         ( non-CP mode)**
***A*****1**** = +0.06 ******** 0.19(stat) ******** 0.04 (sys)        ( CP + mode)**
***A*****2  ****= - 0.18 ******** 0.17 (stat)******** 0.05(sys)         ( CP – mode)**

**We cannot constrain ********3**** with these statistics.**

**25.0 ******** 6.5**

**22.1 ******** 6.1**

**20.5 ******** 5.6**

**29.9 ******** 6.5**

******E******

******E******

**CP**
**even**

**CP**
**odd**

**( r****2**** = 0.31 ****± 0.21 ,  just  1.5******** away from physical boundary)**

**r =  |B********KD|/|B********KD|**

**_**

## B-D0K*-  mode (90 fb-1 data)

**B****-********D****0****K*****- **** mode (90 fb****-1 ****data)**

**Signal MC**

**data**

**Works exactly same way as  B****-**** -> D****CP****K****-****  decay**
**Look for CP asymmetries and double ratios -> constraint ********3**

**169.5****±15.4**

**16 ******

**Flavor **
**specific **
**modes**

## B-DCPK*-  mode 

**B****-********D****CP****K*****- **** mode **

**Can not constraint ********3**** with this statistics -> need more data**

**CP asymmetries :   **

**A****1**** = -0.02 ****± 0.33(stat)  ± 0.07(sys)**

**A****2**** = 0.19****± 0.50(stat) ± 0.04(sys)**

**13.1 ****± 4.3**

**4.3******

**7.2 ****± 3.6**

**2.4******

**CP-even**

**CP-odd**

## B±D(KS +-)K±  Dalitz analysis(140 fb-1)

**B****±********D(K****S ********+********-****)K****±**** **** Dalitz analysis(140 fb****-1****)**

** **

**In case of B****-**** ******** D****CP****K****-****  where D****CP**** =(D****0 ******** D****0**** ) **
**both D****0 ****and D****0**** decays to  CP eigenstates ( K****+****K****-****..) **

**One  can write the total amplitude for B****+**** ******** DK****+ :**
**Amp(B****+**** ->DK****+****) = f(m****+****2****,m****-****2**** ****) + r. e****i(********3**** + ********)**** f(m****-****2  ****, m****+****2**** )**
** ****(B****-**** decay amplitude can be written similar way : ******** ->******** ,********3 ****-> -********3****)**
**m****+****2****(m****-****2****) -> squared of invariant mass of K****S********+****(********-****)combinations**
** ****f   ->  complex amplitude of D****0****-> K****S********+********- ****decay **

**f( m****+****2****,m****-****2****) = ******** a****k****. e****i********  ****A****k****(m****+****2****,m****-****2****) + b e****i******
**                    ****-> both 2-body resonances and non-res component**

**-**

**-**

**D****0********K****0**** ******************

**D****0********K****0**** ******************

**D****0********K****S**** ******************

## Simple example

**D****0********K***************

**K****S **********

**D****0********K***************

**K****S **********

**M(K****S ************)****2**

**M(K****S ************)****2**

**Dalitz plot**

**interference**

**Simple example**

##  reality is more complex(& better) 

**D****0********K****S ******************

**K*******

**K****S******

**K****S******

**K****S****f****2**

** ****reality is more complex(& better) **

**many  amplitudes &**
**strong phases(13)**
**lots of interference**

## Fit results for D ->KS +- decay 

|    Resonance | Amplitude | Phase |
| --- | --- | --- |
|  K*-(892)+
  KS0  
 K*+(892)-
  KS
 KSf0(980)
 KSf0(1370)
 KSf2(1270)
 K*0-(1430)+
 K*2-(1430)+
 K*-(1680)+
 KS1(M=535±6 MeV, =460±15 MeV)
 KS2(M=1063±7 MeV, =101±12 MeV)
 Non-resonance | 1.706 ± 0.015
1.0(fixed)
0.136 ± 0.008
0.032 ± 0.002
0.385 ± 0.011
0.49 ± 0.04
1.66 ± 0.05
2.09 ± 0.05
1.2 ± 0.05
1.62 ± 0.024
1.66 ± 0.09
0.31 ± 0.04
6.51 ± 0.22 | 138 ± 0.9
0 (fixed)
330 ± 3
114 ± 3
214.2 ± 2.3
311 ± 6
341.3 ± 2.3
353.6 ± 1.8
316.9 ± 2.1
84 ± 10
217.3 ± 1.4
257 ± 11
149 ± 1.6 |

## B±D(KS +-)K±  Dalitz analysis 

**B******

**B****+**

**B****±********D(K****S ********+********-****)K****±****  ****Dalitz analysis **

**Fit Dalitz distributions for B****+**** and B****-**** decay simultaneously**
**-> r , ********3**** ****, ******** as free parameters **

**Use D****0********K****S**** ********************  to make Dalitz-plot model **
**fit 58K events with 13 amplitudes **
**Select B****±********K****±**** D****0****(********K****S**** ************************ events**
**107 ****±**** 12 events in 142 fb****-1**** Belle data**
**Form Dalitz plots for B****+**** & B******

## B±D(KS +-)K±  Dalitz analysis

**B****±********D(K****S ********+********-****)K****±**** **** Dalitz analysis**

** **

**Weak phase ********3**** = 95****0 ****±25****0****(stat) ±13****0 ****(sys)±10****0**
**strong phase ******** = 162****0 ****±25****0****(stat) ±12****0****(sys)**** ****±24****0**
**(3****rd**** error is model uncertainty)**
**        ****r  = 0.33 ****± 0.10(stat)**

