Common origin of asymmetric self-interacting dark matter and Dirac leptogenesis

Assuming dark matter to be asymmetric as well as self-interacting and neutrinos to be Dirac fermions, we propose a framework to address the observed baryon imbalance of the Universe. We add three right-handed neutrinos <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mrow> <a:msub> <a:mrow> <a:mi>ν</a:mi> </a:mrow> <a:mrow> <a:msub> <a:mrow> <a:mi>R</a:mi> </a:mrow> <a:mrow> <a:mi>i</a:mi> </a:mrow> </a:msub> </a:mrow> </a:msub> <a:mo>,</a:mo> <a:mrow> <a:mi>i</a:mi> <a:mo>=</a:mo> <a:mn>1</a:mn> </a:mrow> </a:mrow> <a:mo>,</a:mo> <a:mn>2</a:mn> <a:mo>,</a:mo> <a:mn>3</a:mn> </a:mrow> </a:math> , one singlet fermion <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>χ</c:mi> </c:math> , a doublet fermion <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>ψ</e:mi> </e:math> , and heavy scalar doublets <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:msub> <g:mrow> <g:mi>η</g:mi> </g:mrow> <g:mrow> <g:mi>i</g:mi> </g:mrow> </g:msub> <g:mo>,</g:mo> <g:mrow> <g:mi>i</g:mi> <g:mo>=</g:mo> <g:mn>1</g:mn> </g:mrow> <g:mo>,</g:mo> <g:mn>2</g:mn> </g:mrow> </g:math> to the Standard Model. A global <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>B</i:mi> <i:mo>−</i:mo> <i:mi>L</i:mi> </i:math> is imposed to protect the Dirac nature of neutrinos. Both <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>χ</k:mi> </k:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>ψ</m:mi> </m:math> are fermions with nonzero charge under an extended <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>U</o:mi> <o:mo stretchy="false">(</o:mo> <o:mn>1</o:mn> <o:msub> <o:mo stretchy="false">)</o:mo> <o:mrow> <o:mi>B</o:mi> <o:mo>−</o:mo> <o:mi>L</o:mi> </o:mrow> </o:msub> <o:mo>×</o:mo> <o:mi>U</o:mi> <o:mo stretchy="false">(</o:mo> <o:mn>1</o:mn> <o:msub> <o:mo stretchy="false">)</o:mo> <o:mi>D</o:mi> </o:msub> </o:math> symmetry. Additionally, a <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msub> <u:mi mathvariant="script">Z</u:mi> <u:mn>2</u:mn> </u:msub> </u:math> symmetry is imposed, where the singlets <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:mi>χ</x:mi> </x:math> , <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:msub> <z:mi>ν</z:mi> <z:mi>R</z:mi> </z:msub> </z:math> , and <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:mi>η</bb:mi> </bb:math> are negative and the doublet <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"> <db:mi>ψ</db:mi> </db:math> is positive. The <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:mi>C</fb:mi> <fb:mi>P</fb:mi> </fb:math> -violating out-of-equilibrium decay of heavy scalar <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"> <hb:mi>η</hb:mi> </hb:math> generates an equal and opposite <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"> <jb:mi>B</jb:mi> <jb:mo>−</jb:mo> <jb:mi>L</jb:mi> </jb:math> asymmetry among the left-handed ( <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"> <lb:msub> <lb:mi>ν</lb:mi> <lb:mi>L</lb:mi> </lb:msub> </lb:math> ) and right-handed ( <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"> <nb:msub> <nb:mi>ν</nb:mi> <nb:mi>R</nb:mi> </nb:msub> </nb:math> ) neutrinos. The <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"> <pb:msub> <pb:mi>ν</pb:mi> <pb:mi>L</pb:mi> </pb:msub> <pb:mo>−</pb:mo> <pb:msub> <pb:mi>ν</pb:mi> <pb:mi>R</pb:mi> </pb:msub> </pb:math> equilibration process does not take place until below the electroweak phase transition scale because of tiny Yukawa couplings. During this time, sphaleron processes, which are active at temperatures higher than 100 GeV, transform a portion of the <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"> <rb:mi>B</rb:mi> <rb:mo>−</rb:mo> <rb:mi>L</rb:mi> </rb:math> asymmetry stored in left-handed neutrinos into baryon asymmetry. MeV scale gauge boson <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"> <tb:msup> <tb:mi>Z</tb:mi> <tb:mo>′</tb:mo> </tb:msup> </tb:math> of the <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"> <vb:mi>U</vb:mi> <vb:mo stretchy="false">(</vb:mo> <vb:mn>1</vb:mn> <vb:msub> <vb:mo stretchy="false">)</vb:mo> <vb:mi>D</vb:mi> </vb:msub> </vb:math> sector mediates both annihilation of symmetric dark matter component and self-interaction among dark matter particles. Moreover, <zb:math xmlns:zb="http://www.w3.org/1998/Math/MathML" display="inline"> <zb:msup> <zb:mi>Z</zb:mi> <zb:mo>′</zb:mo> </zb:msup> </zb:math> mixes with the Standard Model Z boson and provides a portal for dark matter direct detection.