[Paper Review] Lepton nonuniversality anomalies and implications

Gudrun Hiller|arXiv (Cornell University)|Apr 5, 2018

Particle physics theoretical and experimental studiesPhysics and Astronomy28 references4 citations

TL;DR

This paper investigates lepton nonuniversality anomalies in rare B-meson decays, identifying V-A type operators—particularly $C_9^{\rm NP}$ and $C_{10}^{\rm NP}$—as the dominant source of deviations in $R_K$ and $R_{K^*}$, with $R_K \simeq 0.745$ and $R_{K^*} \simeq 0.69$ at $q^2 \in [1.1,6]~\text{GeV}^2$. It predicts $R_{X_s} \simeq 0.73 \pm 0.07$ for inclusive $B \to X_s \ell\ell$ decays, testable at Belle II, and identifies scalar and vector leptoquarks as viable BSM explanations.

ABSTRACT

We discuss avenues for diagnosing new physics hinted from lepton nonuniversality in rare $b$-decays, and physics implications.

Motivation & Objective

• To diagnose the origin of lepton nonuniversality (LNU) anomalies in rare $b \to s\ell\ell$ decays, particularly in $R_K$ and $R_{K^*}$.
• To determine whether the anomalies arise from new physics (NP) in muons, electrons, or both, using lepton-specific measurements.
• To explore correlations with other flavor sectors, including charm, kaon physics, lepton flavor violation (LFV), and $\tau$-decays.
• To identify viable BSM models—especially leptoquarks—that can explain the anomalies while satisfying existing constraints.
• To provide testable predictions for future experiments, including $R_{X_s}$ and $B \to K^{(*)}ee$ decays, at Belle II and the LHC.

Proposed method

• Uses an effective field theory framework at dimension six, with $\mathcal{H}_{\rm eff} = -4G_F/\sqrt{2} \, V_{tb}V_{ts}^* \sum_i C_i(\mu) O_i(\mu)$, to describe $b \to s\ell\ell$ transitions.
• Applies the linear approximation $\mathcal{B} = |A^{\rm SM} + A^{\rm NP}|^2 \approx |A^{\rm SM}|^2 + 2\,{\rm Re}(A^{\rm SM} A^{\rm NP*}) + |A^{\rm NP}|^2$ to isolate NP contributions.
• Analyzes $R_H = \mathcal{B}(B \to \bar{H}\mu\mu)/\mathcal{B}(B \to \bar{H}ee)$ for $H = K, K^*, X_s$, using $q^2$-integrated branching ratios to reduce hadronic uncertainties.
• Identifies the dominant NP structure via $C_9^{\rm NP}$ and $C_{10}^{\rm NP}$, with $\Delta C_9^{\rm NP} \sim -1.1 \pm 0.3$ and $\Delta C_{10}^{\rm NP} \sim -1.1 \pm 0.3$ for muons.
• Predicts $R_{X_s} \simeq 0.73 \pm 0.07$ based on $R_K$ and $R_{K^*}$ data, using symmetry relations among $R_H$ ratios.
• Evaluates leptoquark models ($S_3, V_3, V_1$) as viable explanations, excluding $\tilde{S}_2$ due to V+A structure, and derives model-independent bounds on masses and couplings.

Experimental results

Research questions

• RQ1 What is the dominant Dirac structure (V-A, V+A, etc.) of the new physics responsible for the $R_K$ and $R_{K^*}$ anomalies?
• RQ2 Can lepton-specific measurements distinguish whether the anomaly arises from new physics in muons, electrons, or both?
• RQ3 Which leptoquark models can simultaneously explain the $R_K$ and $R_{K^*}$ anomalies while satisfying constraints from $B_s \to \mu\mu$?
• RQ4 What are the testable predictions for $R_{X_s}$ and other $R_H$ ratios, and how can they be probed at Belle II?
• RQ5 How do the anomalies correlate with other flavor-sensitive processes such as $R_{D^{(*)}}$, $\mu \to e\gamma$, or $K^0 \to \mu^+\mu^-$?

Key findings

• The $R_K$ and $R_{K^*}$ anomalies—measured as $R_K^{\rm LHCb} = 0.745^{+0.090}_{-0.074} \pm 0.036$ and $R_{K^*}^{\rm LHCb} = 0.69^{+0.11}_{-0.07} \pm 0.05$—indicate a $\sim 2.6\sigma$ deviation from lepton universality.
• The anomalies are best explained by new physics in V-A type operators, with $\Delta C_9^{\rm NP} \sim -1.1 \pm 0.3$ and $\Delta C_{10}^{\rm NP} \sim -1.1 \pm 0.3$ for muons.
• The inclusive $R_{X_s}$ ratio is predicted to be $R_{X_s} \simeq 0.73 \pm 0.07$, a clean testable signal at Belle II.
• Scalar triplet ($S_3$), vector triplet ($V_3$), and vector singlet ($V_1$) leptoquarks are viable tree-level explanations, while scalar doublet ($\tilde{S}_2$) is disfavored.
• Model-independent upper bounds on leptoquark masses are $\sim 40$, $45$, and $20$ TeV for $S_3$, $V_1$, and $V_3$, respectively, with most parameter space beyond the LHC reach.
• The anomalies are consistent with $B_s \to \mu\mu$ constraints, with $0 \lesssim {\rm Re}[C_{10}^{\rm NP\mu} - C_{10}^{\prime\rm NP\mu}] \lesssim 0.9$.