Return of the lepton number: Sterile neutrino dark matter production and the revival of the Shi-Fuller mechanism

We explore resonant production of sterile neutrino dark matter via the Shi-Fuller (SF) mechanism, revisiting its cosmological viability in light of recent results demonstrating that lepton-number asymmetries <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>L</a:mi> <a:mi>α</a:mi> </a:msub> <a:mo>≳</a:mo> <a:mn>1</a:mn> </a:math> at temperatures <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mi mathvariant="normal">T</c:mi> <c:mo>&gt;</c:mo> <c:mn>20</c:mn> <c:mtext> </c:mtext> <c:mtext> </c:mtext> <c:mi>MeV</c:mi> </c:mrow> </c:math> are consistent with big bang nucleosynthesis (BBN). Using a quasiclassical Boltzmann transport calculation of the dark matter production, we compute the nonthermal phase space distributions of sterile neutrinos across a broad range of particle mass <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:msub> <f:mi>m</f:mi> <f:mi>s</f:mi> </f:msub> </f:math> and mixing angle <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msup> <h:mi>sin</h:mi> <h:mn>2</h:mn> </h:msup> <h:mrow> <h:mo stretchy="false">(</h:mo> <h:mn>2</h:mn> <h:mi>θ</h:mi> <h:mo stretchy="false">)</h:mo> </h:mrow> </h:math> parameter space. We then evolve the resulting distributions through linear structure formation using CLASS and fit the resulting matter power spectra to thermal warm dark matter (WDM) transfer functions, enabling a direct mapping between SF models and equivalent thermal WDM particle masses <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:msub> <l:mi>m</l:mi> <l:mi>th</l:mi> </l:msub> </l:math> . This allows us to reinterpret existing structure formation limits and Lyman- <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mi>α</n:mi> </n:math> forest preferences in the context of SF production. We find that lepton asymmetries <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mi>L</p:mi> <p:mo>≳</p:mo> <p:mn>0.5</p:mn> </p:math> at high temperatures open significant viable parameter space in the <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:msub> <r:mi>m</r:mi> <r:mi>s</r:mi> </r:msub> <r:mo>≳</r:mo> <r:mn>10</r:mn> <r:mtext> </r:mtext> <r:mtext> </r:mtext> <r:mi>keV</r:mi> </r:math> and <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:msup> <t:mi>sin</t:mi> <t:mn>2</t:mn> </t:msup> <t:mo stretchy="false">(</t:mo> <t:mn>2</t:mn> <t:mi>θ</t:mi> <t:mo stretchy="false">)</t:mo> <t:mo>≲</t:mo> <t:msup> <t:mn>10</t:mn> <t:mrow> <t:mo>−</t:mo> <t:mn>14</t:mn> </t:mrow> </t:msup> </t:math> regime, compatible with both x-ray constraints from and and recent Lyman- <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:mi>α</x:mi> </x:math> inferences of <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:msub> <z:mi>m</z:mi> <z:mi>th</z:mi> </z:msub> <z:mo>≈</z:mo> <z:mn>4.1</z:mn> <z:mtext> </z:mtext> <z:mtext> </z:mtext> <z:mi>keV</z:mi> </z:math> . Following lepton number evolution below 20 MeV, we also specifically show that this lepton asymmetry parameter space is compatible with BBN and cosmic microwave background constraints. We present updated constraints, a refined <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:msub> <bb:mi>m</bb:mi> <bb:mi>th</bb:mi> </bb:msub> </bb:math> fitting function, and power-law approximations for <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"> <db:mi>L</db:mi> </db:math> across the parameter space. Our results motivate future x-ray observations targeting the <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:mo>∼</fb:mo> <fb:mn>20</fb:mn> <fb:mtext> </fb:mtext> <fb:mtext> </fb:mtext> <fb:mi>keV</fb:mi> </fb:math> photon regime and testing of the <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"> <hb:msub> <hb:mi>m</hb:mi> <hb:mi>th</hb:mi> </hb:msub> <hb:mo>≳</hb:mo> <hb:mn>10</hb:mn> <hb:mtext> </hb:mtext> <hb:mtext> </hb:mtext> <hb:mi>keV</hb:mi> </hb:math> WDM region.