Consistent analysis of the $\nu_\mu \to \nu_e$ sterile neutrinos searches of ICARUS and OPERA

Understand

The two long-baseline experiments ICARUS and OPERA have recently provided bounds on light ($\sim$ eV) sterile neutrinos exploiting the negative results of the $\nu_\mu \to \nu_e$ appearance searches.

• Both collaborations have performed the data analysis using an effective 2-flavor description.
• We show that such a simplified treatment neglects sizable genuine 4-flavor effects, which are induced by the interference of the new large squared-mass splitting $\Delta m^2 _{14}$ with the atmospheric one.
• The inclusion in the data analysis of such effects weakens the upper bounds on the effective appearance amplitude $\sin^2 2\theta_{\mu e}$ approximately by a factor of two.