[Paper Review] Theoretical Status of Rare B Decays with Muons

Christoph Bobeth, Gudrun Hiller+1 more|arXiv (Cornell University)|Nov 20, 2009

Particle physics theoretical and experimental studies15 references3 citations

TL;DR

This paper reviews the theoretical status of rare B decays involving muons, focusing on exclusive semileptonic decays such as $B \to K^{(*)}\mu^{+}\mu^{-}$ and $B_s \to \Phi\mu^{+}\mu^{-}$, using effective field theory to probe new physics beyond the Standard Model. It highlights that T-odd and CP-odd angular asymmetries, especially $A_7$, $A_8$, and $A_9$, are highly sensitive to new physics phases and can reach order-one values in the low $q^2$ region, offering powerful, model-independent probes of physics beyond the Standard Model.

ABSTRACT

Rare B decays allow to investigate fundamental interactions regarding their flavor, chiral, Dirac and CP properties. In anticipation of the large data samples of exclusive B decays into muons from the forthcoming LHC experiments, in particular LHCb, as well as possible super flavor factories, we review the theoretical status and outline future opportunities to explore the borders of the Standard Model and beyond.

Motivation & Objective

• To assess the theoretical status of rare semileptonic $B$ decays into muons, particularly $B \to K^{(*)}\mu^{+}\mu^{-}$, $B_s \to \Phi\mu^{+}\mu^{-}$, and $\Lambda_b \to \Lambda\mu^{+}\mu^{-}$, in the context of upcoming high-luminosity LHC and super flavor factory data.
• To identify and analyze observables sensitive to new physics beyond the Standard Model (BSM), especially those that are model-independent and sensitive to CP phases and lepton flavor non-universality.
• To demonstrate the potential of angular distributions and forward-backward asymmetries in $B \to K\mu^{+}\mu^{-}$ and $B_s \to \Phi\mu^{+}\mu^{-}$ decays to probe new physics effects, including right-handed currents and tensor operators.
• To emphasize the importance of $q^2$-binned measurements and kinematic cuts to isolate physics beyond the $J/\Psi$ and $\Psi'$ resonances, enabling precise comparisons with theory.
• To advocate for the use of $R_K = \mathcal{B}(B \to K\mu^{+}\mu^{-}) / \mathcal{B}(B \to Ke^{+}e^{-})$ and related observables as probes of lepton flavor universality violation in BSM scenarios.

Proposed method

• Uses an effective field theory framework with the Hamiltonian $\mathcal{H}_{\text{eff}} = -4 \frac{G_F}{\sqrt{2}} V_{tb} V_{ts}^* \sum_i C_i(\mu) O_i(\mu)$ to describe $b \to s\mu^{+}\mu^{-}$ transitions, allowing model-independent analysis of Wilson coefficients.
• Classifies operators by chirality and flavor structure, distinguishing between SM contributions (e.g., $C_9, C_{10}$) and BSM-sensitive operators such as $C_{S,P}$, $C'_{S,P}$, and $C_{T,T5}$, which are sensitive to leptoquarks, R-parity violation, or SUSY with large $\tan\beta$.
• Analyzes angular distributions in $B \to K^{(*)}\mu^{+}\mu^{-}$ and $B_s \to \Phi\mu^{+}\mu^{-}$ decays, decomposing the decay rate into terms involving $F_H^l$, $A_{\text{FB}}^l$, and $A_i$ asymmetries to extract information on CP violation and new physics.
• Applies $q^2$-binning of dilepton mass spectra to avoid resonant contamination (e.g., $J/\Psi$, $\Psi'$) and to enable systematic comparison with theoretical predictions in the low- and high-$q^2$ regions.
• Uses T-odd and CP-odd asymmetries ($A_7, A_8, A_9$) that are sensitive to CP phases and do not vanish in the limit of small strong phases, making them ideal for detecting new physics with large CP-violating phases.
• Performs numerical studies of asymmetries as functions of new physics Wilson coefficients, showing that $A_7$, $A_8$, and $A_9$ can reach order-one values in the low $q^2$ region when new physics is present.

Experimental results

Research questions

• RQ1 How can angular asymmetries in $B \to K^{(*)}\mu^{+}\mu^{-}$ decays be used to probe new physics beyond the Standard Model, especially in the presence of CP-violating phases?
• RQ2 What is the sensitivity of T-odd and CP-odd asymmetries to new physics contributions such as right-handed currents or tensor operators, and how do they compare to T-even asymmetries?
• RQ3 To what extent can the ratio $R_K = \mathcal{B}(B \to K\mu^{+}\mu^{-}) / \mathcal{B}(B \to Ke^{+}e^{-})$ serve as a probe of lepton flavor universality violation in BSM models?
• RQ4 How do kinematic cuts in the dilepton invariant mass $q^2$ affect the theoretical interpretation of exclusive $b \to s\mu^{+}\mu^{-}$ decays and the extraction of new physics signals?
• RQ5 What is the role of $B_s \to \Phi\mu^{+}\mu^{-}$ decays in measuring time-integrated CP asymmetries and probing the $B_s$ mixing phase, especially in the absence of self-tagging?

Key findings

• T-odd CP asymmetries $A_7$, $A_8$, and $A_9$ are maximally sensitive to CP phases in the low $q^2$ region and can reach order-one values in the presence of new physics, unlike T-even asymmetries which vanish for small strong phases.
• The forward-backward asymmetry $A_{\text{FB}}^\mu$ in $B \to K\mu^{+}\mu^{-}$ can be as large as 15% in BSM scenarios, while $R_K - 1$ can reach ${\cal{O}}(1)$, indicating significant lepton flavor non-universality effects.
• The $B_s \to \Phi\mu^{+}\mu^{-}$ decay mode allows for time-integrated CP asymmetries sensitive to the $B_s$ mixing phase due to its large width difference $\Delta\Gamma_s / \Gamma_s \sim 0.1$, enabling new physics probes without flavor tagging.
• The $B \to K\mu^{+}\mu^{-}$ decay rate is sensitive to the lepton flavor, with $F_H^l$ and $A_{\text{FB}}^l$ being strongly suppressed in the SM by lepton mass but potentially sizeable in BSM models.
• The $B_s \to \mu^{+}\mu^{-}$ branching ratio is predicted to be $\sim 3 \times 10^{-9}$ in the SM, but can be enhanced in models with large $\tan\beta$ or R-parity violation, with current bounds at $\mathcal{B} < 3.6 \times 10^{-8}$ at 90% C.L.
• The $B_d \to \mu^{+}\mu^{-}$ to $B_s \to \mu^{+}\mu^{-}$ branching ratio ratio is a clean probe of flavor structure and can test the CKM hierarchy in semileptonic decays, with current data beginning to constrain this ratio.