Sensitivity of $W$-boson measurements to low-mass right-handed neutrinos

TL;DR

The paper examines the collider phenomenology of a light right-handed neutrino $\nu_R$ interacting with $W$ bosons through νSMEFT dimension-6 operators, focusing on $W\to\ell\nu_R$ decays and their impact on $W$-boson observables. Using Tevatron and LHC data, it constrains the coupling $c_{HNe}^i/\Lambda^2$ by analyzing shifts in $m_W$, charge asymmetries, and, crucially, boosted-$W$ angular observables such as $2L_p-1$ which approximate $\cos\theta^*$ in the $W$ rest frame. The results show that the CDF $W$-mass measurement is inconsistent with LHC constraints when interpreted in this framework, ruling out the CDF interpretation as $W\to\ell\nu_R$ at the current sensitivity. A boosted, angular analysis in Run 3 is projected to reach $|c_{HNe}^i|v^2/\Lambda^2<0.08$, competitive with or exceeding some low-energy constraints, and HL-LHC could further improve sensitivity. Overall, current and near-future hadron-collider measurements provide a robust strategy to test V+A interactions from light sterile neutrinos, with significant reach in the sub-MeV to MeV mass range for $\nu_R$.

Abstract

A low-mass right-handed neutrino could interact with electroweak bosons via mixing, a mediator particle, or loop corrections. Using an effective field theory, we determine constraints on these interactions from $W$-boson measurements at hadron colliders. Due to the difference in the initial states at the Tevatron and the LHC, $W$-boson decays to a right-handed neutrino would artificially increase the mass measured at the Tevatron while only affecting the difference between $W^+$ and $W^-$ mass measurements at the LHC. Measurements from CDF and the LHC are used to infer the corresponding parameter values, which are found to be inconsistent between the two. The LHC experiments can improve sensitivity to these interactions by measuring the cosine of the helicity angle using $W$ bosons produced with transverse momentum above $\approx 50$ GeV.

Figures (7)

• Figure 1: The production and decay of $W^{\pm}$ bosons at the Tevatron for the final state containing either $\nu_L$ or $\nu_R$. On average the $W^\pm$ boson $p_z$ is in the direction of the interacting (anti-)$u$ quark, since $\langle p_z^u \rangle > \langle p_z^d \rangle$. Due to the V$-$A interaction, the initial spin is along the anti-proton direction, so the left-handed neutrino is produced in the direction of the $W$ boson. In the case of $\nu_R$, the $W$-boson interaction with the charged lepton is V+A, so the direction is reversed.
• Figure 2: The lepton $p_T$ (a) and $m_T$ (b) distributions for SM production and decay of the $W$ boson ($W\to \ell\nu_L$) at CDF, and for the $W$ boson decaying to a right-handed neutrino ($W\to \ell\nu_R$) with effective coupling $c_{HNe}/\Lambda^2 = 1/v^2$.
• Figure 3: The production and decay of $W^\pm$ bosons at the LHC for the final state containing either $\nu_L$ or $\nu_R$. The $W^\pm$ boson momentum projected along the $z$-axis is in the direction of the proton contributing a valence quark. The decay to $\nu_L$ is V-A, so the $\nu_L$ direction is opposite to that of the $W^+$ boson. In the case of $\nu_R$, the decay is V+A, and the direction is reversed.
• Figure 4: The lepton $p_T$ distribution for SM production and decay of the $W^+$ and $W^-$ bosons to a given lepton ($W^\pm \to \ell\nu_L$) at the LHC with a center-of-mass energy of (a) 7 TeV or (b) 13 TeV, and for the corresponding decays to a right-handed neutrino ($W^\pm \to \ell\nu_R$) with effective coupling $c_{HNe}/\Lambda^2 = 1/v^2$.
• Figure 5: The negative log likelihood as a function of $|c_{HNe}|$ inferred from the CDF $m_W$ measurement and the ATLAS and CMS $m_{W^+} - m_{W^-}$ measurements. Also shown is the likelihood from a combination of the LHC measurements, neglecting correlations.