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Register a new userThe $Z_3$ symmetric I(2+1)HDM
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We introduce a 3-Higgs Doublet Model (3HDM) with two Inert (or dark) scalar doublets and an active Higgs one, hence termed I(2+1)HDM, in the presence of a discrete $Z_3$ symmetry acting upon the three doublet fields. We show that such a construct yields a Dark Matter (DM) sector with two mass-degenerate states of opposite CP parity, both of which contribute to DM dynamics, which we call textit{Hermaphrodite DM}, distinguishable from a (single) complex DM candidate. We show that the relic density contributions of both states are equal, saturating the observed relic density compliant with (in)direct searches for DM as well as other experimental data impinging on both the dark and Higgs sectors of the model, chiefly, in the form of Electro-Weak Precision Observables (EWPOs), Standard Model (SM)-like Higgs boson measurements at the Large Hadron Collider (LHC) and void searches for additional (pseudo)scalar states at the CERN machine and previous colliders.
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As an effective model corresponding to $Z_3$-symmetric QCD ($Z_3$-QCD), we construct a $Z_3$-symmetric effective Polyakov-line model ($Z_3$-EPLM) by using the logarithmic fermion effective action. Since $Z_3$-QCD tends to QCD in the zero temperature limit, $Z_3$-EPLM also agrees with the ordinary effective Polyakov-line model (EPLM) there; note that ordinary EPLM does not possess $Z_3$ symmetry. Our main purpose is to discuss a sign problem appearing in $Z_3$-EPLM. The action of $Z_3$-EPLM is real, when the Polyakov line is not only real but also its $Z_3$ images. This suggests that the sign problem becomes milder in $Z_3$-EPLM than in EPLM. In order to confirm this suggestion, we do lattice simulations for both EPLM and $Z_3$-EPLM by using the reweighting method with the phase quenched approximation. In the low-temperature region, the sign problem is milder in $Z_3$-EPLM than in EPLM. We also propose a new reweighting method. This makes the sign problem very weak in $Z_3$-EPLM.
Inspired by the fact that relatively small values of the effective higgsino mass parameter of the $Z_3$-symmetric Next-to-Minimal Supersymmetric Standard Model (NMSSM) could render the scenario `natural, we explore the plausibility of having relatively light neutralinos and charginos (the electroweakinos or the ewinos) in such a scenario with a rather light singlino-like Lightest Supersymmetric Particle (LSP), which is a Dark Matter (DM) candidate, and singlet-dominated scalar excitations. By first confirming the indications in the existing literature that finding simultaneous compliance with results from the Large Hadron Collider (LHC) and those from various DM experiments with such light states is, in general, a difficult ask, we proceed to demonstrate, with the help of a few representative benchmark points, how exactly and to what extent could such a highly motivated `natural setup with a singlino-like DM candidate still remains plausible.
The stability of the magnetization $m=1/3$ plateau phase of the XXZ spin-1/2 Heisenberg chain with competing interactions is investigated upon switching on a staggered transverse magnetic field. Within a bosonization approach, it is shown that the low-energy properties of the model are described by an effective two-dimensional XY model in a three-fold symmetry-breaking field. A phase transition in the three-state Potts universality class is expected separating the $m=1/3$ plateau phase to a phase where the spins are polarized along the staggered magnetic field. The Z$_3$ critical properties of the transition are determined within the bosonization approach.
A highly bino-like Dark Matter (DM), which is the Lightest Supersymmetric Particle (LSP), could be motivated by the stringent upper bounds on the DM direct detection rates. This is especially so when its mass is around or below 100 GeV for which such a bound tends to get most severe. Requiring not so large a higgsino mass parameter, that would render the scenario reasonably natural, prompts such a bino-like state to be relatively light. In the Minimal Supersymmetric Standard Model (MSSM), in the absence of comparably light scalars, such an excitation, if it has to be a thermal relic, is unable to meet the stringent experimental upper bound on its abundance unless its self-annihilation hits a funnel involving either the $Z$-boson or the Standard Model (SM)-like Higgs boson. We demonstrate that, in such a realistic situation, a highly bino-like DM of the popular $Z_3$-symmetric Next-to-Minimal Supersymmetric Standard Model (NMSSM) is viable over an extended range of its mass, from our targeted maximum in the vicinity of the mass of the top quark down to about 30 GeV. This is facilitated by the presence of comparably light singlet-like states that could serve as funnel (scalars) and/or coannihilating (singlino) states even as the bino-like LSP receives a minimal (but optimal) tempering triggered by suitably light higgsino states that, in the first place, evade stringent lower bounds on their masses that can be derived from the Large Hadron Collider (LHC) experiments only in the presence of a lighter singlino-like state. An involved set of blind spot conditions is derived for the DM direct detection rates by considering for the very first time the augmented system of neutralinos comprising of the bino, the higgsinos and the singlino which highlights the important roles played by the NMSSM parameters $lambda$ and $tanbeta$ in delivering a richer phenomenology.
Multi-component dark matter scenarios are studied in the model with $U(1)_X$ dark gauge symmetry that is broken into its product subgroup $Z_2 times Z_3$ {a} la Krauss-Wilczek mechanism. In this setup, there exist two types of dark matter fields, $X$ and $Y$, distinguished by different $Z_2 times Z_3$ charges. The real and imaginary parts of the $Z_2$-charged field, $X_R$ and $X_I$, get different masses from the $U(1)_X$ symmetry breaking. The field $Y$, which is another dark matter candidate due to the unbroken $Z_3$ symmetry, belongs to the Strongly Interacting Massive Particle (SIMP)-type dark matter. Both $X_I$ and $X_R$ may contribute to $Y$s $3rightarrow 2$ annihilation processes, opening a new class of SIMP models with a local dark gauge symmetry. Depending on the mass difference between $X_I$ and $X_R$, we have either two-component or three-component dark matter scenarios. In particular two- or three-component SIMP scenarios can be realised not only for small mass difference between $X$ and $Y$, but also for large mass hierarchy between them, which is a new and unique feature of the present model. We consider both theoretical and experimental constraints, and present four case studies of the multi-component dark matter scenarios.
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