Matter Effect of Light Sterile Neutrino: An Exact Analytical Approach

Abstract

The light sterile neutrino, if it exists, will give additional contribution to matter effect when active neutrinos propagate through terrestrial matter. In the simplest 3+1 scheme, three more rotation angles and two more CP-violating phases in lepton mixing matrix make the interaction complicated formally. In this work, the exact analytical expressions for active neutrino oscillation probabilities in terrestrial matter, including sterile neutrino contribution, are derived. It is pointed out that this set of formulas contain information both in matter and in vacuum, and can be easily tuned by choosing related parameters. Based on the generic exact formulas, we present oscillation probabilities of typic medium and long baseline experiments. Taking NO$\nu$A experiment as an example, we show that in particular parameter space sterile neutrino gives important contribution to terrestrial matter effect, and Dirac phases play a vital role.

arXiv comment17 pages, 8 figures for V1; typos are corrected, accepted by JHEP for V2

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• Prospects of light sterile neutrino searches in long-baseline neutrino oscillations
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• Analytic Neutrino Oscillation Probabilities
• Matter Effects of Sterile Neutrino in Light of Renormalization-Group Equations