Interplay between Vector-like Lepton and Seesaw Mechanism:Oblique Corrections

TL;DR

The paper analyzes how mixing between type-I seesaw right-handed neutrinos and vector-like lepton doublets affects electroweak oblique corrections, focusing on the oblique parameters $S$, $T$, and $U$. It constructs a minimal VLL–RHN model and derives full Majorana-aware one-loop expressions for the oblique parameters, with a UV completion in a local $(B-L)_{13}$ framework. Numerically, $S$ and $U$ are small while $T$ can reach ${ m O}(0.1)$ for sub-TeV RHN masses with sizable mixing, offering a potential connection to the $W$-boson mass measurements and EWPO fits depending on the data set used. The work identifies the well-mixed VLL–RHN region as a promising target for future collider and precision tests of seesaw-extended Standard Model scenarios, and provides detailed methodology for calculating oblique corrections in Majorana-extended vector-like lepton sectors.

Abstract

The non-vanishing neutrino mass strongly hints the existence of right-handed neutrinos (RHNs), singlets of the standard model (SM). However, they are highly decoupled from the SM and difficult to probe. In this work, we consider the Majorana RHNs from the type-I seesaw mechanism may well mix with the heavy neutral lepton dwelling in certain vector-like lepton (VLL), thus acquiring a sizable electroweak charge. Such a simple scenario yields many interesting consequences, and the imprint on oblique corrections, well expected from the mass splitting between components of VLL by virtue of VLL-RHN mixing, is our focus here. We analytically calculate the Peskin-Takeuchi parameters S, T and U with full details, carefully treating the Majorana loop to obtain the self consistent expressions free of divergence. Then, we constrain on the VLL-RHN system which only gives a sizable $T$ parameter using the PDG-2021 data and CDF-II data, separately, by imposing $T\lesssim{\cal O}(0.1)$. It is found that for the RHN and VLL below the TeV scale, with a properly large mixing, stands in the frontier of the electroweak precision test such as W-boson mass.

Figures (5)

• Figure 1: Vacuum polarization amplitudes for the electroweak vector bosons $V/V'$; $\ell$ and $\ell'$ denote the BSM fermions like $e_4$ and the heavy neutral leptons.
• Figure 3: The distributions of parameters $S$ (red-dashed) and $T$ (black-dotted) in the $M_N - m_L$ plane for three typical points - $\lambda_n = 0.5 ~(\rm left) ,\, 1 ~ (\rm middle) ,\, 2~ (\rm right)$.
• Figure 4: Comparison of the $S$ and $T$ parameters between our calculation (black-solid lines) and the results (red-dotted lines) quoted from Fig. 1 and Fig. 2 of Ref. Ma:1992uc, taking the same inputs.
• Figure 5: The figures show the effect of phase with $|\lambda_n| = 2$, $|\lambda'_n| = 1$, $M_N =1 \; {\rm TeV}$, taking $m_L = 0.2, \, 0.48, \, 0.51, \, 0.7, \, 0.9 \; {\rm TeV}$ labeled as the red, green, blue, black, gray lines respectively. $T(\theta)/T(0)$ for the left panel and $T(\theta)$ for the right panel.
• Figure 6: The corresponding Feynman rules of $W^3$ vertex: The Majorana-induced $\frac{1}{2}$ factor (the left) is compensated by two possible contractions compared with the right one. However one more $\frac{1}{2}$ appear subsequently as a symmetry factor at the expense of Majorana.