On Structure of cluster algebras of geometric type I: In view of sub-seeds and seed homomorphisms

Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type sub-seeds, the theory of seed homomorphisms and the view-point of gluing of seeds. As an application, for (rooted) cluster algebras, we completely classify rooted cluster subalgebras and characterize rooted cluster quotient algebras in detail. Also, we build the relationship between the categorification of a rooted cluster algebra and that of its rooted cluster subalgebras. Note that cluster algebras of geometric type studied here are of the sign-skew-symmetric case.Comment: 41 page

University Students’ Perspectives of Visual-based Cyberbullying on Instagram

Researchers have been investigating the cyberbullying phenomenon since the early 21st century. There is a substantial body of cyberbullying studies focused on text-based formats. However, studies revealed that visual-based social media platforms are more powerful than text-based platforms in affecting people’s emotions, causing significant psychological impact. Young adults ages 18-29 use visual-based social media heavily in their daily lives; therefore, visual cyberbullying on various sites has become a critical issue for this generation. Yet, the majority of existing cyberbullying studies focused on age groups under 18. The studies that did investigate this phenomenon among young adults focused mainly on text-based types of cyberbullying. Few studies have investigated visual-based cyberbullying of the adult population. Thus, this dissertation study explored university students’ perspectives of visual-based cyberbullying, with a specific focus on Instagram, because of its popularity. A Holistic Theoretical Framework was proposed to guide the study. This framework is grounded in the Social Ecological Model and the Cognitive-Affective-Behavioral frameworks. This study applied a mixed-method approach to collect data using four techniques: surveys, interviews, visual narrative inquiry, and scans of policy documents. Findings reported in this study have disclosed the nature of visual-based cyberbullying on Instagram as experienced by university students, revealed students’ perspectives of visual-based cyberbullying, unveiled the visual elements from actual incidents narrated by students, generated a novel definition of visual cyberbullying, and illuminated the gap between current university policies and real-world practices regarding the visual-based cyberbullying issue. This study contributes to the cyberbullying theoretical foundation, especially in exploring visual cyberbullying from cognitive, affective, and behavioral perspectives. Furthermore, the study collected visual cyberbullying cases that were crafted and narrated by study participants who witnessed cyberbullying incidents in real life. Future studies and practitioners may benefit from this study by applying the visual cases participants created to inform the design of research instruments and literacy educational materials. In addition, policymakers in higher education may learn from this study about the need to address cyberbullying more effectively in policy documents targeting undergraduate students. This study may also serve as a reference for the definition and examples of visual cyberbullying

Corrections to di-Higgs boson production with light stops and modified Higgs couplings

The Higgs pair production in gluon fusion is a sensitive probe of beyond-Standard Model (BSM) phenomena and its detection is a major goal for the LHC and higher energy hadron collider experiments. In this work we reanalyze the possible modifications of the Higgs pair production cross section within low energy supersymmetry models. We show that the supersymmetric contributions to the Higgs pair production cross section are strongly correlated with the ones of the single Higgs production in the gluon fusion channel. Motivated by the analysis of ATLAS and CMS Higgs production data, we show that the scalar superpartners' contributions may lead to significant modification of the di-Higgs production rate and invariant mass distribution with respect to the SM predictions. We also analyze the combined effects on the di-Higgs production rate of a modification of the Higgs trilinear and top-quark Yukawa couplings in the presence of light stops. In particular, we show that due to the destructive interference of the triangle and box amplitude contributions to the di-Higgs production cross section, even a small modification of the top-quark Yukawa coupling can lead to a significant increase of the di-Higgs production rate.Comment: 33 pages, 13 figures v2: minor improvements, PRD versio

Search for a heavy dark photon at future e+e−e^+e^- colliders

A coupling of a dark photon $A'$ from a $U(1)_{A'}$ with the standard model (SM) particles can be generated through kinetic mixing represented by a parameter $\epsilon$. A non-zero $\epsilon$ also induces a mixing between $A'$ and $Z$ if dark photon mass $m_{A'}$ is not zero. This mixing can be large when $m_{A'}$ is close to $m_Z$ even if the parameter $\epsilon$ is small. Many efforts have been made to constrain the parameter $\epsilon$ for a low dark photon mass $m_{A'}$ compared with the $Z$ boson mass $m_Z$. We study the search for dark photon in $e^+e^- \to \gamma A' \to \gamma \mu^+ \mu^-$ for a dark photon mass $m_{A'}$ as large as kinematically allowed at future $e^+e^-$ colliders. For large $m_{A'}$, care should be taken to properly treat possible large mixing between $A'$ and $Z$. We obtain sensitivities to the parameter $\epsilon$ for a wide range of dark photon mass at planed $e^+\;e^-$ colliders, such as Circular Electron Positron Collider (CEPC), International Linear Collider (ILC) and Future Circular Collider (FCC-ee). For the dark photon mass $20~\text{GeV}\lesssim m_{A^{\prime}}\lesssim 330~\text{GeV}$, the $2\sigma$ exclusion limits on the mixing parameter are $\epsilon\lesssim 10^{-3}-10^{-2}$. The CEPC with $\sqrt{s}=240~\text{GeV}$ and FCC-ee with $\sqrt{s}=160~\text{GeV}$ are more sensitive than the constraint from current LHCb measurement once the dark photon mass $m_{A^{\prime}}\gtrsim 50~\text{GeV}$. For $m_{A^{\prime}}\gtrsim 220~\text{GeV}$, the sensitivity at the FCC-ee with $\sqrt{s}=350~\text{GeV}$ and $1.5~\text{ab}^{-1}$ is better than that at the 13~TeV LHC with $300~\text{fb}^{-1}$, while the sensitivity at the CEPC with $\sqrt{s}=240~\text{GeV}$ and $5~\text{ab}^{-1}$ can be even better than that at 13~TeV LHC with $3~\text{ab}^{-1}$ for $m_{A^{\prime}}\gtrsim 180~\text{GeV}$.Comment: 21 pages, 5 figures, 2 table