<p>We propose a new, minimal Majorana neutrino mass matrix texture and study its predictions within a partial tri-bimaximal (TBM) mixing scheme, where <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\sin \theta _{12} = 1/\sqrt{3}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>sin</mo> <msub> <mi>θ</mi> <mn>12</mn> </msub> <mo>=</mo> <mn>1</mn> <mo stretchy="false">/</mo> <msqrt> <mn>3</mn> </msqrt> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\sin \theta _{23} = 1/\sqrt{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>sin</mo> <msub> <mi>θ</mi> <mn>23</mn> </msub> <mo>=</mo> <mn>1</mn> <mo stretchy="false">/</mo> <msqrt> <mn>2</mn> </msqrt> </mrow> </math></EquationSource> </InlineEquation>, with <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\theta _{13}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>θ</mi> <mn>13</mn> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\delta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation> treated as free parameters. The texture forbids <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\theta _{13} = 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>θ</mi> <mn>13</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> and does not correspond to a <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mu \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation>–<InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\tau \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation> symmetric structure. As a notable feature, the texture predicts the equality of the Majorana phases. In addition, we find that the predictions show distinct behavior depending on the sign of a single real texture parameter. The texture is realized through a hybrid framework of one Type-I seesaw and two Type-II seesaw mechanisms under an extended symmetry group, <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(SU(2)_L \otimes U(1)_Y \otimes A_4 \otimes Z_{10} \otimes Z_{7}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>U</mi> <msub> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> <mi>L</mi> </msub> <mo>⊗</mo> <mi>U</mi> <msub> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mi>Y</mi> </msub> <mo>⊗</mo> <msub> <mi>A</mi> <mn>4</mn> </msub> <mo>⊗</mo> <msub> <mi>Z</mi> <mn>10</mn> </msub> <mo>⊗</mo> <msub> <mi>Z</mi> <mn>7</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> with properly chosen model parameters. The texture is seen to favor the normal hierarchy for neutrino masses.</p>

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Equal Majorana Phases from a Minimal and Predictive Neutrino Texture

  • Sagar Tirtha Goswami,
  • Pralay Chakraborty,
  • Subhankar Roy

摘要

We propose a new, minimal Majorana neutrino mass matrix texture and study its predictions within a partial tri-bimaximal (TBM) mixing scheme, where \(\sin \theta _{12} = 1/\sqrt{3}\) sin θ 12 = 1 / 3 and \(\sin \theta _{23} = 1/\sqrt{2}\) sin θ 23 = 1 / 2 , with \(\theta _{13}\) θ 13 and \(\delta \) δ treated as free parameters. The texture forbids \(\theta _{13} = 0\) θ 13 = 0 and does not correspond to a \(\mu \) μ \(\tau \) τ symmetric structure. As a notable feature, the texture predicts the equality of the Majorana phases. In addition, we find that the predictions show distinct behavior depending on the sign of a single real texture parameter. The texture is realized through a hybrid framework of one Type-I seesaw and two Type-II seesaw mechanisms under an extended symmetry group, \(SU(2)_L \otimes U(1)_Y \otimes A_4 \otimes Z_{10} \otimes Z_{7}\) S U ( 2 ) L U ( 1 ) Y A 4 Z 10 Z 7 with properly chosen model parameters. The texture is seen to favor the normal hierarchy for neutrino masses.