Introduction
Overview
Teaching: 15 min
Exercises: 0 minQuestions
What is the physics motivation for measuring $B_s^0 \to \mu^+\mu^-$?
What is the overall analysis strategy?
Objectives
Understand why $B_s^0 \to \mu^+\mu^-$ is a sensitive probe of new physics.
Know the key ingredients of the branching fraction measurement.
Understand the role of the normalization channel.
Physics motivation
The decay $B_s^0 \to \mu^+\mu^-$ is a Flavour-Changing Neutral Current (FCNC) process. In the Standard Model it is loop- and helicity-suppressed, giving a branching fraction of:
$\text{BF}(B_s^0 \to \mu^+\mu^-) \approx 3.66 \times 10^{-9}$
Many beyond-SM scenarios (SUSY, leptoquarks, extra dimensions) predict significant deviations from this value, making it one of the most sensitive indirect probes of new physics at the LHC.
Analysis strategy
The measurement follows the strategy of the CMS Run-2 paper BPH-21-006:
- Select $B_s \to \mu\mu$ candidates and classify them into 8 BDT categories based on signal/background discrimination.
- Model the signal PDF using a double Gaussian + Crystal Ball shape fitted to MC.
- Model background PDFs: combinatorial (Bernstein), peaking (KDE from MC), semileptonic (KDE from MC).
- Fit the normalization channel $B^+ \to J/\psi K^+$ in data to extract the observed yield and efficiency.
- Perform a simultaneous unbinned maximum likelihood fit across all 8 categories to extract BF($B_s \to \mu\mu$).
Branching fraction formula
The branching fraction is extracted via:
\[\text{BF}(B_s \to \mu\mu) = \frac{N_{B_s}}{N_{B^+}} \cdot \frac{\varepsilon_{B^+}}{\varepsilon_{B_s}} \cdot \frac{f_u}{f_s} \cdot \text{BF}(B^+ \to J/\psi K^+)\]where $f_u/f_s$ is the ratio of $B^+$ to $B_s^0$ production fractions.
Key Points
$B_s^0 \to \mu^+\mu^-$ is a FCNC decay heavily suppressed in the SM — new physics can enhance it.
The branching fraction is extracted from a simultaneous fit across BDT categories.
$B^+ \to J/\psi K^+$ serves as the normalization channel to cancel many systematic uncertainties.