Calculable neutrino Dirac mass matrix and one-loop θ¯ in the minimal left-right symmetric model

We revisit the contribution to the strong <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>C</a:mi><a:mi>P</a:mi></a:math> parameter <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mover accent="true"><c:mi>θ</c:mi><c:mo stretchy="false">¯</c:mo></c:mover></c:math> from leptonic <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>C</g:mi><g:mi>P</g:mi></g:math> violation at one-loop level in the minimal left-right symmetric model in the case of generalized parity as the left-right symmetry. The Hermitian neutrino Dirac mass matrix <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>M</i:mi><i:mi>D</i:mi></i:msub></i:math> can be calculated using the light and heavy neutrino masses and mixings. We propose a parametrization of the right-handed neutrino mixing matrix <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>V</k:mi><k:mi>R</k:mi></k:msub></k:math> and construct the heavy neutrino mass that maintains the Hermiticity of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>M</m:mi><m:mi>D</m:mi></m:msub></m:math>. We further apply it to evaluate the one-loop <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mover accent="true"><o:mi>θ</o:mi><o:mo stretchy="false">¯</o:mo></o:mover></o:math>, denoted as <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mover accent="true"><s:mi>θ</s:mi><s:mo stretchy="false">¯</s:mo></s:mover><s:mi>loop</s:mi></s:msub></s:math>, as a function of the sterile neutrino masses for explicit examples of <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msub><w:mi>V</w:mi><w:mi>R</w:mi></w:msub></w:math>. By requiring the magnitude of <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mover accent="true"><y:mi>θ</y:mi><y:mo stretchy="false">¯</y:mo></y:mover><y:mi>loop</y:mi></y:msub><y:mo>≲</y:mo><y:msup><y:mn>10</y:mn><y:mrow><y:mo>−</y:mo><y:mn>10</y:mn></y:mrow></y:msup></y:math>, we derive the upper limits on the sterile neutrino masses, which are within reach of direct searches at the Large Hadron Collider and neutrinoless double beta decay experiments. Furthermore, our parametrization is pertinent for other phenomenological investigations. Published by the American Physical Society 2024