Lepton parity dark matter and naturally unstable domain walls

We propose a simple and predictive setup that connects neutrino masses, dark matter (DM), and gravitational waves. A minimal lepton parity DM scenario is considered where the residual symmetry <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mo stretchy="false">(</a:mo> <a:mo>−</a:mo> <a:mn>1</a:mn> <a:msup> <a:mo stretchy="false">)</a:mo> <a:mi>L</a:mi> </a:msup> </a:math> from the type I seesaw acts as the dark parity <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>D</e:mi> <e:mo>=</e:mo> <e:mo stretchy="false">(</e:mo> <e:mo>−</e:mo> <e:mn>1</e:mn> <e:msup> <e:mo stretchy="false">)</e:mo> <e:mrow> <e:mi>L</e:mi> <e:mo>+</e:mo> <e:mn>2</e:mn> <e:mi>j</e:mi> </e:mrow> </e:msup> </e:math> , ensuring DM stability without imposing any new symmetry. A singlet Majorana fermion <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>S</i:mi> </i:math> with even lepton parity serves as the DM candidate, interacting via a real scalar <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>σ</k:mi> </k:math> which is also even lepton parity. The scalar potential possesses an accidental <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mi mathvariant="script">Z</m:mi> <m:mn>2</m:mn> </m:msub> </m:math> symmetry, whose spontaneous breaking gives rise to unstable domain walls in the presence of explicit <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:msub> <p:mi mathvariant="script">Z</p:mi> <p:mn>2</p:mn> </p:msub> </p:math> -breaking terms allowed by the lepton parity. The subsequent domain wall annihilation generates a stochastic gravitational wave background potentially observable at different gravitational wave experiments.