Dark matter in the scale-invariant 3-3-1-1 model

We propose a novel scale-invariant model with the 3-3-1-1 gauge symmetry featuring a universal seesaw mechanism for all fermion masses, which, through the inclusion of additional vectorlike quarks, provides a partial explanation for the observed fermion mass hierarchies. A discrete remnant of the gauge group, the matter parity ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>P</a:mi> <a:mi>M</a:mi> </a:msub> </a:math> ), stabilizes a fermionic dark matter candidate, and the scalar sector includes two triplets (minimal for <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mn>3</c:mn> <c:mtext>−</c:mtext> <c:mn>3</c:mn> <c:mtext>−</c:mtext> <c:mn>1</c:mn> </c:mrow> </c:math> breaking) and two scalar singlets. We identify the lightest <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>P</e:mi> <e:mi>M</e:mi> </e:msub> </e:math> -odd fermion, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>f</g:mi> <g:mi mathvariant="normal">d</g:mi> </g:msub> </g:math> , as a viable dark matter candidate. Our analysis shows that <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:msub> <j:mi>f</j:mi> <j:mi mathvariant="normal">d</j:mi> </j:msub> </j:math> satisfies the observed relic density constraint within the mass range <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mn>220</m:mn> <m:mtext> </m:mtext> <m:mtext> </m:mtext> <m:mi>GeV</m:mi> <m:mo>≲</m:mo> <m:msub> <m:mi>m</m:mi> <m:msub> <m:mi>f</m:mi> <m:mi mathvariant="normal">d</m:mi> </m:msub> </m:msub> <m:mo>≲</m:mo> <m:mn>555</m:mn> <m:mtext> </m:mtext> <m:mtext> </m:mtext> <m:mi>GeV</m:mi> </m:math> , primarily due to resonant annihilation via the new scalar <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:msub> <p:mi>H</p:mi> <p:mn>2</p:mn> </p:msub> </p:math> . While this mass range depends on the symmetry-breaking scale <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:msub> <r:mi>v</r:mi> <r:mi>χ</r:mi> </r:msub> </r:math> , which has a lower bound of <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:msub> <t:mi>v</t:mi> <t:mi>χ</t:mi> </t:msub> <t:mo>≳</t:mo> <t:mn>3.6</t:mn> <t:mtext> </t:mtext> <t:mtext> </t:mtext> <t:mi>TeV</t:mi> </t:math> from LEP constraints on the <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:msub> <v:mi>ρ</v:mi> <v:mn>0</v:mn> </v:msub> </v:math> parameter, we adopt a more conservative lower bound of <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:msub> <x:mi>v</x:mi> <x:mi>χ</x:mi> </x:msub> <x:mo>&gt;</x:mo> <x:mn>10</x:mn> <x:mtext> </x:mtext> <x:mtext> </x:mtext> <x:mi>TeV</x:mi> </x:math> . This choice is made to ensure that the <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:msup> <z:mi>Z</z:mi> <z:mo>′</z:mo> </z:msup> </z:math> boson mass remains above approximately 4 TeV, and is motivated by recent LHC results and future projections for <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:msup> <bb:mi>Z</bb:mi> <bb:mo>′</bb:mo> </bb:msup> </bb:math> boson searches, which provide more stringent constraints than previous bounds or those from the <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"> <db:msub> <db:mi>ρ</db:mi> <db:mn>0</db:mn> </db:msub> </db:math> parameter. Spin-independent (SI) interactions dominate the direct detection phenomenology of <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:msub> <fb:mi>f</fb:mi> <fb:mi mathvariant="normal">d</fb:mi> </fb:msub> </fb:math> . We calculate the SI elastic scattering cross section and find that parameter points satisfying the relic density constraint are consistent with current experimental limits from LZ and PandaX-4T for certain parameter choices, particularly depending on the <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:msub> <ib:mi>α</ib:mi> <ib:mn>12</ib:mn> </ib:msub> </ib:math> angle. Some regions of the viable parameter space lie below the neutrino floor. Prospects for detection by future experiments like XLZD and PandaX-xT are also presented and discussed.