Type-II Seesaw Triplet Scalar Effects on Neutrino Trident Scattering

Abstract

In Type-II seesaw model, an electroweak triplet scalar field $\Delta$ with a non-zero vacuum expectation value (vev) $v_{\Delta }$ is introduced to facilitate the generation of small neutrino masses. A non-zero $v_{\Delta }$ also affects the W mass through the electroweak $\rho$ parameter, making it to be less than 1 as predicted by standard model (SM). The component fields in $\Delta$ come along introduce additional contributions to reduce the SM rare neutrino trident scattering cross section. These fields also induce new processes not existed in SM, such as $l_i\to \overline{l_j}{l}_k{l}_l$ and $l_i\to l_j\gamma$. There are severe constraints on these processes which limit the effects on neutrino trident scattering and the $\rho$ parameter and therefore the W mass. The newly measured W mass by CDF makes the central value of $\rho$ parameter to be larger than 1, even larger than previously expected. Combining neutrinoless double beta decay, direct neutrino mass and oscillation data, we find a lower limit for $v_{\Delta }$ as a function of the triplet scalar mass $m_{\Delta }$, $v_{\Delta }>(6.3\sim 8.4)\mathrm{eV}(100\mathrm{GeV}/m_{\Delta })$. To have significant effect on $\rho$ in this model, $v_{\Delta }$ needs to be in the range of a GeV or so. However this implies a very small $m_{\Delta }$ which is ruled out by data. We conclude that the effect of triplet vev $v_{\Delta }$ on the W mass can be neglected. We also find that at 3$\sigma$ level, the deviation of the ratio for Type-II Seesaw to SM neutrino trident scattering cross section predictions is reduced to be below 1, but is restricted to be larger than 0.98.

9 pages, 5 figures, match the published version in PLB

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