B_{s,d} -> l+ l- in the Standard Model with Reduced Theoretical Uncertainty (1311.0903v3)

Abstract: We combine our new results for the O(alpha_em) and O(alpha_s^2) corrections to B_{s,d} -> l^+ l^-, and present updated branching ratio predictions for these decays in the standard model. Inclusion of the new corrections removes major theoretical uncertainties of perturbative origin that have just begun to dominate over the parametric ones. For the recently observed muonic decay of the B_s meson, our calculation gives BR(B_s -> mu^+ mu^-) = (3.65 +_ 0.23) * 10^-9.

• The paper significantly reduces theoretical uncertainties in predicting Bₛ,d → ℓ⁺ℓ⁻ branching ratios, achieving non-parametric errors near 1.5%.
• It employs NLO electroweak and NNLO QCD corrections to update the Bₛ decay rate to (3.65 ± 0.23) × 10⁻⁹.
• The refined predictions provide a robust benchmark for testing new physics and inform future improvements in lattice QCD calculations.

Analysis of Theoretical Uncertainties Reduction in Leptonic Decays of Neutral B Mesons

The paper "$B_{s,d} \to \ell^+ \ell^-$ in the Standard Model with Reduced Theoretical Uncertainty" presents a comprehensive paper on the theoretical predictions of rare leptonic decays of neutral B mesons within the Standard Model (SM). This work is particularly significant as it reduces the theoretical uncertainties associated with these decay processes, which can impose important constraints on new physics models.

Background and Motivation

Rare leptonic decays, such as $B_s \to \mu^+ \mu^-$, are highly suppressed in the SM due to their nature as flavor-changing neutral current (FCNC) processes. These decays occur only at the loop level via W-box and Z-penguin diagrams and are subject to helicity suppression. Thus, precise theoretical predictions of their branching ratios are crucial to provide constraints on the parameter space of potential extensions to the SM, such as models with additional Higgs doublets. Accurate SM predictions also serve as a benchmark for observing deviations that may hint at new physics.

Methodology and Results

The authors provide an updated prediction for the branching ratios of the $B_{s,d} \to \ell^+ \ell^-$ decays, particularly focusing on $B_s \to \mu^+ \mu^-$. They incorporate next-to-leading order (NLO) electroweak (EW) and next-to-next-to-leading order (NNLO) quantum chromodynamics (QCD) corrections. This comprehensive inclusion of higher-order corrections is pivotal in reducing the theoretical uncertainties, which have been significant barriers in the quest for new physics through these decays.

Numerically, the prediction for the branching ratio $\overline{\mathcal B}(B_s \to \mu^+ \mu^-)$ was updated to $(3.65 \pm 0.23) \times 10^{-9}$. This includes substantial improvements in calculational accuracy, reducing non-parametric uncertainties in the predictions to around 1.5%. This contrasts sharply with the prior uncertainty estimates of approximately 8%. The parametric uncertainties remain dominated by inputs such as the decay constant $f_{B_s}$ and the CKM matrix elements, particularly $|V_{cb}|$.

Implications

With the theoretical uncertainties now substantially reduced to a level that aligns with current experimental capabilities, the results provided in this paper enhance the robustness of SM predictions, facilitating more stringent tests of new physics models against the experimental data. As experimental precision improves, especially with upgrades to facilities such as LHCb, these theoretical advancements will become integral to interpreting or perhaps confirming new physics signals.

Future Directions

The refinement of the theoretical framework for rare B meson decays paves the way for further investigations into potential beyond-SM physics scenarios. Continued efforts in enhancing lattice QCD calculations to improve determinations of $f_{B_q}$ and $B_{B_q}$ will further compress parametric uncertainties in branching ratios, refining the predictions for observables like $\kappa_{q\ell}$. The research community will benefit from applying the methodologies demonstrated in this work to other processes where theoretical precision is critical.

Overall, the paper acts as a crucial reference point in the ongoing endeavor to match theoretical predictions with the precision achievable by current and future experimental endeavors, setting the stage for potential discoveries in the field of particle physics.