Observation of $B^0_s$-$\bar{B}^0_s$ mixing and measurement of mixing frequencies using semileptonic B decays (1308.1302v3)

Abstract: The $B^0_s$ and $B^0$ mixing frequencies, $\Delta m_s$ and $\Delta m_d$, are measured using a data sample corresponding to an integrated luminosity of 1.0 fb^{-1} collected by the LHCb experiment in $pp$ collisions at a centre of mass energy of 7 TeV during 2011. Around 1.8x10^6 candidate events are selected of the type $B^0_{(s)} \to D^-_{(s)} \mu^+$ (+ anything), where about half are from peaking and combinatorial backgrounds. To determine the B decay times, a correction is required for the momentum carried by missing particles, which is performed using a simulation-based statistical method. Associated production of muons or mesons allows us to tag the initial-state flavour and so to resolve oscillations due to mixing. We obtain \Delta m_s = (17.93 \pm 0.22 (stat) \pm 0.15 (syst)) ps^{-1}, \Delta m_d = (0.503 \pm 0.011 (stat) \pm 0.013 (syst)) ps^{-1}. The hypothesis of no oscillations is rejected by the equivalent of 5.8 standard deviations for $B^0_s$ and 13.0 standard deviations for $B^0$. This is the first observation of $B^0_s$ mixing to be made using only semileptonic decays.

• The paper reports the first observation of significant B⁰ₛ mixing, measuring mixing frequencies with 5.8σ and 13.0σ confidence levels.
• It utilizes approximately 1.8 million semileptonic B decay events and corrects for missing momentum using simulation-based statistical methods.
• The robust analysis, including likelihood fitting and Fourier cross-checks, reinforces understanding of CP violation and flavor dynamics in the Standard Model.

Observation of $B^0_s$-$\bar{B}^0_s$ Mixing and Measurement of Mixing Frequencies Using Semileptonic $B$ Decays

The paper discusses the observation of $B^0_s$-$\bar{B}^0_s$ mixing and the measurement of the mixing frequencies $\Delta m_s$ and $\Delta m_d$ using semileptonic $B$ decays. The analysis utilizes data collected by the LHCb experiment at CERN, corresponding to an integrated luminosity of 1.0 fb$^{-1}$ from $pp$ collisions at a center-of-mass energy of 7 TeV.

Key Methods and Experimental Setup

The paper employs a sample of approximately 1.8 million candidate events of the type $B^0_{(s)} \to D^-_{(s)} \mu^+ (+ \text{anything})$. One critical aspect of the analysis is the correction for momentum carried by missing particles in the $B$ decay products, which is addressed using a simulation-based statistical method.

The LHCb detector's ability to tag the initial state flavor via associated production of muons or mesons is essential for identifying the flavor oscillations indicative of mixing. The experimental setup consists of several subsystems, including a silicon-strip vertex detector, RICH detectors, a dipole magnet, tracking stations, calorimeters, and muon detection systems, which together enable precise momentum measurement and particle identification.

Analysis and Results

Candidate $B^0_{(s)}$ events are selected based on vertex and track quality, momenta, invariant masses, and PID variables. A multidimensional log-likelihood fit is performed on the data, and an additional Fourier analysis serves as a cross-check. The mixing hypothesis is strongly supported, with oscillations being statistically significant at 5.8 standard deviations for $B^0_s$ and 13.0 standard deviations for $B^0$.

Systematic uncertainties are carefully evaluated, accounting for factors such as the $k$-factor correction, detector alignment, and assumptions related to decay models. The results are consistent with previous measurements and provide significant evidence of $B^0_s$ mixing using semileptonic decays alone.

Implications and Future Directions

The findings of this paper have substantial implications for our understanding of neutral $B$ mesons and their behavior under the weak force, particularly in validating the mixing process using semileptonic decay channels. This offers insight into CP violation and flavor dynamics in the Standard Model. The robust methodology and detection capabilities demonstrated here will be crucial for future studies that might seek to explore new physics through deviations in mixing parameters or rare decay processes.

This work exemplifies how precise measurements at collider experiments like LHCb can improve our grasp of fundamental particle interactions, reinforcing the pursuit of physics beyond the Standard Model. Further analyses with increased datasets and improved detector technologies will continue to enhance the precision of such measurements.