Measurement of the Dependence of the Hadron Production Fraction Ratios $f_s/f_u$ and $f_d/f_u$ on $B$ Meson Kinematic Variables in Proton-Proton Collisions at $\sqrt{s}=13\mathrm{TeV}$

The dependence of the ratio between the $B_s^0$ and $B^{+}$ hadron production fractions, $f_s/f_u$, on the transverse momentum ($p_T$) and rapidity of the $B$ mesons is studied using the decay channels $B_s^0\to J/\psi \varphi$ and $B^{+}\to J/\psi K^{+}$. The analysis uses a data sample of proton-proton collisions at a center-of-mass energy of 13 TeV, collected by the CMS experiment in 2018 and corresponding to an integrated luminosity of $61.6{\mathrm{fb}}^{-1}$. The $f_s/f_u$ ratio is observed to depend on the $B$ $p_T$ and to be consistent with becoming asymptotically constant at large $p_T$. No rapidity dependence is observed. The ratio of the $B^0$ to $B^{+}$ meson production fractions, $f_d/f_u$, is also measured, for the first time in proton-proton collisions, using the $B^0\to J/\psi K^{*0}$ decay channel. The result is found to be within 1 standard deviation of unity and independent of $p_T$ and rapidity, as expected from isospin invariance.

Figure 1

The $J/\psi \varphi$, $J/\psi K^{+}$, and $J/\psi K^{*0}$ invariant mass distributions for $B$ meson candidates with $20<p_T<23\mathrm{GeV}$, and associated fits as described in the text.

Figure 2

Efficiency-corrected yield ratio ${\mathcal{R}}_s$, as a function of $p_T$ (left) and $|y|$ (right). The vertical bars (boxes) represent the statistical (bin-to-bin systematic) uncertainties, while the horizontal bars give the bin widths. The global uncertainty (of 2.3%) is not graphically represented. The blue line represents the average for $p_T>18\mathrm{GeV}$. For comparison, the LHCb measurement [12] is also shown.

Figure 3

The ratio of the $B^0$ to $B^{+}$ hadron production fractions $f_d/f_u$, as a function of $p_T$ (left) and $|y|$ (right). The vertical bars (boxes) represent the statistical (bin-to-bin systematic) uncertainties, while the horizontal bars give the bin widths. The horizontal blue line and band represent the average value and uncertainty. The global uncertainty (of 5.7%) is included in the blue bands but not in the individual data points.