#
Updated Branching Ratio Measurements of Exclusive b→sμ^{+}μ^{-} Decays and
Angular Analysis in
B→K^{(*)}μ^{+}μ^{-} Decays

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

# Introduction

Rare decays of bottom hadrons mediated by the flavor-changing neutral current (FCNC) process b→sμ^{+}μ^{-} occur in the standard model (SM) through higher order amplitudes. A variety of beyond-the-standard-model (BSM) theories, on the other hand, favor enhanced rates for these
FCNC decays.
One can obtain rich information about the
b→sμ^{+}μ^{-} dynamics by the measurements of
the branching ratio, their dependence on the di-lepton mass distributions,
and the angular distributions of the decay products.

This page summarizes analysis results for the decays governed by the b→sμ^{+}μ^{-} transition;
B^{+}→K^{+}μ^{+}μ^{-},
B^{0}→K^{*0}(892)μ^{+}μ^{-},
B^{0}→K_{S}^{0}μ^{+}μ^{-},
B^{+}→K^{*+}(892)μ^{+}μ^{-},
B_{s}^{0}→φμ^{+}μ^{-}, and
Λ_{b}^{0}→Λμ^{+}μ^{-},
In addition to BR and differential BR of the decays above, we measure the angular distributions in B→K^{(*)}μ^{+}μ^{-} decays.

This analysis is based on a dataset of 9.6 fb^{-1}.

The measurements are described in Public
note 10894.
Previous iterations used 6.8 fb^{-1}(
Phys. Rev. Lett. 107, 201802 (2011),
Phys. Rev. Lett. 108, 081807(2012).

,
web page),
4.4 fb^{-1} (
Phys. Rev. Lett. 106, 161801 (2011),
web page),
and 924 pb^{-1}(
Phys. Rev. D79, 011104(R) (2009),
web page).

# Overview of the analysis

We study the following FCNC decays:

B^{+}→K^{+}μ^{+}μ^{-},

B^{0}→K^{*0}(892)μ^{+}μ^{-},

B^{0}→K_{S}^{0}μ^{+}μ^{-},

B^{+}→K^{*+}(892)μ^{+}μ^{-},

B_{s}^{0}→φμ^{+}μ^{-}, and

Λ_{b}^{0}→Λμ^{+}μ^{-},

in 9.6 fb^{-1} of data collected by the CDF detector with a dimuon trigger.

After trigger and loose offline selection, the final selection is
obtained using an artificial neural network discriminator optimized in
an unbiased way to yield the best expected average resolution on the
quantities to be measured. Various physics backgrounds are reduced
using mass vetoes. Signal yields are obtained by an unbinned maximum
log-likelihood fit to H_{b} mass distribution.

The result precision is limited by the statistical uncertainty.
No evidence for non-SM physics is found.
## Branching ratios (Total and Differential)

To cancel dominant systematic uncertainties, the branching ratio of each rare decay H_{b}→hμ^{+}μ^{-}
is measured relative to the corresponding resonant channel
H_{b}→J/ψh, used as a normalization and a cross-check
of the whole analysis. H_{b} stands for Λ_{b}, B_{s}, B^{+}, and B^{0},
and h stands for K^{+}, K_{S}^{0}, K^{*0}, K^{*+}, φ, and Λ.
We also measure the differential branching ratio with respect to the
squared dimuon mass. Events populating the signal region in mass are
divided into six exclusive and two additional q^{2} bins,
where q^{2}=M_{μμ}c^{2}. Since each q^{2} bin has a different amount of signal and background,
we fit for the signal in each q^{2} bin with the same procedure used for the global fits.
During the fit, we fix the mean of the H_{b} mass and BG slope to the number obtained from the global fit, therefore only the signal fraction is floated.
Combined BRs between B^{0} and B^{+} are obtained by isospin symmetry assumption using B mass lifetime ratio.
Isospin asymmetry is also obtained from the asymmetry of differential BRs between B^{0} and B^{+} decays.
## Angular analysis

The full differential decay distribution for the decay
B→K^{*}μ^{+}μ^{-}
is described by four independent kinematic variables: the di-muon invariant
mass squared q^{2}, the angle θ_{μ} between
the μ^{+} (μ^{-}) direction and the direction
opposite to the B (Bbar) meson in the di-muon rest frame, the angle
θ_{K} between the kaon direction and the direction
opposite to the B meson in the K^{*} rest frame, and the angle φ
between the two planes formed by the di-muon and the K-π systems.
The distributions of θ_{μ}, θ_{K}, and φ
are projected from the full differential
decay distribution and can be parametrized with four angular observables,
A_{FB}, F_{L}, A_{T}^{(2)} and A_{im}:

1/Γ×dΓ/dcosθ_{K} = 3/2 F_{L} cos^{2}θ_{K} + 3/4 (1-F_{L}) (1-cos^{2}θ_{K}),

1/Γ×dΓ/dcosθ_{μ} = 3/4 F_{L} (1-cos^{2}θ_{μ}) + 3/8 (1-F_{L}) (1+cos^{2}θ_{μ}) + A_{FB}cosθ_{μ},

1/Γ×dΓ/dcosφ = 1/2π[ 1+1/2(1-F_{L})A_{T}^{(2)} cos2φ + A_{im} sin2φ ],

where Γ = Γ (B→K^{*}μ^{+}μ^{-}),
A_{FB} is the muon forward-backward asymmetry,
F_{L} is the K^{*} longitudinal polarization fraction,
A_{T}^{(2)} is the transverse polarization asymmetry, and
A_{im} is the T-odd CP asymmetry of the transverse polarizations.

