Exact parametrization of a minimal seesaw model

We propose a parametrization of neutrino masses and mixing in the minimal seesaw model (MSM). The MSM, which introduces two heavy sterile neutrinos, is the minimal extension of the Standard Model in addressing the tiny masses of active neutrinos. The parametrization includes 11 free parameters: six neutrino oscillation parameters (two mass-squared differences <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi mathvariant="normal">Δ</a:mi> <a:msubsup> <a:mi>m</a:mi> <a:mn>21</a:mn> <a:mn>2</a:mn> </a:msubsup> </a:math> , <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi mathvariant="normal">Δ</d:mi> <d:msubsup> <d:mi>m</d:mi> <d:mn>31</d:mn> <d:mn>2</d:mn> </d:msubsup> </d:math> three mixing angles <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>θ</g:mi> <g:mn>12</g:mn> </g:msub> </g:math> , <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mi>θ</i:mi> <i:mn>13</i:mn> </i:msub> </i:math> , <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>θ</k:mi> <k:mn>23</k:mn> </k:msub> </k:math> , and one Dirac phase <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mi>δ</m:mi> <m:mrow> <m:mi>C</m:mi> <m:mi>P</m:mi> </m:mrow> </m:msub> </m:math> ), one mass parameter in <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mn>0</o:mn> <o:mi>ν</o:mi> <o:mn>2</o:mn> <o:mi>β</o:mi> </o:math> decay <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msub> <q:mi>m</q:mi> <q:mrow> <q:mi>e</q:mi> <q:mi>e</q:mi> </q:mrow> </q:msub> </q:math> , and four additional parameters: two heavy neutrino masses <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msub> <s:mi>M</s:mi> <s:mn>1</s:mn> </s:msub> </s:math> and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msub> <u:mi>M</u:mi> <u:mn>2</u:mn> </u:msub> </u:math> , one active-sterile mixing angle <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:msub> <w:mi>θ</w:mi> <w:mn>14</w:mn> </w:msub> </w:math> , and one <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mi>C</y:mi> <y:mi>P</y:mi> </y:math> -violating phase <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:msub> <ab:mi>δ</ab:mi> <ab:mn>14</ab:mn> </ab:msub> </ab:math> . This parametrization is derived exactly from the most general neutrino mass matrix in the MSM without any approximation. We further discuss its implications in phenomenological studies.