Measurement of $f_s/f_u$ Variation with Proton-Proton Collision Energy and $B$-Meson Kinematics

The ratio of the $B_s^0$ and $B^{+}$ fragmentation fractions $f_s$ and $f_u$ is studied with $B_s^0\to J/\psi \varphi$ and $B^{+}\to J/\psi K^{+}$ decays using data collected by the LHCb experiment in proton-proton collisions at 7, 8, and 13 TeV center-of-mass energies. The analysis is performed in bins of $B$-meson momentum, longitudinal momentum, transverse momentum, pseudorapidity, and rapidity. The fragmentation-fraction ratio $f_s/f_u$ is observed to depend on the $B$-meson transverse momentum with a significance of $6.0\sigma$. This dependency is driven by the 13 TeV sample ($8.7\sigma$), while the results for the other collision energies are not significant when considered separately. Furthermore, the results show a $4.8\sigma$ evidence for an increase of $f_s/f_u$ as a function of collision energy.

Figure 1

Mass distributions of (a) $B^{+}\to J/\psi K^{+}$ and (b) $B_s^0\to J/\psi \varphi$ candidates in the 2012 data. The result of the fit is drawn with a blue solid line. The model components are denoted with a red dashed line for the signal, green dot-dashed line for the combinatorial background, magenta triple-dot-dashed line for misidentified $B^{+}\to J/\psi {\pi }^{+}$, and cyan triple-dot-dashed line for the misidentified inclusive $B^0\to J/\psi K^{+}{\pi }^{-}$ contribution.

Figure 2

Efficiency-corrected $B_s^0\to J/\psi \varphi$ and $B^{+}\to J/\psi K^{+}$ yield ratios ($\mathcal{R}$) at different $pp$ collision energies with the total (uncorrelated, including statistical) uncertainties denoted by dashed (solid) error bars. The fit result is shown with the blue solid line; the blue band denotes the 68% confidence region. The 13 TeV measurements are shifted horizontally for clarity.

Figure 3

Efficiency-corrected $B_s^0\to J/\psi \varphi$ and $B^{+}\to J/\psi K^{+}$ yield ratios ($\mathcal{R}$) in bins of (a) $p_T^B$, (c) $p_L^B$, and (d) ${\eta }^B$. The ratios are scaled to match the measured $f_s/f_d$ value (horizontal blue lines; the $\pm 1\sigma$ interval is indicated by the dashed blue lines) at the positions indicated by the vertical gray lines. The red dashed lines denote the results of the exponential fits used to estimate the statistical significances of the variations (see text). (b) The results as a function of $p_T^B$ are obtained separately in the three collision energies.