# Presentation: 300811

## Phenomenology ofCharmless Hadronic B Decays

**Denis  Suprun**
**University of Chicago**

- Thanks to C.-W. Chiang, M. Gronau, Z. Luo, J. Rosner
- for enjoyable collaborations

## Motivation

**sin2********=0.736********0.049**** from ********K****S**** based upon BaBar’s 81 fb****-1**** and Belle’s 140 fb****-1**** data (LP03)**
**	****	****era of precision measurement**
**sin2******** can also determined using other modes: ********K****S****, ********’K****S****, K****S****K****+****K****-**
**	****	**
**We also want to observe ****direct CPV**** ****in B system**** and to check whether it is consistent with SM expectation**
**	****	****BaBar announced first observation of direct CPV:**
**	****   ****	****    ****A****CP****(π****-****K****+****) = -0.133********0.030********0.009   at  4.2σ level**
**Most branching ratios of charmless B ******** PP and PV are currently measured with errors about 10%~20%**
**	****	****5%~10% errors in amplitude**
**One hopes to have <5% errors on the amplitudes of most modes**
**	****	****more precise information on ******** and ******** (<10****o****)**

**Motivation**

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## CKM Matrix and Unitarity Triangle

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## 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**

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## CKM Fitter results

**CKM Fitter ****results**

**Upper limit on ****γ will become more strict when Run II of the Tevatron will become sensitive **
**to B****s**** oscillations at the level of Δm****s****=15 ps****-1**** **

## 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 some information on strong phases

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## Importance of Strong Phases

**Importance of Strong Phases**

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## B VP decays

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## Dominant types of amplitudes

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## Assumptions

- 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

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## Approach

- Take all available information on charmless *B* decays to a *VP* 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*.

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## Conservative statistical errors 

**Take account of the PDG scaling factor S when BaBar and Belle values are disparate.    **S is a measure of discrepancy between several measurements.
**S(********K****S****) problem**.
- 	S(KS) is predicted to be equal to sin2β=0.74±0.05, as measured in J/ψKS decays. However, BaBar and Belle measurements of S(KS) are quite different:
-    			BaBar: S(KS) = 0.47±0.34±0.07
-  	  		Belle:   S(KS) = -0.96±0.50±0.10.
- 	Belle claims that the value of 0.74 is excluded at 3.5σ confidence level. The world average is
- 			WA:     S(KS) = 0.02±0.29
- 	but when S factor is taken into account
- 			WA:     S(KS) = 0.02±0.66   (S=2.33).
- 	With the uncertainty being too large, it is too early to say that there is a clear problem with the SM description of the KS decay.
**It is not the only measurement where BaBar and Belle disagree**. Others include
- 			S(π+π-)  with  S=1.91
- ΔS(ρπ)  with  S=2.00

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## Data and Fit Parameters

- 34 data points:
- branching ratios and *CP* asymmetries in
- strangeness-preserving ***ρπ******, ******ρη,****** ******ρη************, ******ωπ*** decays  (***ΔS=0***)
- strangeness-changing ***K*************π******, K*************η,****** K*************η************, ******ρ******K, ******ω******K, ************K*** decays (***ΔS=1***)
- direct and mixing-induced asymmetries in ***ρ******±******π***   and *******K******S*** decays
- 12 fit parameters:
- weak phase ***γ***
- amplitudes: |***t******P******|, |t******V******|, |C******P******|, |C******V******|, |P************P******|, |P************V******|, |P************EW,P******|, |P************EW,V******|***
- strong phases: ***δ******V****** ******, ******δ******P ******, ******φ***

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## χ2-γ plot

- Three minima of about
- equal depth: ***γ=26******o******, 63******o******, 162******o***
- Ambiguity can not be resolved from the *B****VP* data alone.
- Appeal to experiment:
- CKM Fitter: ***39******o******<γ<80******o***
- Appeal to theory:
- Minima at ***26******o ***and*** 162******o ***feature*** ***large strong phases leading to
*Arg(**t**P**/**t**V**)=-(87**±10)**o *and
-  	       *(38**±12)**o*,
- 		     respectively.
*Arg(**t**P**/**t**V**)=-(20**±10)**o *at * ****γ=63******o***

