#
Measurement of Forward-Backward Asymmetry in B→K^{(*)}&mu^{+}&mu^{-} and
Search for B_{s}^{0}→&phi&mu^{+}&mu^{-}

### Primary authors: Hideki Miyake, Shinhong Kim, Fumihiko Ukegawa

This page summarizes analysis results for rare B decays dominated by FCNC b→s&mu^{+}&mu^{-} transition ;
B^{0}→K^{*0}(892)&mu^{+}&mu^{-},
B^{+}→K^{+}&mu^{+}&mu^{-} and
B_{s}^{0}→&phi&mu^{+}&mu^{-}.

In addition to BR, we measured differential BR, kaon longitudinal polarization (F_{L}), and muon forward-backward asymmetry (A_{FB}) with respect to square of dimuon mass.

This analysis is based on a dataset of 4.4fb^{-1} and
previous CDF analysis was performed by 924pb^{-1}(
Phys. Rev. D79, 011104(R) (2009),
web page).

The results have been approved by B group as of Nov. 12th, 2009. Details
are described in CDF Note 10047.

Update: In Apr. 8th, 2010,
BR measurements and angular analyses in 1 &le q^{2} < 6 (GeV^{2}/c^{2}) were approved.

## Analysis outline:

### Reconstruction

We start from the rare B di-muon (RAREB_LXY) trigger, which reqires Pt> 1.5 or 2.0 GeV/c muon pairs.

After several pre-selection cuts, final selection is performed by Neural Network that is trained by Pythia+EvtGen signal MC and sideband data.

NN cut is optimized to maximize S=S/sqrt(S+B) for B^{0}→K^{*0}(K^{+}&pi^{-})&mu^{+}&mu^{-} and
B^{+}→K^{+}&mu^{+}&mu^{-}, while
B_{s}^{0}→&phi(K^{+}K^{-})&mu^{+}&mu^{-}
is optimized to maximize S=S/(5*0.5+sqrt(B)) since the channel is the first observation stage.

We extract the signal yield from B mass distribution, with using unbinned maximum log likelihood.

Signal PDF is parameterized by double Gaussian that have different means, and background are first order polynomial.

Signal shape is determined from the signal MC except the signal fraction and mean of narrow Gaussian (mean difference is fixed).

During the yield fit, parameters above and slope of the background are floated.

For B^{0}→K^{*0}(K^{+}&pi^{-})&mu^{+}&mu^{-} and
B^{+}→K^{+}&mu^{+}&mu^{-},
there are significant physics backgrounds that consist of partially reconstructed b hadrons
including feed-down from the rare B decays, in the lower sideband. We excluded these sideband from the fit region.

Signal yield is obtained from ±2&sigma window from the B PDG mass, where &sigma=20Mev/c^{2}.
### BR

Branching Ratio is measured as relative BR to control channel, where control channels are corresponding J/&psi h decay.
### Differential BR

After event selection, we divide dimuon mass spectrum into
five or six q^{2} bin, where q^{2} is square of dimuon mass.
Differential BR is measured in each q^{2} bin.
### Angular Analysis (F_{L} and A_{FB})

A_{FB} is measured from muon angular distribution in dimuon restframe.
We employ unbinned maximum likelihood method to extract A_{FB} and
use same q^{2} binning as differential BR.
Angular acceptances are taken from signal MC and considered in the fit.
In case of B^{0}→K^{*0}&mu^{+}&mu^{-},
we measure kaon longitudinal polarization F_{L} from kaon angular distribution in K^{*0}
restframe prior to measure A_{FB}.

## Blessed plots:

### B mass distribution

B^{0}→K^{*0}(K^{+}&pi^{-})&mu^{+}&mu^{-} unblinded yield:
(png)
(eps)

B^{+}→K^{+}&mu^{+}&mu^{-} unblinded yield:
(png)
(eps)

B_{s}^{0}→&phi(K^{+}K^{-})&mu^{+}&mu^{-} unblinded yield:
(png)
(eps)

### Differential BR

B^{0}→K^{*0}(K^{+}&pi^{-})&mu^{+}&mu^{-} Differential BR:
(png)
(eps)

B^{+}→K^{+}&mu^{+}&mu^{-} Differential BR:
(png)
(eps)

### Angular Analysis (6 bin)

B^{0}→K^{*0}(K^{+}&pi^{-})&mu^{+}&mu^{-} F_{L}:
(png)
(eps)

B^{0}→K^{*0}(K^{+}&pi^{-})&mu^{+}&mu^{-} A_{FB}:
(png)
(eps)

B^{+}→K^{+}&mu^{+}&mu^{-} A_{FB}:
(png)
(eps)

### Angular Analysis (5 bin)

B^{0}→K^{*0}(K^{+}&pi^{-})&mu^{+}&mu^{-} F_{L} (5bin):
(png)
(eps)

B^{0}→K^{*0}(K^{+}&pi^{-})&mu^{+}&mu^{-} A_{FB} (5bin):
(png)
(eps)

B^{+}→K^{+}&mu^{+}&mu^{-} A_{FB} (5bin):
(png)
(eps)

### Angular Distributions

B^{0}→K^{*0}(K^{+}&pi^{-})&mu^{+}&mu^{-} kaon angular distributions:
(png)
(eps)

B^{0}→K^{*0}(K^{+}&pi^{-})&mu^{+}&mu^{-} muon angular distributions:
(png)
(eps)

## Blessed numbers:

### Signal yield :

###
- Signal yield of B
^{0}→K^{*0}(K^{+}&pi^{-})&mu^{+}&mu^{-}:
101±12 (102 expected)
- Signal yield of B
^{+}→K^{+}&mu^{+}&mu^{-}:
121±16 (142 expected)
- Signal yield of B
_{s}^{0}→&phi(K^{+}K^{-})&mu^{+}&mu^{-}:
27±6 (31 expected)

- Significance of B
^{0}→K^{*0}(K^{+}&pi^{-})&mu^{+}&mu^{-}:~9.7 sigmas
- Significance of B
^{+}→K^{+}&mu^{+}&mu^{-}:~8.5 sigmas
- Significance of B
_{s}^{0}→&phi(K^{+}K^{-})&mu^{+}&mu^{-}:~6.3 sigmas

Significance is deterimined from the likelihood ratio to a null signal hypothesis.

### Relative BR

###
- B(B
^{0}→K^{*0}&mu^{+}&mu^{-}) /
B(B^{0}→J/ψK^{*0})=[0.80±0.10(stat)±0.06(syst)]×10^{-3}
- B(B
^{+}→K^{+}&mu^{+}&mu^{-}) /
B(B^{+}→J/ψK^{+})=[0.38±0.05(stat)±0.02(syst)]×10^{-3}
- B(B
_{s}^{0}→φ&mu^{+}&mu^{-}) /
B(B_{s}^{0}→J/ψφ)=[1.11±0.25(stat)±0.09(syst)]×10^{-3}

### Absolute BR

###
- B(B
^{0}→K^{*0}&mu^{+}&mu^{-})
=[1.06±0.14(stat)±0.09(syst)]×10^{-6}
- B(B
^{+}→K^{+}&mu^{+}&mu^{-})
=[0.38±0.05(stat)±0.03(syst)]×10^{-6}
- B(B
_{s}^{0}→φ&mu^{+}&mu^{-})
=[1.44±0.33(stat)±0.46(syst)]×10^{-6}

### Differential BR, F_{L}, and A_{FB}

- B
^{0}→K^{*0}&mu^{+}&mu^{-}

- B
^{+}→K^{+}&mu^{+}&mu^{-}