Weinberg’s Higgs portal confronting recent LUX and LHC results together with upper limits on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>decay into invisibles

Abstract

We discuss a number of experimental constraints on Weinberg's Higgs portal model. In this framework, the standard model (SM) particle spectrum is extended to include one complex scalar field $S$ and one Dirac fermion $\ensuremath{\psi}$. These new fields are singlets under the SM gauge group and are charged under a global $U(1)$ symmetry. Breaking of this $U(1)$ symmetry results in a massless Goldstone boson $\ensuremath{\alpha}$ and a massive $CP$-even scalar $r$ and splits the Dirac fermion into two new mass-eigenstates ${\ensuremath{\psi}}_{\ifmmode\pm\else\textpm\fi{}}$, corresponding to Majorana fermions. The interest on such a minimal SM extension is twofold. On the one hand, if the Goldstone bosons are in thermal equilibrium with SM particles until the era of muon annihilation, their contribution to the effective number of neutrino species can explain the hints from cosmological observations of extra relativistic degrees of freedom at the epoch of last scattering. On the other hand, the lightest Majorana fermion ${\ensuremath{\psi}}_{\ensuremath{-}}$ provides a plausible dark matter candidate. Mixing of $r$ with the Higgs doublet $\ensuremath{\phi}$ is characterized by the mass of hidden scalar ${m}_{h}$ and the mixing angle $\ensuremath{\theta}$. We constrain this parameter space using a variety of experimental data, including heavy meson decays with missing energy, the invisible Higgs width, and direct dark matter searches. We show that different experimental results compress the allowed parameter space in complementary ways, covering a large range of ${\ensuremath{\psi}}_{\ensuremath{-}}$ masses ($5\ensuremath{\lesssim}{m}_{\ensuremath{-}}\ensuremath{\lesssim}100\text{ }\text{ }\mathrm{GeV}$). Though current results narrow the parameter space significantly (for the mass range of interest, $\ensuremath{\theta}\ensuremath{\lesssim}{10}^{\ensuremath{-}3}$ to ${10}^{\ensuremath{-}4}$), there is still room for discovery ($\ensuremath{\alpha}$ decoupling at the muon annihilation era requires $\ensuremath{\theta}\ensuremath{\gtrsim}{10}^{\ensuremath{-}5}$ to ${10}^{\ensuremath{-}4}$). In the near future, measurements from ATLAS, CMS, LHCb, NA62, XENON1T, LUX, and CDMSlite will probe nearly the full parameter space.