Consistent analysis of the νμ →νe sterile neutrinos searches of ICARUS and OPERA

The two long-baseline experiments ICARUS and OPERA have recently provided bounds on light (∼eV) sterile neutrinos exploiting the results of the νμ→νe 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 Δm142 with the atmospheric one. The inclusion in the data analysis of such effects weakens the upper bounds on the effective appearance amplitude sin22θμe approximately by a factor of 2. In addition, we point out that, in a 4-flavor scheme, the flavor oscillations involve also the νe 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 νe disappearance effects leads to a further weakening of the upper bounds on sin22θμe, which overall are relaxed by a factor of 3 with respect to those obtained in the effective 2-flavor description.