[Paper Review] Modified lepton couplings and the Cabibbo-angle anomaly

Antônio Coutinho, Andreas Crivellin+1 more|arXiv (Cornell University)|Sep 8, 2020

Particle physics theoretical and experimental studies27 references4 citations

TL;DR

The paper proposes that the Cabibbo-angle anomaly—discrepancies in $V_{us}$ determinations—arises from lepton flavour universality violation (LFUV) in neutrino couplings to gauge bosons. Using a model-independent Bayesian global fit, it finds strong evidence ($>99.99\%$ C.L., $>4\sigma$) for non-zero modifications to electron and muon neutrino couplings, requiring constructive interference in the muon sector and ruling out simple right-handed neutrino models.

ABSTRACT

Significant discrepancies between the different determinations of the Cabibbo angle have been observed. Here, we point out that this "Cabibbo-angle anomaly" can be explained by lepton flavour universality (LFU) violating New Physics (NP) in the neutrino sector. However, modified neutrino couplings to Standard Model gauge bosons also affect many other observables sensitive to LFU violation, which have to be taken into account in order to assess the viability of this explanation. Therefore, we perform a model-independent Bayesian global analysis and find that non-zero modifications of electron and muon neutrino couplings are preferred at more than $99.99\%\,{ m C.L.}$ (corresponding to more than $4\,σ$). Our results show that constructive effects in the muon sector are necessary, meaning simple models with right-handed neutrinos are discarded and more sophisticated NP models required.

Motivation & Objective

• To resolve the Cabibbo-angle anomaly, a persistent tension in $V_{us}$ determinations from different processes.
• To investigate whether lepton flavour universality violation (LFUV) in the neutrino sector can explain the anomaly.
• To assess the viability of modified neutrino couplings to $W$ and $Z$ bosons as a New Physics explanation.
• To perform a global fit incorporating precision electroweak, LFU-testing, and $V_{us}$-determining observables.
• To determine whether simple models like right-handed neutrinos are compatible with the data.

Proposed method

• Uses an effective field theory (EFT) approach at dimension-6 to model modified neutrino couplings to $W$ and $Z$ bosons via a single operator.
• Parametrizes the Wilson coefficient effects through modified couplings: $W\ell\nu \sim (\delta_{ij} + \frac{1}{2}\varepsilon_{ij})$ and $Z\nu\nu \sim (\delta_{ij} + \varepsilon_{ij})$.
• Performs a Bayesian global fit using the HEPfit package, incorporating $G_F$, $\alpha$, $M_Z$, $m_t$, $m_H$, $V_{us}^\mathcal{L}$, and $\varepsilon_{ii}$ with appropriate priors.
• Includes precision electroweak observables (LEP, Tevatron, LHC), LFU ratios (W decays, $K/\pi/\tau$ decays), and $V_{us}$ determinations from $K_{\mu3}$, $K/\pi$, $\tau$, and super-allowed $\beta$ decay.
• Accounts for indirect effects via $G_F$ shift: $G_F = G_F^\mathcal{L}(1 + \frac{1}{2}\varepsilon_{ee} + \frac{1}{2}\varepsilon_{\mu\mu})$.
• Uses the Information Criterion (IC) to compare SM and NP models, with lower IC indicating better predictive accuracy and fit.

Experimental results

Research questions

• RQ1 Can lepton flavour universality violation in neutrino couplings explain the Cabibbo-angle anomaly?
• RQ2 What are the constraints on modified neutrino couplings from a global fit to precision electroweak and LFU-violating observables?
• RQ3 Is the SM consistent with current data, or is there strong evidence for New Physics in the neutrino sector?
• RQ4 Do simple models with right-handed neutrinos remain viable in light of the global fit?
• RQ5 What is the required interplay between $\varepsilon_{ee}$ and $\varepsilon_{\mu\mu}$ to resolve the anomaly?

Key findings

• Non-zero modifications to electron and muon neutrino couplings are preferred at more than $99.99\%$ credibility level, corresponding to over $4\sigma$ significance.
• The $\varepsilon_{ee}$ and $\varepsilon_{\mu\mu}$ parameters exhibit an anti-correlation with opposite signs, indicating constructive interference in the muon sector.
• The SM is strongly disfavored: $\text{IC}_{\rm SM} \simeq 93$ versus $\text{IC}_{\rm NP} \simeq 76$, indicating 'very strong' evidence for New Physics.
• Simple models with right-handed neutrinos are ruled out due to their requirement for destructive interference, which is inconsistent with the data.
• The anomaly is most strongly affected by modifications in super-allowed $\beta$ decay and $K_{\mu3}$ decays, where $V_{us}^{K_{\mu3}} \simeq |V_{us}^\mathcal{L}|(1 - \frac{1}{2}\varepsilon_{ee})$ and $V_{us}^{\beta} \simeq \sqrt{1 - |V_{ud}^\mathcal{L}|^2(1 - \frac{1}{2}\varepsilon_{\mu\mu})^2}$.
• The global fit shows that the posterior for $V_{us}$ under NP is consistent across inputs, with the largest shift occurring in super-allowed $\beta$ decay due to $G_F$ modification.