***γ=(63****±6)****o******: ****Fit quality 55%*

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## Predictions

**Largest predicted *****CP *****asymmetries:**
-  	*A**CP**(**ρ**0**π**+**)=-0.16**±0.04**	**A**CP**(**ρ**0**K**+**)=0.21**±0.10*
*	**A**CP**(**ρ**-**π**+**)=-0.13**±0.06**	**A**CP**(**ρ**-**K**+**)=0.16**±0.07*
*	**	**	**	**	**A**CP**(**ω**K**+**)=0.19**±0.08*
**As yet unseen modes to be observed soon (in 10****-6****):**
- 	Predicted br. ratios:	    *Current UL*
- 	*B(K***+**π**0**)=15.0**±3.1              <31          **	*
*	**B(**ρ**0**K**0**)=7.2**±2.0**	**          <12.4       **	*
*     **B(**ρ**+**K**0**)=12.6**±1.6 **	**          <48**	**             **	**	*
*	****	******ρ******+******K******0 *****is a pure***** p************V  *****penguin***** *****and its measurement is ****	****particularly important**

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## Comments on SU(3) 

- In the last few months I saw new and more precise measurements shifting closer to our predictions.
- Despite smaller errors the quality of the fit improved: χ2 dropped by 1.8 units to 18.7/22. Fit parameters remained stable.
- Probably, we can not yet see significant SU(3) breaking effects in the current *B **VP* data.
- I expect that the predictions of this method will remain reliable for at least another year.
- Recent BaBar measurement of B(B0ωη)=4.0±1.6 is a challenge.

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## B PP decays

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## Dominant types of amplitudes

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## ππ, Kπ Fit

- A nonzero relative strong phase *δC* between tree *T* and color suppressed *C* amplitudes is the key to getting a good fit.
- It doesn’t lead to predictions of large CP asymmetries in the modes where we didn’t expect them before. For example, π+π0 decays (*t+c*)  are still predicted to have zero CP asymmetry because of zero weak phase difference between *t* and *c* amplitudes.
- With *δC* we can get a good fit to all ππ, Kπ decay modes: χ2=7.34/8, fit quality: 50%.
- Problem: |C/T|=1.4.

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## Ptu as a solution to the large |C/T| problem

- Penguins that feature bd, bs transitions can be  mediated by u, c, or t quarks. For the bd case the corresponding CKM matrix elements are V*ubVud, V*cbVcd, and V*tbVtd. Typically, one uses the unitarity relation to replace V*tbVtd = –V*cbVcd –V*ubVud an write a “pure” penguin as
*	**	**	**p* =  V*cbVcd P – V*ubVud Ptu.
- Original versions of the fit neglected the second term. Note that it features the same CKM matrix elements as a tree or a color-suppressed amplitude. Thus, Ptu can disguise itself as a part of  T or C.
- When Ptu is not explicitly used as a parameter in π0π0 (*c-p*) and π+π- (*t+p*) decay modes, this may lead to a larger C and a smaller T amplitude because they invisibly include Ptu contributions.

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## Ptu as a solution to the large |C/T| problem

- Now use Ptu and its strong phase δPtu (with respect to P) as fit parameters.
- Ptu was found to be of about the same size as P.
- In bs transitions its influence is much less prominent for two reasons:
- 		(a) P' term is larger than P by  |Vcs/Vcd|  λ
- 		(b) P'tu term is smaller than Ptu by  |Vus/Vud|  λ
- Ptu interferes constructively with C and destructively with T. Now that Ptu was explicitly taken into account, |C/T| went down to a more reasonable |C/T|=0.46.
- δPtu was found to be very small, just 3.
- The “pure” penguin modes (K+K0bar, K0K0bar, π+K0) are actually an interference of P and Ptu with a weak phase difference γ between them. Due to small strong phase difference δPtu , CP asymmetry in these decays is still expected to be small.

