Deviation from $$\mu -\tau $$ reflection symmetry under radiative corrections in MSSM

Abstract Recent results from T2K and NO $$\nu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ν</mml:mi> </mml:math> A experiments indicates a value of the Dirac CP phase $$\delta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>δ</mml:mi> </mml:math> which is centered at the maximal value $${270}^\circ $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mn>270</mml:mn> </mml:mrow> <mml:mo>∘</mml:mo> </mml:msup> </mml:math> . In view of this, the role of $$\mu -\tau $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mo>-</mml:mo> <mml:mi>τ</mml:mi> </mml:mrow> </mml:math> reflection symmetry becomes important in lepton flavour mixing as it accommodates both maximal CP violation ( $$\delta = (\pi /2)/(3\pi /2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>δ</mml:mi> <mml:mo>=</mml:mo> <mml:mo>(</mml:mo> <mml:mi>π</mml:mi> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> <mml:mo>/</mml:mo> <mml:mo>(</mml:mo> <mml:mn>3</mml:mn> <mml:mi>π</mml:mi> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> ) and maximal atmospheric mixing ( $$\theta _{23}=\pi /4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>θ</mml:mi> <mml:mn>23</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>π</mml:mi> <mml:mo>/</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> ) along with non-zero $$\theta _{13}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>θ</mml:mi> <mml:mn>13</mml:mn> </mml:msub> </mml:math> . In this work we account the deviations from $$\mu -\tau $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mo>-</mml:mo> <mml:mi>τ</mml:mi> </mml:mrow> </mml:math> reflection symmetry under radiative corrections in the MSSM framework. We use integral solution method to the one-loop RGE of the light effective Majorana neutrino mass matrix and derive analytical expressions for the low energy mass eigenvalues and lepton mixing parameters. Through numerical analysis we observe that low energy predictions of mass squared differences, cosmological upper bound of the sum of mass eigenvalues ( $$\Sigma {m_i}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Σ</mml:mi> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>i</mml:mi> </mml:msub> </mml:mrow> </mml:math> ) and the mixing angles $$\theta _{12}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>θ</mml:mi> <mml:mn>12</mml:mn> </mml:msub> </mml:math> and $$\theta _{13}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>θ</mml:mi> <mml:mn>13</mml:mn> </mml:msub> </mml:math> under radiative corrections can be made very well agreement with observational data. In comparison to $$\theta _{12}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>θ</mml:mi> <mml:mn>12</mml:mn> </mml:msub> </mml:math> , the deviations of $$\theta _{23}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>θ</mml:mi> <mml:mn>23</mml:mn> </mml:msub> </mml:math> and $$\delta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>δ</mml:mi> </mml:math> under radiative corrections are found relatively small. Nonetheless, their low energy predictions are consistent with $$3\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>3</mml:mn> <mml:mi>σ</mml:mi> </mml:mrow> </mml:math> range of global analysis data.