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^-, B⁰→K^*0(892)μ⁺μ^-, B⁰→K_S⁰μ⁺μ^-, B⁺→K^*+(892)μ⁺μ^-, B_s⁰→φμ⁺μ^-, and Λ_b⁰→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^-,
B⁰→K^*0(892)μ⁺μ^-,
B⁰→K_S⁰μ⁺μ^-,
B⁺→K^*+(892)μ⁺μ^-,
B_s⁰→φμ⁺μ^-, and
Λ_b⁰→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 B⁰, and h stands for K⁺, K_S⁰, 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 q² bins, where q²=M_μμc². Since each q² bin has a different amount of signal and background, we fit for the signal in each q² 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 B⁰ 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 B⁰ 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 q², 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 cos²θ_K + 3/4 (1-F_L) (1-cos²θ_K),

1/Γ×dΓ/dcosθ_μ = 3/4 F_L (1-cos²θ_μ) + 3/8 (1-F_L) (1+cos²θ_μ) + A_FBcosθ_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)
B⁰→K^*0μ⁺μ^- yield: (png) (eps)
B⁰→K_S⁰μ⁺μ^- yield: (png) (eps)
B⁺→K^*+μ⁺μ^- yield: (png) (eps)
B_s⁰→φμ⁺μ^- yield: (png) (eps)
Λ_b⁰→Λμ⁺μ^- yield: (png) (eps)

Differential BR

B⁺→K⁺μ⁺μ^- differential BR: (png) (eps)
B⁰→K^*0μ⁺μ^- differential BR: (png) (eps)
B⁰→K_S⁰μ⁺μ^- differential BR: (png) (eps)
B⁺→K^*+μ⁺μ^- differential BR: (png) (eps)
B_s⁰→φμ⁺μ^- differential BR: (png) (eps)
Λ_b⁰→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

B⁰→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

B⁰→K^*0μ⁺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)
B⁰→K^0μ⁺μ^-: 288±20 (s=15.8σ)
B⁰→K_S⁰μ⁺μ^-: 32±8 (s=4.6σ)
B⁺→K^+μ⁺μ^-: 24±6 (s=4.2σ)
B_s⁰→φμ⁺μ^-: 62±9 (s=8.9σ)
Λ_b⁰→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(B⁰→K^0μ⁺μ^-) / B(B⁰→J/ψK^0)=[0.85±0.07(stat)±0.03(syst)]×10^-3
B(B⁰→K⁰μ⁺μ^-) / B(B⁰→J/ψK⁰)=[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_s⁰→φμ⁺μ^-) / B(B_s⁰→J/ψφ)=[0.90±0.14(stat)±0.07(syst)]×10^-3
B(Λ_b⁰→Λμ⁺μ^-) / B(Λ_b⁰→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(B⁰→K^0μ⁺μ^-) =[1.14±0.09(stat)±0.06(syst)]×10^-6
B(B⁰→K⁰μ⁺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_s⁰→φμ⁺μ^-) =[1.17±0.18(stat)±0.37(syst)]×10^-6
B(Λ_b⁰→Λμ⁺μ^-) =[1.95±0.34(stat)±0.61(syst)]×10^-6

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