## Results

### H_{b} mass distributions (control sample)

### H_{b} mass distributions (rare decays)

B^{+}→K^{+}μ^{+}μ^{-} yield:
(png)
(eps)

B^{0}→K^{*0}μ^{+}μ^{-} yield:
(png)
(eps)

B^{0}→K_{S}^{0}μ^{+}μ^{-} yield:
(png)
(eps)

B^{+}→K^{*+}μ^{+}μ^{-} yield:
(png)
(eps)

B_{s}^{0}→φμ^{+}μ^{-} yield:
(png)
(eps)

Λ_{b}^{0}→Λμ^{+}μ^{-} yield:
(png)
(eps)

### Differential BR

B^{+}→K^{+}μ^{+}μ^{-} differential BR:
(png)
(eps)

B^{0}→K^{*0}μ^{+}μ^{-} differential BR:
(png)
(eps)

B^{0}→K_{S}^{0}μ^{+}μ^{-} differential BR:
(png)
(eps)

B^{+}→K^{*+}μ^{+}μ^{-} differential BR:
(png)
(eps)

B_{s}^{0}→φμ^{+}μ^{-} differential BR:
(png)
(eps)

Λ_{b}^{0}→Λμ^{+}μ^{-} differential BR:
(png)
(eps)

B^{}→Kμ^{+}μ^{-} combined differential BR:
(png)
(eps)

B^{}→K^{*}μ^{+}μ^{-} combined differential BR:
(png)
(eps)

### Isospin Asymmetry

B^{}→K^{*}μ^{+}μ^{-} and
B^{}→Kμ^{+}μ^{-} isospin asymmetry

(png)
(eps)

### Angular Analysis

B^{0}→K^{*0}(K^{+}π^{-})μ^{+}μ^{-} (single channel)

- F_{L} (png)
(eps)

- A_{FB}:
(png)
(eps)

- A_{T}^{(2)}:
(png)
(eps)

- A_{im}:
(png)
(eps)

B→K^{*}μ^{+}μ^{-} (simultaneous fit of K^{*0} and K^{*+} channels)

- F_{L} (png)
(eps)

- A_{FB}:
(png)
(eps)

- A_{T}^{(2)}:
(png)
(eps)

- A_{im}:
(png)
(eps)

B^{+}→K^{+}μ^{+}μ^{-}

- A_{FB}:
(png)
(eps)

### Angular Distributions

B^{0}→K^{*0}μ^{+}μ^{-}

- kaon angular distributions:
(png)
(eps)

- muon angular distributions:
(png)
(eps)

- phi angular distributions:
(png)
(eps)

B→K^{*}μ^{+}μ^{-}

- kaon angular distributions:
(png)
(eps)

- muon angular distributions:
(png)
(eps)

- phi angular distributions:
(png)
(eps)

### Signal yields and significances

###
- B
^{+}→K^{+}μ^{+}μ^{-}: 319±23 (s=15.6σ)
- B
^{0}→K^{*0}μ^{+}μ^{-}: 288±20 (s=15.8σ)
- B
^{0}→K_{S}^{0}μ^{+}μ^{-}: 32±8 (s=4.6σ)
- B
^{+}→K^{*+}μ^{+}μ^{-}: 24±6 (s=4.2σ)
- B
_{s}^{0}→φμ^{+}μ^{-}: 62±9 (s=8.9σ)
- Λ
_{b}^{0}→Λμ^{+}μ^{-}: 51±7 (s=7.6σ)

where the significance s is determined from the likelihood ratio to a null signal hypothesis.

### Relative BR

###
- B(B
^{+}→K^{+}μ^{+}μ^{-}) /
B(B^{+}→J/ψK^{+})=[0.44±0.03(stat)±0.02(syst)]×10^{-3}
- B(B
^{0}→K^{*0}μ^{+}μ^{-}) /
B(B^{0}→J/ψK^{*0})=[0.85±0.07(stat)±0.03(syst)]×10^{-3}
- B(B
^{0}→K^{0}μ^{+}μ^{-}) /
B(B^{0}→J/ψK^{0})=[0.44±0.10(stat)±0.03(syst)]×10^{-3}
- B(B
^{+}→K^{*+}μ^{+}μ^{-}) /
B(B^{+}→J/ψK^{*+})=[0.62±0.18(stat)±0.06(syst)]×10^{-3}
- B(B
_{s}^{0}→φμ^{+}μ^{-}) /
B(B_{s}^{0}→J/ψφ)=[0.90±0.14(stat)±0.07(syst)]×10^{-3}
- B(Λ
_{b}^{0}→Λμ^{+}μ^{-}) /
B(Λ_{b}^{0}→J/ψΛ)=[2.75±0.48(stat)±0.27(syst)]×10^{-3}

### Absolute BR

###
- B(B
^{+}→K^{+}μ^{+}μ^{-})
=[0.45±0.03(stat)±0.02(syst)]×10^{-6}
- B(B
^{0}→K^{*0}μ^{+}μ^{-})
=[1.14±0.09(stat)±0.06(syst)]×10^{-6}
- B(B
^{0}→K^{0}μ^{+}μ^{-})
=[0.33±0.08(stat)±0.03(syst)]×10^{-6}
- B(B
^{+}→K^{*+}μ^{+}μ^{-})
=[0.89±0.25(stat)±0.09(syst)]×10^{-6}
- B(B
_{s}^{0}→φμ^{+}μ^{-})
=[1.17±0.18(stat)±0.37(syst)]×10^{-6}
- B(Λ
_{b}^{0}→Λμ^{+}μ^{-})
=[1.95±0.34(stat)±0.61(syst)]×10^{-6}