[Paper Review] Determination of the branching fractions of $B_{s}^{0} o D_{s}^{\mp} K^{\pm}$ and $B^{0} o D_{s}^{-} K^{+}$

LHCb collaboration, R. Aaij+703 more|arXiv (Cornell University)|Dec 24, 2014

Particle physics theoretical and experimental studies19 references4 citations

TL;DR

This paper presents a precise measurement of the branching fractions for $B_s^0 \to D_s^\mp K^\pm$ and $B^0 \to D_s^- K^+$ decays using 3.0 fb$^{-1}$ of proton-proton collision data from the LHCb experiment at $\sqrt{s} = 7$ and $8$ TeV. The ratios $\mathcal{B}(B_s^0 \to D_s^\mp K^\pm)/\mathcal{B}(B_s^0 \to D_s^- \pi^+) = 0.0752 \pm 0.0015 \pm 0.0019$ and $\mathcal{B}(B^0 \to D_s^- K^+ among the most precise to date, providing key inputs for testing $C\!P$ violation and $W$-exchange contributions in $B$ decays.

ABSTRACT

Measurements are presented of the branching fractions of the decays $B_{s}^{0} o D_{s}^{\mp} K^{\pm}$ and $B^{0} o D_{s}^{-} K^{+}$ relative to the decays $B_{s}^{0} o D_{s}^{-} π^{+}$ and $B^{0} o D^{-} π^{+}$, respectively. The data used correspond to an integrated luminosity of 3.0 fb$^{-1}$ of proton-proton collisions. The ratios of branching fractions are $\dfrac{\mathcal{B}(B_{s}^{0} o D_{s}^{\mp} K^{\pm})}{\mathcal{B}(B_{s}^{0} o D_{s}^{-} π^{+})} = 0.0752 \pm 0.0015 \pm 0.0019$ and $\dfrac{\mathcal{B}(B^{0} o D_{s}^{-} K^{+})}{\mathcal{B}(B^{0} o D^{-} π^{+})} = 0.0129 \pm 0.0005 \pm 0.0008,$ where the uncertainties are statistical and systematic, respectively.

Motivation & Objective

• To measure the branching fraction ratio of $B_s^0 \to D_s^\mp K^\pm$ relative to $B_s^0 \to D_s^- \pi^+$ to probe $C\!P$ violation and CKM angle $\gamma$.
• To determine the branching fraction of $B^0 \to D_s^- K^+$ relative to $B^0 \to D^- \pi^+$ to assess the size of $W$-exchange amplitudes in $B$ decays.
• To improve the precision of absolute branching fractions for $B_s^0 \to D_s^\mp K^\pm$ and $B^0 \to D_s^- K^+$, reducing uncertainties compared to world averages.
• To test theoretical predictions based on SU(3) flavor symmetry and $W$-exchange contributions, particularly in the context of $B_s^0$ decays.

Proposed method

• The analysis uses 3.0 fb$^{-1}$ of $pp$ collision data at $\sqrt{s} = 7$ and $8$ TeV collected by the LHCb detector.
• Decay vertices are reconstructed using a multivariate algorithm to identify secondary vertices from $b$-hadron decays with significant displacement from primary vertices.
• Branching fraction ratios are extracted using the formula $\mathcal{B}(B_s^0 \to D_s^\mp K^\pm)/\mathcal{B}(B_s^0 \to D_s^- \pi^+) = \varepsilon_{K}/\varepsilon_{\pi} \cdot f_K/f_\pi \cdot N_K/N_\pi \cdot \mathcal{B}(D_s^\mp \to K^\pm \pi^\mp \pi^\mp)/\mathcal{B}(D_s^- \to K^+ K^- \pi^-)$, with input branching fractions from world averages.
• Systematic uncertainties are evaluated through dedicated control samples and variations in reconstruction and selection criteria.
• The absolute branching fractions are derived by combining the measured ratios with the world-average branching fractions of the reference decays.
• Efficiencies and acceptance corrections are determined using simulation and data-driven methods, with validation via control decays.

Experimental results

Research questions

• RQ1 What is the precise branching fraction ratio of $B_s^0 \to D_s^\mp K^\pm$ relative to $B_s^0 \to D_s^- \pi^+$, and how does it compare to theoretical expectations?
• RQ2 What is the absolute branching fraction of $B^0 \to D_s^- K^+$, and how does it compare to previous measurements from BaBar and Belle?
• RQ3 To what extent does the $W$-exchange topology contribute to the $B^0 \to D_s^- K^+$ decay, as inferred from the branching fraction suppression relative to $B^0 \to D^- \pi^+$?
• RQ4 How well do SU(3) symmetry predictions describe the $B_s^0 \to D_s^\mp K^\pm$ decay rate relative to the $\pi^+$ mode?
• RQ5 What is the impact of $C\!P$ violation and mixing interference on the $B_s^0 \to D_s^\mp K^\pm$ decay amplitude, as constrained by this measurement?

Key findings

• The ratio $\mathcal{B}(B_s^0 \to D_s^\mp K^\pm)/\mathcal{B}(B_s^0 \to D_s^- \pi^+) = 0.0752 \pm 0.0015 \text{ (stat)} \pm 0.0019 \text{ (syst)}$ is the most precise measurement to date, consistent with theoretical predictions of $0.086^{+0.009}_{-0.007}$.
• The absolute branching fraction of $B_s^0 \to D_s^\mp K^\pm$ is measured as $(2.29 \pm 0.05 \text{ (stat)} \pm 0.06 \text{ (syst)} \pm 0.17 \text{ (br)}) \times 10^{-4}$, with the last uncertainty from input branching fraction errors.
• The ratio $\mathcal{B}(B^0 \to D_s^- K^+)/\mathcal{B}(B^0 \to D^- \pi^+) = 0.0129 \pm 0.0005 \text{ (stat)} \pm 0.0007 \text{ (syst)} \pm 0.0004 \text{ (br)}$ confirms the suppression expected from $W$-exchange topology.
• The absolute branching fraction for $B^0 \to D_s^- K^+$ is $(3.45 \pm 0.14 \text{ (stat)} \pm 0.20 \text{ (syst)} \pm 0.20 \text{ (br)}) \times 10^{-5}$, which is larger than the Belle measurement by more than three standard deviations.
• The measured $B_s^0 \to D_s^\mp K^\pm$ ratio is compatible with the SU(3)-symmetry-based prediction and the lower bound of $0.080 \pm 0.007$, indicating no significant new physics effects in this channel.
• The result for $B_s^0 \to D_s^- \pi^+$ branching fraction, $\mathcal{B} = (2.95 \pm 0.01 \text{ (stat)}) \times 10^{-3}$, is consistent with the world average and validates the analysis method.