**@90% C.L  :**
**0.15<r<0.5 ,61****0****<********3****<142****0****, 104****0****<********<214****0**

******3**

**r**

****

******3**

**r =  |B********KD|/|B********KD|**

**_**

## B -> +0 mode(first observation)

**B -> ********+********0**** mode****(first observation)**

**data used:78 fb****-1**

**B****(B****+ ****-> ********+********0****) =(31.7********7.1(stat) ********6.4(sys) ********2.1(pol))x10****-6**** **

**A****CP****(B******** -> ****************0****) = (0.1 ****±22.4(stat) ±2.8(sys))%**** **

**First observation of charmless**
** ****vector-vector mode**

******0**

******+**

******0**

******+**

**B****+**

**B****+**

**u**

**b**

**d**

**-**

**W**

**-**

**-**

**-**

**u**

**u**

**u**

**u**

**u**

**b**

**d**

**u**

**u**

**-**

**-**

**W**

**Z/******

**EWP**

## Helicity analysis

******0**** momentum requirement**

****** ****final state is vector-vector system -> give S ,P or D wave**
** ****Both longitudinal and transverse polarization are possible**
**Longitudinal pol. ratio ,      = (94.8********10.6(stat) ********2.1(sys))%**

******L**

****

- longitudinally polarized

**fit result**

## B ->K(*) (78 fb-1) BF’s

**-**

**-**

**b**

**s**

**u **

**-**

**Penguin **

| Mode | BF x 10 -6 |
| --- | --- |
| K+
K0
K*0
K*+ | 9.4 ± 1.1 ± 0.7
9.0 ± 2.2 ± 0.7
10.0 ± 1.6 ± 0.8
6.7 ± 2.1 ± 1.0 |

**s**

**s**

**u **

**W**

**u , c, t**

**-**

**-**

**-**

**136****±15**

**35.6****±8.4**

**58.5****±9.1**

**8****±4.3**
**11.3****±4.5**

**V****ts**

## B -> K* (78 fb-1) polarization

**K****+**

**|A****0****|****2**** = 0.43 ****± 0.09 ± 0.04**
**|A |****2**** = 0.41 ****± 0.10 ± 0.04**
** ****(CP odd and CP even states)**
**   **
**                ****and**
**arg(A ) = 0.48 ****± 0.32 ± 0.06**
**arg(A ) = -2.57 ****± 0.39 ± 0.09**

**T**

**T**

**=**

**Distribution of decays**
**->****A****0**** , A  , A****  , ********tr**** , ********   , ********tr**** **

**T**

**=**

**K*******

**A****x**** -> complex amplitudes**

**Amplitudes are determined by**
**unbinned max likelihood fit:**

**z**

******tr**

## Summary

**Now we have better measurement on  **
**  ****CP asymmetries and ratio of BF’s in B****-**** -> D****CP****K****-**** mode**
** ****Constrained ********3**** using Dalitz analysis of B****-**** -> D(K****S********+********-****)K****-**** decay**
** ****Measured the branching fractions and different helicity   **
**   ****amplitudes in B -> ******** mode.**
** ****Measured the branching fractions and helicity amplitudes  **
**   ****in B -> ********K****(*)**** mode **
** ****Lot more other hadronic rare B-decays........  **

## MC with

**MC with**
******3**** = 70****o**
**B****+**** ****/ ****B**********

## B±D(KS +-)K±  Dalitz analysis 

**~2.4****σ**** separation**

**B******

**B****+**

**B****±********D(K****S ********+********-****)K****±****  ****Dalitz analysis **

**Fit Dalitz distributions for **
**B****+**** and B****-**** decay simultaneously**
**-> r , ********3**** ****, ******** as free parameters **

## KEKB Accelerator

**Two separate rings**

**Finite crossing angle**

** ****L****designed****= ****10****34**** ****cm****-2****s****-1**

_**Achieved:**_

- Lpeak** ****> ****10****34**** ****cm****-2****s****-1**

**Integrated Luminosity**

**~ 158 fb****-1**

**E****e **** = 3.5 GeV**

**E****e **** = 8.0 GeV**

**+**

**-**

- interaction point

## Detector Performance

**K/******** separation is done using:**

**ACC, TOF, dE/dx( CDC)**

**PID(K) =**** **

**Wide momentum range**

***L*****(K)**

***L*****(K) + *****L*****(********)**

- Belle detector

## Background Suppression

**Variables to distinguish signal from continuum events**
****** ****Cos********B**

**Event Shape variable: (Fisher)**
** ****BB           : Spherical**
**Continuum: back-to-back(jet-like)**

**–**

******B**

**e****+**

**e****-**

**B**

**CONTINUUM**

**SIGNAL**

## Background Suppression

**Cos********B**

**Fisher**

**Likelihood ratio**

**Background Suppression**

**Signal**

**Continuum**

## Main question: “Is V unitary” ?

**Three generation quark mixing matrix(V)**

**V = **

******3 ****= arg(V********* ****)**

**ub**

**(Also known as ********)**

**V****ud****V****ub****+ V****cd****V****cb****+ V****td****V****tb**** = 0**

**Orthogonality of 1****st**** and 3****rd**** column gives:**

*****

*****

*****

**a**

**b**

**-b**

****

****** ****= arg(       )**

**a**

**-b**

*****

**–**

******3 ****= arg(           )**

**V****cd****V****cb**

**V****ud****V****ub**

*****

**V****ud****V****ub**

**V****cd****V****cb**

**V****td****V****tb**

*****

*****

*****

******3****(********)**

******2****(********)**

******1****(********)**