$WWh$ anomalous couplings at one loop from a seesaw variant of radiatively-induced neutrino masses

TL;DR

The study investigates whether a radiative seesaw mechanism for neutrino masses leaves observable imprints on the $WWh$ coupling at one loop. Using an explicit Majorana-neutrino framework and tensor-reduction techniques within the SILH effective-Lagrangian basis, it computes the loop-induced anomalous $WWh$ couplings, identifying two CP-even ($\\lambda_3^{\\rm NP}$, $\\lambda_4^{\\rm NP}$) and two CP-odd ($\\tilde{\\lambda}_1^{\\rm NP}$, $\\tilde{\\lambda}_2^{\\rm NP}$) form factors (with $\\lambda_2^{\\rm NP}=0$ and $\\lambda_4^{\\rm NP}=\\lambda_5^{\\rm NP}$). The contributions are UV finite and largely governed by the heavy-neutrino sector, notably with near-degenerate masses $m_N$, while light-neutrino masses enter only subdominantly. Numerical estimations in two physical scenarios—$pp\to Wh$ and vector-boson fusion in lepton colliders—show CP-even effects can reach ~$10^{-3}$, potentially near HL-LHC sensitivity, whereas CP-odd effects are typically ~$10^{-4}$, generally below future lepton-collider reach. These results connect low-scale radiative neutrino-mass models to measurable Higgs-gauge couplings, informing the prospects for testing such new physics with precision Higgs measurements.

Abstract

After the successful measurement of the Higgs-like particle at the Large Hadron Collider, the determination of whether it corresponds to either the minimal version of the Higgs scalar, provided by the Standard Model, or to some new physics, so far unknown, has become a main objective of the high-energy-physics community. In particular, the investigation of the couplings of this particle with the rest of the Standard-Model field content is a central task. To this aim, in the present paper we consider a variant of the seesaw neutrino-mass-generating mechanism in which the masses of light neutrinos are generated via radiative corrections of the neutrino 2-point function. In this framework, we calculate the contributions from virtual Majorana neutrinos to the $WWh$ vertex, at one loop. A set of anomalous couplings, some of them $CP$-even and the others $CP$-odd, emerge from this calculation. We perform numerical estimations of these anomalous couplings by taking into account the role of the $WWh$ vertex in (1) $Wh$ production from $pp$ collisions and (2) in Higgs production by vector-boson fusion, occurring in some lepton collider. Our estimations show that all the generated anomalous couplings are beyond current experimental sensitivity. However, we note that $CP$-conserving anomalous couplings could be as large as $\sim10^{-3}$, which would be near the reach of the high-luminosity phase of the Large Hadron Collider. On the other hand, $CP$-odd effects, amounting to $\sim10^{-4}$, turn out to be well below expectations for the Compact Linear Collider by about 2 orders of magnitude.

Figures (8)

• Figure 1: Conventions for the momenta and for the Lorentz indices adopted for both the vertex function associated to ${\cal L}^{\rm eff}_{WWh}$ and the one-loop calculation of the vertex function $WWh$.
• Figure 2: Generic Feynman diagram illustrating how light and heavy neutrinos contribute to the subprocess $ud\to Wh$, at one loop, occurring $pp$ collisions.
• Figure 3: Contributions, in the context of $Wh$ production, to $CP$-even AC $|\lambda_3^{\rm NP}|$ and $|\lambda_4^{\rm NP}|$, plotted in the $( m_N,\sqrt{s} )$ plane, for fixed $\hat{\rho}=0.65$. Values ranging within $100\,{\rm GeV}\leqslant m_N\leqslant3\,{\rm TeV}$ and $m_h+m_W\leqslant\sqrt{s}\leqslant39\,{\rm TeV}$ have been used. Contributions as large as $|\lambda_3^{\rm NP}|\sim10^{-3}$ and $|\lambda_4^{\rm NP}|\sim10^{-4}$ are generated.
• Figure 4: Contributions, in the context of $Wh$ production, to $CP$-odd AC $|\tilde{\lambda}_1^{\rm NP}|$ and $|\tilde{\lambda}_2^{\rm NP}|$, plotted in the $( m_N,\sqrt{s} )$ plane, for fixed $\hat{\rho}=0.65$. Values ranging within $100\,{\rm GeV}\leqslant m_N\leqslant3\,{\rm TeV}$ and $m_h+m_W\leqslant\sqrt{s}\leqslant39\,{\rm TeV}$ have been used. Contributions as large as $|\tilde{\lambda}_1^{\rm NP}|\sim10^{-4}$ and $|\tilde{\lambda}_2^{\rm NP}|\sim10^{-3}$ are generated.
• Figure 5: Generic Feynman diagram illustrating how light and heavy neutrinos contribute to Higgs production by VBF, in the context of some lepton collider.