Anomalies in $B$-decays and $U(2)$ flavour symmetry (1512.01560v1)

Abstract: The collection of a few anomalies in semileptonic $B$-decays invites to speculate about the emergence of some strikingly new phenomena. Here we offer a possible interpretation of these anomalies in the context of a weakly broken $U(2)^5$ flavour symmetry and lepto-quark mediators.

• The paper introduces a model using a weakly broken U(2)^5 symmetry with a vector-singlet lepto-quark to explain 3.9σ and 2.6σ anomalies in B-decays.
• It demonstrates that post-symmetry breaking, small couplings to lighter generations align with observed deviations from Standard Model predictions.
• The study examines one-loop effects on charged and neutral currents, setting key constraints and guiding future experimental searches.

Overview of Anomalies in $B$-decays and $U(2)$ Flavour Symmetry

The paper in question presents an analysis of observed anomalies in semileptonic $B$-decays within the framework of flavour symmetries. The focus is on interpreting these anomalies through a weakly broken $U(2)^5$ flavour symmetry with lepto-quark (LQ) mediators. This approach provides a theoretical interpretation that could potentially elucidate deviations from the Standard Model (SM) observed in experimental data.

Key Findings and Results

1. Anomalies Detected: The paper highlights two primary anomalies:
   • A $3.9\sigma$ deviation from $\tau/l$ universality in $B \rightarrow D^{(*)}$ decays.
   • A $2.6\sigma$ deviation from $\mu/e$ universality in the $b \rightarrow s$ transitions.
2. Flavour Symmetry Framework:
   • A $U(2)^5$ symmetry is posited, encompassing quarks and leptons, with specific focus on a vector-singlet LQ model.
   • The authors propose couplings where, in an unbroken $U(2)$ symmetry limit, the LQ primarily couples to the third generation of quarks and leptons.
   • Post-symmetry breaking, these interactions yield small but non-zero couplings with other generations, aligning with observed anomalies.
3. Model Implementations: The paper evaluates three LQ scenarios with distinct gauge group representations, ultimately favoring a vector-singlet model ($U_\mu = (3,1)_{2/3}$). This model showed consistency with data through its interplay within a specified $U(2)^5$ symmetry breaking.
4. Implications of Results:
   • The analysis links LQ exchange with $30\%$ deviations in charged-current interactions and $20\%-30\%$ in neutral-current processes.
   • Key predictions include enhancements in processes such as $b \rightarrow s \tau^+ \tau^-$ which remain challenging to SM predictions.
5. Counterbalancing Loop Effects:
   • One-loop corrections are explored, revealing potential impacts on observables like $\tau \rightarrow 3\mu$, $\mu \rightarrow 3e$, and $b\bar{s}\rightarrow \bar{b}s$ mixings.
   • The loop-induced interactions suggest sizeable constraints for the model to fit the data, emphasizing the critical role of the LQ couplings and masses.

Implications and Future Directions

The implications of this paper rest significantly on the interplay between symmetry considerations and experimental anomalies, offering a pathway toward extending the SM. The exact parameter space informed by these symmetry principles has the potential to guide future experimental searches, particularly in the behavior of LQs at current and future colliders like the LHC.

From a theoretical standpoint, this framework poses pressing questions regarding the ultraviolet completion of the phenomenological model. It hints at strong dynamics at higher scales, possibly involving new composite states or sectors beyond the SM.

Further exploration in this domain could leverage precise measurements of rare decays and pursue searches for direct LQ production. Additionally, addressing the hierarchy and naturalness concerns in extending such frameworks could inspire new model-building exercises within the ambit of flavor symmetries.

Collectively, the proposed model, underpinned by empirical observations, offers a potent tool in the particle physics toolkit, setting the stage for nuanced explorations that could substantially refine our understanding of fundamental interactions.