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Measurement of the $B_s^0 \to \phi \phi$ branching fraction and search for the decay $B^0 \to \phi \phi$

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Abstract

Using a dataset corresponding to an integrated luminosity of 3.0 fb$^{-1}$ collected in $pp$ collisions at centre-of-mass energies of 7 and 8 TeV, the $B_s^0 \to \phi \phi$ branching fraction is measured to be \[ \mathcal{B}(B_s^0 \to \phi \phi) = ( 1.84 \pm 0.05 (\text{stat}) \pm 0.07 (\text{syst}) \pm 0.11 (f_s/f_d) \pm 0.12 (\text{norm}) ) \times 10^{-5}, \] where $f_s/f_d$ represents the ratio of the $B_s^0$ to $B^0$ production cross-sections, and the $B^0 \to \phi K^*(892)^0$ decay mode is used for normalization. This is the most precise measurement of this branching fraction to date, representing a factor five reduction in the statistical uncertainty compared with the previous best measurement. A search for the decay $B^0 \to \phi \phi$ is also made. No signal is observed, and an upper limit on the branching fraction is set as \[ \mathcal{B}(B^0 \to \phi \phi) < 2.8 \times 10^{-8} \] at 90 confidence level. This is a factor of seven improvement compared to the previous best limit.

Figures and captions

The $K^+K^-K^+K^-$ invariant mass distribution. The total fitted function as described in the text is shown by the (red) solid line, the $ B ^0_ s \rightarrow \phi\phi$ component by the (blue) long-dashed line, and the combinatorial background as the (purple) dotted line.

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The $K^+K^-K^+\pi^-$ invariant mass distribution. The total fitted function is shown by the (red) solid line, the $ B ^0 \rightarrow \phi K ^* $ component by the (blue) short-dashed line, the $ B ^0_ s \rightarrow \phi\overline{ K }{} {}^* (892)^0$ component by the (blue) long-dashed line, the $\Lambda ^0_ b \rightarrow \phi p \pi^-$ and $\Lambda ^0_ b \rightarrow \phi p K^-$ contribution by the (green) dashed-dotted line, and the combinatoral background by the (purple) dotted line.

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The $K^+K^-K^+K^-$ invariant mass with the tight BDT selection applied. A fit to the total PDF as described in the text is shown as a (red) solid line, $ B ^0_ s \rightarrow \phi\phi$ as a (blue) long-dashed line, $ B ^0 \rightarrow \phi\phi$ as a (blue) short-dashed line, and the combinatorial background as a (purple) dotted line.

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Results of the $\text{CL}_\text{s}$ scan as a function of the $ B ^0 \rightarrow \phi\phi$ branching fraction ($BF$). The observed $\text{CL}_\text{s}$ distribution is given by the (black) points and solid line, while the expected distribution is given by the (black) dashed line. The dark (green) and light (yellow) bands mark the $1\sigma$ and $2\sigma$ confidence regions on the expected $\text{CL}_\text{s}$. The upper limits at 90$ \%$ and 95$ \%$ confidence level are where the observed $\text{CL}_\text{s}$ line intercepts the (red) solid and dashed horizontal lines, respectively.

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Animated gif made out of all figures.

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Tables and captions

Predictions for the $ B ^0_ s \rightarrow \phi \phi$ branching fraction. The first and second uncertainties of Refs. [8,9] reflect the knowledge of CKM parameters and power corrections, respectively.

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Summary of the systematic uncertainties on the measurement of the ratio of branching fractions $\mathcal{B}( B ^0_ s \rightarrow \phi \phi)/\mathcal{B}( B ^0 \rightarrow \phi K^*)$.

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Created on 27 April 2024.