[Paper Review] $B^0_s ightarrow \mu^+\mu^-$ at the LHC

F. Archilli|arXiv (Cornell University)|Sep 10, 2014

Particle physics theoretical and experimental studies10 references3 citations

TL;DR

This paper presents a combined analysis of $B^0_s \to \mu^+\mu^-$ and $B^0 \to \mu^+\mu^-$ decays using Run I data from the LHCb and CMS experiments. The $B^0_s \to \mu^+\mu^-$ decay is observed for the first time with a significance of 6.2\sigma, and the measured branching fraction is $ (2.8^{+0.7}_{-0.6}) \times 10^{-9} $, consistent with the Standard Model within 1.2\sigma.

ABSTRACT

Rare leptonic decays of $B_{(s)}^0$ mesons are sensitive probes of New Physics effects. A combination of the CMS and LHCb analyses on the search of the rare decays $B_{s}^0 \ ightarrow \\mu^+\\mu^-$ and $B^0 \ ightarrow \\mu^+\\mu^-$ is presented. The branching fractions of $B_{s}^0 \ ightarrow \\mu^+\\mu^-$ and $B^0 \ ightarrow \\mu^+\\mu^-$ are measured to be $\\mathcal{B}(B_{s}^0 \ ightarrow \\mu^+\\mu^-) = (2.8 \\,^{+0.7}_{-0.6}) \ imes 10^{-9}$ and $\\mathcal{B}(B^0 \ ightarrow \\mu^+\\mu^-) = (3.9 \\,^{+1.6}_{-1.4}) \ imes 10^{-10}$ respectively. A statistical significances of $6.2\\,\\sigma$ is evaluated for $B_{s}^0 \ ightarrow \\mu^+\\mu^-$ from the Wilks' theorem while a significance of $3.0\\, \\sigma$ is measured for $B^0 \ ightarrow \\mu^+\\mu^-$ from the Feldman-Cousins procedure.

Motivation & Objective

• To combine the LHCb and CMS experimental results on rare $B^0_s \to \mu^+\mu^-$ and $B^0 \to \mu^+\mu^-$ decays to improve statistical significance and precision.
• To evaluate the compatibility of the measured branching fractions with Standard Model predictions, especially in the context of New Physics models.
• To perform a simultaneous unbinned extended maximum likelihood fit that properly accounts for correlations between input parameters from both experiments.
• To assess the statistical significance of the $B^0_s \to \mu^+\mu^-$ signal using Wilks’ theorem and the $B^0 \to \mu^+\mu^-$ signal using the Feldman-Cousins procedure.
• To measure the ratio of branching fractions $\mathcal{R} = \mathcal{B}(B^0 \to \mu^+\mu^-)/\mathcal{B}(B^0_s \to \mu^+\mu^-)$ and compare it with the SM prediction to test for New Physics.

Proposed method

• A simultaneous unbinned extended maximum likelihood fit is performed on the dimuon invariant mass spectra from both LHCb and CMS datasets.
• The fit includes signal components for $B^0_s \to \mu^+\mu^-$ and $B^0 \to \mu^+\mu^-$, along with contributions from combinatorial, semileptonic, and peaking backgrounds.
• Multivariate classifiers (BDT) trained using the TMVA framework are used to separate signal from background, based on kinematic and geometric variables.
• The dimuon mass is calibrated using resonances such as $J/\psi \to \mu^+\mu^-$ and $B^0_s \to \phi \to K^+K^-$, with additional corrections for lifetime bias in $\Lambda^0_b \to p\mu^-\bar{\nu}$ decays.
• Signal yields are normalized to $B^+ \to J/\psi K^+$ and $B^0 \to K^+\pi^-$ decays, using measured b-hadron fragmentation fractions from LHCb.
• Statistical significance is evaluated using Wilks’ theorem for $B^0_s \to \mu^+\mu^-$ and the Feldman-Cousins procedure for $B^0 \to \mu^+\mu^-$ to handle low-significance cases.

Experimental results

Research questions

• RQ1 Is the $B^0_s \to \mu^+\mu^-$ decay observed with sufficient significance to claim discovery?
• RQ2 How do the measured branching fractions of $B^0_s \to \mu^+\mu^-$ and $B^0 \to \mu^+\mu^-$ compare with Standard Model predictions?
• RQ3 What is the compatibility of the measured $B^0_s \to \mu^+\mu^-$ and $B^0 \to \mu^+\mu^-$ branching fractions with the SM, including theoretical uncertainties?
• RQ4 Is the ratio $\mathcal{R} = \mathcal{B}(B^0 \to \mu^+\mu^-)/\mathcal{B}(B^0_s \to \mu^+\mu^-)$ consistent with the SM prediction?
• RQ5 What is the statistical significance of the $B^0 \to \mu^+\mu^-$ signal, and how does it compare to the background-only hypothesis?

Key findings

• The $B^0_s \to \mu^+\mu^-$ decay is observed for the first time with a statistical significance of 6.2\sigma, using Wilks’ theorem.
• The measured branching fraction is $\mathcal{B}(B^0_s \to \mu^+\mu^-) = (2.8^{+0.7}_{-0.6}) \times 10^{-9}$, in agreement with the SM prediction of $3.66 \times 10^{-9}$ within 1.2\sigma.
• A $3.0\sigma$ excess is observed for $B^0 \to \mu^+\mu^-$, with a measured branching fraction of $ (3.9^{+1.6}_{-1.4}) \times 10^{-10} $, compatible with the SM at 2.2\sigma.
• The ratio of branching fractions $\mathcal{R} = 0.14^{+0.08}_{-0.06}$ is consistent with the SM prediction of $0.0295^{+0.0028}_{-0.0025}$ within 2.3\sigma.
• The compatibility of $\mathcal{B}(B^0_s \to \mu^+\mu^-)$ with the SM is $1.2\sigma$, and for $\mathcal{B}(B^0 \to \mu^+\mu^-)$ it is $2.2\sigma$, including theoretical uncertainties.
• The likelihood profile for $\mathcal{R}$ shows no significant deviation from the SM, with the 95% confidence interval encompassing the SM value.