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Register a new userRigorous treatment of the $mathcal{S}^1 / mathbb{Z}_2$ orbifold model with brane-Higgs couplings
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We build rigorously the attractive five-dimensional model where bulk fermions propagate along the $ mathcal{S}^1 / mathbb{Z}_2$ orbifold and interact with a Higgs boson localised at a fixed point of the extra dimension. The analytical calculation of the fermion mass spectrum and effective Yukawa couplings is shown to require the introduction of either Essential Boundary Conditions (EBC) imposed by the model definition or certain Bilinear Brane Terms (BBT) in the action, instead of the usual brane-Higgs regularisations. The obtained fermion profiles along the extra dimension turn out to undergo some discontinuities, in particular at the Higgs brane, which can be mathematically consistent if the action is well written with improper integrals. We also show that the $mathbb{Z}_2$ parity transformations in the bulk do not affect the fermion chiralities, masses and couplings, in contrast with the EBC and BBT, but when extended to the fixed points, they can generate the chiral nature of the theory and even select the Standard Model chirality set-up while fixing as well the fermion masses and couplings. Thanks to the strict analysis developed, the duality with the interval model is scrutinised.
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We perform a digital pseudoquantum simulation of $mathbb{Z}_2$ gauge Higgs model on a $3times 3$ lattice. First we propose the quantum algorithm for the digital quantum simulation, based on Trotter decomposition, quantum adiabatic algorithm and its circuit realization. Then we classically demonstrate it in a GPU simulator, obtaining useful results, which indicate the topological properties of deconfined phase and clarify the phase diagram. Especially, our work suggests that the tricitical point, where the two critical lines of second-order transitions meet, lies on the critical line of the first-order transition rather than its end.
The class of higher-dimensional scenarios, based on a brane-localised Higgs boson coupled to bulk fermions, can address both the flavour puzzle and gauge hierarchy problem. A key question arises due to the possibility of fermion profile discontinuities at the Higgs boundary: how to calculate rigorously the fermion mass spectrum and effective four-dimensional (4D) Yukawa couplings? We show that the proper treatment, leading to physically consistent solutions, does not rely on any Higgs peak regularisation but requires the presence of certain Bilinear Brane Terms (BBT). In particular, no profile jump should appear and the Higgs regularisations turn out to suffer from mathematical discrepancies reflected in two non-commutativities of calculation steps debated in the literature. The introduction of BBT can by replaced by vanishing conditions for probability currents at the considered flat interval boundaries. Both contribute to the definition of the field geometrical configuration of the model, even in the free case. The BBT could allow to elaborate an ultra-violet origin of the chiral nature of the Standard Model and of its chirality distribution among quarks/leptons. The current conditions are implemented via essential boundary conditions to be contrasted with the natural boundary conditions derived from the action variation. All these theoretical conclusions are confirmed in particular by the converging exact results of the 4D versus 5D approaches. The analysis is completed by a description of the appropriate energy cut-off procedure. The new calculation methods presented, implying the independence of excited fermion masses and 4D Yukawa couplings on the wrong-chirality Yukawa terms, have impacts on phenomenological results like the relaxing of previously obtained strong bounds on Kaluza-Klein masses induced by flavour changing reactions generated through exchanges of the Higgs field.
The cosmology of the Twin Higgs requires the breaking of the $mathbb{Z}_2$ symmetry, but it is still an open question whether this breaking needs to be explicit. In this paper, we study how the Mirror Twin Higgs could be modified to be compatible with current cosmological constraints without explicit $mathbb{Z}_2$ breaking. We first present a simple toy model that can realize baryogenesis without explicit $mathbb{Z}_2$ breaking or reaching temperatures that would lead to domain walls. The model can also either solve the $N_{text{eff}}$ problem and bring the abundance of mirror atoms to an allowed level or provide the correct dark matter abundance. We then present another simple model that leads to mirror neutron dark matter and thus acceptable dark matter self-interactions. We also include in appendix a series of results on energy exchange between different sectors that might prove useful for other cosmological problems.
We present a model with $S_3 otimes mathbb{Z}_2$ model plus a sterile neutrino and its phenomenological expectations for the production of charged scalars at the Compact Linear Collider. At tree level, our model predicts a total cross section in between 0.1 and $10^{-5}$ pb for the $e^- e^+ to H^+ H^-$ process, considering all possible mass values for the charged scalar in the CLIC experiment. We also show that this prediction holds regardless of the masses of the other exotic particles and their couplings.
We report the results of the lattice simulation of the ${mathbb C} P^{N-1}$ sigma model on $S_{s}^{1}$(large) $times$ $S_{tau}^{1}$(small). We take a sufficiently large ratio of the circumferences to approximate the model on ${mathbb R} times S^1$. For periodic boundary condition imposed in the $S_{tau}^{1}$ direction, we show that the expectation value of the Polyakov loop undergoes a deconfinement crossover as the compactified circumference is decreased, where the peak of the associated susceptibility gets sharper for larger $N$. For ${mathbb Z}_{N}$ twisted boundary condition, we find that, even at relatively high $beta$ (small circumference), the regular $N$-sided polygon-shaped distributions of Polyakov loop leads to small expectation values of Polyakov loop, which implies unbroken ${mathbb Z}_{N}$ symmetry if sufficient statistics and large volumes are adopted. We also argue the existence of fractional instantons and bions by investigating the dependence of the Polyakov loop on $S_{s}^{1}$ direction, which causes transition between ${mathbb Z}_{N}$ vacua.
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