We report the first observation of the radiative decay B⁰ → φ K⁰ γ using a data sample of 772 × 10⁶ BB pairs collected at the Υ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e⁺e^- collider. We observe a signal of 37±8 events with a significance of 5.4 σ including systematic uncertainties. The measured branching fraction is ℬ (B⁰ → φ K⁰ γ) = (2.74±0.60±0.32) × 10^-6. We also measure ℬ (B⁺ → φ K⁺ γ) to be (2.48±0.30±0.24) × 10^-6 with a significance of 9.6 σ. The uncertainties are statistical and systematic, respectively.

Belle has previously reported branching fraction for B⁺ → φ K⁺ γ and an upper limit on B⁰ → φ K⁰ γ using 96 × 10⁶ BB pairs [ PRL 92, 051801 (2004) ]. BaBar also obtain branching fraction measurements using 228 × 10⁶ BB pairs [ PRD 75, 051102 (2007) ].

The signal is reconstructed in the decays B⁺ → φ K⁺ γ and B⁰ → φ K_S⁰ γ , with φ → K⁺K^- and K_S⁰ → π⁺π^-. We obtain 144±17 charged and 37±8 neutral events from an extended unbinned maximum-likelihood fit to the two-dimensional ΔE-M_bc distribution [M_bc > 5.2 GeV/c² and |ΔE|<0.3 GeV]. The signal shapes are adjusted for small differences between MC simulations and data using a B⁰ → K^*(892)⁰ (→ K⁺ &pi^-) γ control sample, with M_K^+- &isin [820, 970] MeV/c².

&Delta E and M_bc projections of the two-dimensional fit for B⁺ → φ K⁺ γ

&Delta E and M_bc projections of the two-dimensional fit for B⁰ → φ K_S⁰ γ

Color Convention :

Points with error bars	data
Total fit function	solid red
Total background function	long-dashed black
Continuum function	dotted blue
The b → c function	dashed-dotted green
The non-resonant component as well as other charmless backgrounds	filled magenta histogram

B⁰ → φ K⁰ γ

• Yield = 37±8, Efficiency = (10.0±0.1)%
• Branching Fraction = (2.74±0.60±0.32) × 10^-6, Significance of 5.4σ

We also examine the φ K invariant mass distribution of the signal. Nearly 72% of the signal events are concentrated in the low-mass region, M_{φ K} &isin [1.5, 2.0] GeV/c². These spectra are in qualitative agreement with the expectations from the pQCD model for non-resonant B⁺ → φ K⁺ γ decays (after including the kinematic effect of the kaon mass) [ PRD 70, 054006 (2004) ]. With the present statistics no clear evidence is found for the existence of a kaonic resonance decaying to φ K.

Background subtracted and efficiency-corrected &phi K mass distributions for B⁺ → φ K⁺ γ (left) and B⁰ → φ K_S⁰ γ (right). The points with error bars represent data and blue circles is the three-body phase-space from MC.

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TCPV Measurement

The neutral mode is used for the first time to measure the time-dependent CP asymmetry, which is suppressed in the standard model by the quark mass ratio (2m_s/m_b). The expected asymmetry is nearly 3% for S and 0.6% for A. The emitted photons are predominantly left-handed (right-handed) in b → s γ (b → s γ). In several extensions of SM, both photon helicites might contribute to the decay. Therefore, any significantly larger CP asymmetry would be clear hint of new physics.

We have 75 events in the signal region, M_bc &isin [5.27, 5.29] GeV/c² and ΔE &isin [-0.2, 0.1] GeV, for CP fit with a purity of 45%.
The measured CP violation parameters are :

• S = +0.74^+0.72_-1.05 (stat)^+0.10_-0.24 (syst)
• A = +0.35 ±0.58(stat)^+0.23_-0.10 (syst)

We find that the error on S in the MINUIT minimization is much smaller than the expectation from MC simulation and has a probability of only 0.6%. This is due to low statistics and the presence of a single special event (with &Delta t = -3.64 ps and r = 0.96). Instead of the errors from MINUIT, we use the ±68% confidence intervals in the residual distributions of S and A, determined from toy MC simulations as the statistical uncertainities on the result.
With the present statistics, these measurements are consistent with the SM predictions and there is no indication of new physics from right-handed currents.

&Delta t distributions for q=+1 adn q=-1 (left) and the raw asymmetry (right) for events with good tagging quality (r>0.5, 48% of total events). The dashed curves in the &Delta t plot are the sum of backgrounds while the solid curves are the sum of signal and backgrounds.
We also measure the charge asymmetry in B⁺ → φ K⁺ γ as A_CP = -0.03 ± 0.11 (stat) ±0.08 (syst)
The signal yields for both B⁺ and B^- decays are obtained from a simultaneous 2D fit.

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