Consistent analysis of the ${\nu }_{\mu }\to {\nu }_e$ sterile neutrinos searches of ICARUS and OPERA

The two long-baseline experiments ICARUS and OPERA have recently provided bounds on light ($\sim \mathrm{eV}$) sterile neutrinos exploiting the 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 $\mathrm{\Delta }{m}_{14}^2$ 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 2. In addition, we point out that, in a 4-flavor scheme, the flavor oscillations involve also the ${\nu }_e$ component of the CNGS beam and can suppress the theoretical expectation of the background in a substantial way. The inclusion in the data analysis of the ${\nu }_e$ disappearance effects leads to a further weakening of the upper bounds on ${\sin }^{2}2{\theta }_{\mu e}$, which overall are relaxed by a factor of 3 with respect to those obtained in the effective 2-flavor description.

Figure 1

Behavior of the three terms of the ${\nu }_{\mu }\to {\nu }_e$ transition probability for the CNGS parameters ($L=732\mathrm{km}$, $E=17\mathrm{GeV}$) as a function of ${\sin }^{2}2{\theta }_{\mu e}$ in the case $|U_{e4}|=|U_{\mu 4}|$.

Figure 2

Transition probability as a function of the neutrino energy. The dotted curve represents the atmospheric term, while the dot-dashed (horizontal) line is the sterile one. The sum of these two contributions, represented by the dashed curve, is the probability implemented in the official analyses. The two solid lines correspond to the (averaged) $4\nu$ probability in the NH case for the two values ${\delta }^{\prime }=\pm \pi /2$.

Figure 3

Upper bounds (90% C.L.) obtained for a fixed (large) value of $\mathrm{\Delta }{m}_{14}^2$ in the two cases of NH and IH. The effect of the oscillations on the ${\nu }_e$ component is neglected setting $P_{ee}=1$.

Figure 4

Upper bounds (90% C.L.) obtained in the case of NH. The $CP$-phase ${\delta }^{\prime }$ is marginalized away. The effect of the oscillations on the ${\nu }_e$ component is neglected setting $P_{ee}=1$.

Figure 5

Upper bounds (90% C.L.) obtained from the OPERA experiment for the case of normal hierarchy. The $CP$-violating phase ${\delta }^{\prime }$ is marginalized away. See the text for details.