[Paper Review] Leptoquark models for the $B$-physics anomalies

Olcyr Sumensari|arXiv (Cornell University)|May 22, 2017

Particle physics theoretical and experimental studies3 references6 citations

TL;DR

This paper proposes a leptoquark model with a (3,2)₁/₆ scalar leptoquark and light right-handed neutrinos to simultaneously explain the $B$-physics anomalies: $R_K^\text{exp} < R_K^\text{SM}$ and $R_{D^{(*)}}^\text{exp} > R_{D^{(*)}}^\text{SM}$. The model predicts observable lepton flavor violating decays like $B \to K\mu\tau$ with branching ratios up to $6.7 \times 10^{-6}$, and enhanced $B_c \to \eta_c\tau\nu$ and $B_c \to \tau\nu$ rates, offering testable signatures at LHCb and future B-factories.

ABSTRACT

The $B$-physics experiments at LHCb, BaBar and Belle hint towards deviations from Lepton Flavor Universality in both the tree-level and loop-induced $B$ meson semileptonic decays. We propose a leptoquark model with light right-handed neutrinos which can accommodate both $R_K^\mathrm{exp}R_{D^{(\ast)}}^\mathrm{SM}$. We discuss several of its predictions which can be tested in modern day experiments. We also comment on the recent finding at LHCb, namely $R_{K^\ast}^{\mathrm{exp}}

Motivation & Objective

• To resolve the persistent lepton flavor universality (LFU) violations observed in $B$-meson decays, particularly $R_K < 1$ and $R_D > 1$.
• To construct a renormalizable, viable model that accommodates both $R_K$ and $R_D$ anomalies without conflicting with existing flavor physics constraints.
• To provide testable predictions for lepton flavor violating decays and $B_c$ decays that can be probed in ongoing and future experiments.
• To address the recent LHCb hint of $R_{K^*}^\text{exp} < R_{K^*}^\text{SM}$, exploring whether the model can be extended to explain this new anomaly.

Proposed method

• Introduces a scalar leptoquark with quantum numbers $(3,2)_{1/6}$ and a light right-handed neutrino to mediate both $b \to s\ell\ell$ and $b \to c\ell\nu$ transitions via tree-level couplings.
• Constructs the effective Lagrangian at low energies using the Yukawa couplings $Y_L$ and $Y_R$, with the Wilson coefficients derived from loop suppression via $m_\Delta \sim 1\ \text{TeV}$.
• Applies constraints from $B \to K\mu\mu$, $B \to D\tau\nu$, $B \to K\mu\tau$, $B_c \to \eta_c\tau\nu$, and $B_c \to \tau\nu$ decays, along with $\tau \to \mu\gamma$ and $B_s \to \bar{B}_s$ mixing.
• Uses lattice QCD form factors for $B \to D$ and $B \to D^*$ transitions to compute $R_D$ and $R_{D^*}$, with $R_{D^*}$ treated qualitatively due to incomplete LQCD data.
• Performs a global fit of the Yukawa couplings under experimental and theoretical constraints to derive predictive branching ratios.
• Considers alternative LQ states such as $(\bar{3},3)_{1/3}$ and $(3,2)_{7/6}$ to explain $R_{K^*}$ anomalies via loop-induced contributions, preserving proton stability.

Experimental results

Research questions

• RQ1 Can a single leptoquark model with light right-handed neutrinos simultaneously explain the $R_K < 1$ and $R_D > 1$ anomalies in $B$-meson decays?
• RQ2 What are the observable lepton flavor violating decay modes predicted by such a model, and what are their branching ratios?
• RQ3 How does the model affect the $B_c \to \eta_c\tau\nu$ and $B_c \to \tau\nu$ decay rates compared to the Standard Model?
• RQ4 Can the model account for the recent LHCb hint of $R_{K^*}^\text{exp} < R_{K^*}^\text{SM}$, and if so, through which mechanism?
• RQ5 What are the implications of the model for proton stability and other flavor-changing processes?

Key findings

• The model predicts $R_K = 0.88(8)$, consistent with the experimental value $R_K^\text{exp} = 0.745 \pm 0.090_{-0.074}^{+0.036}$ at the $2.4\sigma$ level.
• The model accommodates $R_D^\text{exp} > R_D^\text{SM}$ at the $1\sigma$ level, with $R_D = 0.41 \pm 0.05$.
• The branching ratio for the lepton flavor violating decay $B \to K\mu\tau$ is predicted to range from $2.1 \times 10^{-10}$ to $6.7 \times 10^{-6}$, making it potentially observable at LHCb.
• The model predicts a significant enhancement in $B_c \to \eta_c\tau\nu$ decay rate, with $R_{\eta_c}/R_{\eta_c}^\text{SM}$ ranging from 1.02 to 1.21.
• The branching ratio for $B_c \to \tau\nu$ is predicted to be enhanced by a factor of 5.5 to 16.1 compared to the SM value.
• The model cannot explain $R_{K^*}^\text{exp} < R_{K^*}^\text{SM}$ via tree-level contributions, but a different LQ state $(3,2)_{7/6}$ with loop-induced $C_9 = -C_{10} < 0$ could explain it while preserving proton stability.