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## B  πK Puzzle

**From experiment ** Br(Bπ-K+) / 2Br(Bπ0K0) = 0.76±0.10
- 		while it is expected to be around 1.
- Buras, Fleischer, Recksiegel, Schwab solution:
- Solve Bππ system by neglecting EWPs. Extract T, C, P and strong phases.
- Scale the values of amplitudes and phases to get T', C' and P' using SU(3) flavor symmetry and CKM parameters.
- Use them and **enhanced** EW penguins with **a large CP-violating New Physics phase** to get a good description of πK data.
- Our approach is less radical and is within the SM. We don’t use any NP parameters. We manage to get a good fit which adequately describes both ππ and πK data simultaneously (without being a precise solution to any of the two subsets). The fit doesn’t give a good “prediction” for Br(Bπ0K0) (deviation 1.7σ) but the fit quality (50%) implies that the SM still gives an adequate description of ππ, πK data.

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## Data and Parameters of the Full PP Fit

- 26 data points:
- branching ratios and *CP* asymmetries in
- strangeness-preserving ***ππ******, ******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
- 13 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 ***
***δ******EW ***factor that relates EW penguins to tree-level diagrams

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## χ2-γ plot

- Three minima of about equal depth. Ambiguity can not be resolved from the *B****PP* data alone.
- Appeal to experiment:
- CKM Fitter: ***39******o******<γ<80******o***

- Fit without ***S******tu***: χ2=18.1/15;   ***γ=(66****±14)****o***
-  Fit with ***S******tu***:     χ2=16.0/13;   ***γ=(54****±21)****o***

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## Predictions for some Bs decays

- CDF blessed measurement:
- 		Br(BsK+K-) / Br(BdK+π-) = 2.71±0.73±0.35±0.81
- 					          = 2.71±1.15
-     We predict:
- 		Br(BsK+K-) / Br(BdK+π-) = 0.93
- CDF preliminary result (presented at APS):
- 	 	Br(BsK-π+) ~ 10·10-6
-  	We predict:
- 		Br(BsK-π+) = 4.2·10-6
- Predictions for all Bs charmless hadronic decay modes will appear in a paper to be posted on the Net next month.

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun

## Flavor nonet symmetry is employed to analyze B decays into VP and PP final states; symmetry breaking effect is partially taken into account for tree amplitudes.
Flavor SU(3) generally fits data well, with some exceptions.  Predictions are made based upon current measurements.
Our preferred 63o fit in VP modes favors a weak phase  within the range 57o-69o at 1 level and 51o-73o at 95%CL.  It is compatible with other determinations of .
Our preferred 54o fit in PP modes favors a weak phase  within the range 30o~72o at 1 level.  It is also compatible with the CKM Fitter favored  range: 39o<γ<80o
Expect Bs decays to be measured at Tevatron Run II. Predictions on the branching ratios and CP asymmetries can be made on the basis of SU(3) flavor symmetry and the magnitudes and phases of the topological diagrams extracted from Bd decays to PP and VP final states.

- Flavor SU(3) generally fits data well, with some exceptions.  Predictions are made based upon current measurements.
- Our preferred 63o fit in VP modes favors a weak phase  within the range 57o-69o at 1 level and 51o-73o at 95%CL.  It is compatible with other determinations of .
- Our preferred 54o fit in PP modes favors a weak phase  within the range 30o~72o at 1 level.  It is also compatible with the CKM Fitter favored  range: ***39******o******<γ<80******o***
- Expect Bs decays to be measured at Tevatron Run II. Predictions on the branching ratios and CP asymmetries can be made on the basis of SU(3) flavor symmetry and the magnitudes and phases of the topological diagrams extracted from Bd decays to PP and VP final states.

**Summary and Outlook**

- hep-ph/0307395 and hep-ph/0404073

- Denis Suprun