BBN constraint on heavy neutrino production and decay

We explore the big-bang nucleosynthesis (BBN) constraint on heavy neutrino that is a mixture of gauge-singlet fermion and active neutrinos in the Standard Model. We work in the minimal model with only two parameters, the heavy neutrino mass <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>m</a:mi><a:mn>4</a:mn></a:msub></a:math> and the mixing parameter <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mo stretchy="false">|</c:mo><c:msub><c:mi>U</c:mi><c:mrow><c:mi>a</c:mi><c:mn>4</c:mn></c:mrow></c:msub><c:msup><c:mo stretchy="false">|</c:mo><c:mn>2</c:mn></c:msup></c:math>, where <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>a</g:mi><g:mo>=</g:mo><g:mi>e</g:mi></g:math>, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>μ</i:mi></i:math>, or <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>τ</k:mi></k:math> stands for the active neutrino flavor. We show that both the early Universe production mechanism and decay products of the heavy neutrino are determined by <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>m</m:mi><m:mn>4</m:mn></m:msub></m:math> and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mo stretchy="false">|</o:mo><o:msub><o:mi>U</o:mi><o:mrow><o:mi>a</o:mi><o:mn>4</o:mn></o:mrow></o:msub><o:msup><o:mo stretchy="false">|</o:mo><o:mn>2</o:mn></o:msup></o:math>, with little room for further assumptions. This predictability allows us to present a portrait of the entire BBN excluded parameter space. As a novel result, we derive the lower boundary of the BBN exclusion in the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mo stretchy="false">|</s:mo><s:msub><s:mi>U</s:mi><s:mrow><s:mi>a</s:mi><s:mn>4</s:mn></s:mrow></s:msub><s:msup><s:mo stretchy="false">|</s:mo><s:mn>2</s:mn></s:msup></s:math> versus <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msub><w:mi>m</w:mi><w:mn>4</w:mn></w:msub></w:math> parameter space. Our analysis includes various effects including temporary matter domination, energy injections in the form of charged mesons, photons, and light neutrinos. The BBN constraint is complementary to the terrestrial search for heavy neutrinos (heavy neutral leptons) behind the origin of neutrino masses and a portal to the dark sector.