Question of Peccei-Quinn symmetry and quark masses in the economical 3-3-1 model

We show that there is an infinite number of U(1) symmetries like Peccei-Quinn symmetry in the 3-3-1 model with minimal scalar sector---two scalar triplets. Moreover, all of them are completely broken due to the model's scalars by themselves (notice that these scalars as known have been often used to break the gauge symmetry and generating the masses for the model's particles). There is no any residual Peccei-Quinn symmetry. Because of the minimal scalar content there are some quarks that are massless at tree-level, but they can get consistent mass contributions at one-loop due to this fact. Interestingly, axions as associated with the mentioned U(1)s breaking (including Majoron due to lepton-charge breaking) are all gauged away because they are also the Goldstone bosons responsible for the gauge symmetry breaking as usual.Comment: 25 pages, 4 figures, revised version, to appear in Physical Review

Large signal of h→μτh \rightarrow \mu \tau within the constraints of ei→ejγe_i \rightarrow e_j\gamma decays in the 3-3-1 model with neutral leptons

In the framework of the 3-3-1 model with neutral leptons, we have investigated the lepton-flavor-violating sources based on the Higgs mass spectrum which has two neutral Higgses identitied with corresponding ones in the Two-Higgs-Doublet model (THDM). On the $13~\mathrm{TeV}$ scale of the LHC, we point out the parameter space regions where the experimental limits of $e_i \rightarrow e_j\gamma$ decays are satisfied. These regions depend heavily on the mixing of exotic leptons but are predicted to have large $h^0_1\rightarrow \mu \tau$ signals. We also show that $\mathrm{Br}(h^0_1\rightarrow \mu \tau)$ can reach a value of $10^{-4}$.Comment: 30 pages, 9 figure

State-constraint static Hamilton-Jacobi equations in nested domains

We study state-constraint static Hamilton-Jacobi equations in a sequence of domains $\{\Omega_k\}_{k \in \mathbb{N}}$ in $\mathbb{R}^n$ such that $\Omega_k \subset \Omega_{k+1}$ for all $k\in \mathbb{N}$. We obtain rates of convergence of $u_k$, the solution to the state-constraint problem in $\Omega_k$, to $u$, the solution to the corresponding problem in $\Omega = \bigcup_{k \in \mathbb{N}} \Omega_k$. In many cases, the rates obtained are proven to be optimal. Various new examples and discussions are provided at the end of the paper.Comment: 23 pages, 1 figur

Tournament-Based Incentives and Mergers and Acquisitions

This research examines the relation between tournament-based incentives, which are proxied by the difference between a firm’s CEO pay and the median pay of the senior managers, and mergers and acquisitions (M&As). We find that tournament-based incentives are positively related to firm acquisitiveness and acquiring firms’ stock and operating performance. Further analysis indicates that positive acquisition performance increases the likelihood of the CEO being promoted from inside the acquiring firm. Our evidence is consistent with the view that tournament-based incentives motivate acquiring firms’ managers to make greater efforts and take more risk that result in superior acquisition performance