Measurement of the fragmentation fraction ratio $f_{s}/f_{d}$ and its dependence on $B$ meson kinematics

Abstract: The relative production rate of $B^{0}_{s}$ and $B^{0}$ mesons is determined with the hadronic decays $B^{0}_{s} \rightarrow D^{-}_{s}\pi^{+}$ and $B^0 \rightarrow D^{-}K^{+}$. The measurement uses data corresponding to 1.0 fb$^{-1}$ of $pp$ collisions at a centre-of-mass energy of $\sqrt{s}=7$ TeV recorded in the forward region with the LHCb experiment. The ratio of production rates, $f_{s}/f_{d}$, is measured to be $0.238 \pm 0.004 \pm 0.015 \pm 0.021 $, where the first uncertainty is statistical, the second systematic, and the third theoretical. This is combined with a previous LHCb measurement to obtain $f_{s}/f_{d} = 0.256 \pm 0.020$. The dependence of $f_{s}/f_{d}$ on the transverse momentum and pseudorapidity of the $B$ meson is determined using the decays $B^{0}_{s} \rightarrow D^{-}_{s}\pi^{+}$ and $B^{0} \rightarrow D^{-}\pi^{+}$. There is evidence for a decrease with increasing transverse momentum, whereas the ratio remains constant as a function of pseudorapidity. In addition, the ratio of branching fractions of the decays $B^{0} \rightarrow D^{-}K^{+}$ and $B^{0} \rightarrow D^{-}\pi^{+}$ is measured to be $0.0822 \pm 0.0011 (\textrm{stat}) \pm 0.0025 (\textrm{syst})$.

• The paper presents a precise measurement of the fₛ/f_d ratio, obtaining 0.238 with quantified statistical, systematic, and theoretical uncertainties.
• It reveals a significant decrease in fₛ/f_d with increasing transverse momentum, while no pseudorapidity dependence is observed.
• Accurate measurement of the branching fraction ratio for B⁰ decays is used to refine fragmentation models and enhance Standard Model tests.

Measurement of the Fragmentation Fraction Ratio $f_s/f_d$ and its Dependence on $B$ Meson Kinematics

This paper, submitted by the LHCb collaboration, explores the measurement of the fragmentation fraction ratio $f_s/f_d$, focusing on its dependence on $B$ meson kinematics. Through meticulous experimentation with $pp$ collisions at a center-of-mass energy of $\sqrt{s}=7$ TeV, this research utilizes data from an integrated luminosity of 1.0 $\text{fb}^{-1}$, recorded using the LHCb detector.

Key Findings

1. Fragmentation Fraction Ratio:
   • The ratio $f_s/f_d$, which quantifies the relative production rates of $B^0_s$ to $B^0$ mesons, reveals a fundamental aspect of how $b$ quarks hadronize into different meson types. It is measured to be $$0.238 \pm 0.004 \,(\text{stat}) \pm 0.015 \,(\text{syst}) \pm 0.021 \,(\text{theo})$$.
   • A combined analysis incorporating previous LHCb measurements provides a refined value of $0.256 \pm 0.020$.
2. Kinematic Dependence:
   • The study also investigates how $f_s/f_d$ varies with different kinematic properties of the $B^0_{(s)}$ mesons, particularly transverse momentum ($p_T$) and pseudorapidity ($\eta$).
   • A statistically significant decrease in $f_s/f_d$ with increasing $p_T$ was observed, which deviates significantly from zero, suggesting a potential area for further theoretical exploration.
   • No dependence on $\eta$ was detected, indicating a potential universality across this variable.
3. Branching Fraction Ratio:
   • The ratio of branching fractions $$\frac{\text{BR}(B^0 \rightarrow D^-K^+)}{\text{BR}(B^0 \rightarrow D^-\pi^+)}$$ is quantified to be $$0.0822 \pm 0.0011 \,(\text{stat}) \pm 0.0025 \,(\text{syst})$$, a measurement pivotal for subsequent use in determining effective fragmentation fractions and improving precision on branching fraction normalizations.

Implications and Future Directions

The implications of this research are substantial, both in advancing theoretical physics and in practical application within particle collider experiments. The precise determination of the $f_s/f_d$ ratio provides foundational input for testing the Standard Model, especially in rare $B$ meson decays such as $B^0_s \to \mu^+\mu^-$.

Practically, the observed dependence on $p_T$ might indicate complex underlying dynamics in $b$-quark hadronization processes, which challenge existing theoretical frameworks and necessitate refined models that better account for kinematic variables.

Moving forward, further research could explore the kinematic dependencies with even larger datasets at varying energy levels to discern possible systematics or statistical effects. Additionally, theoretical work could aim to develop new models or simulations that match the empirical results concerning $p_T$-dependent fragmentation processes.

Overall, this paper enriches our understanding of $B$ meson production in high-energy physics and sets the groundwork for future inquiries into the behavior of fundamental particles in collider environments.