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Analytical solutions to renormalization-group equations of effective neutrino masses and mixing parameters in matter

Analytical solutions to renormalization-group equations of effective neutrino masses and mixing parameters in matter

A bstract Neutrino oscillations in matter can be fully described by six effective parameters, namely, three neutrino mixing angles $$ \left\{{\tilde{\theta}}_{12},{\tilde{\theta}}_{13},{\tilde{\theta}}_{23}\right\} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:msub> <mml:mover> <mml:mi>θ</mml:mi> <mml:mo>˜</mml:mo> </mml:mover> <mml:mn>12</mml:mn> </mml:msub> <mml:msub> <mml:mover> <mml:mi>θ</mml:mi> <mml:mo>˜</mml:mo> </mml:mover> <mml:mn>13</mml:mn> </mml:msub> <mml:msub> <mml:mover> <mml:mi>θ</mml:mi> <mml:mo>˜</mml:mo> </mml:mover> <mml:mn>23</mml:mn> </mml:msub> </mml:mfenced> </mml:math> , one …