Algebraic Birkhoff decomposition and its applications

Central in the Hopf algebra approach to the renormalization of perturbative quantum field theory of Connes and Kreimer is their Algebraic Birkhoff Decomposition. In this tutorial article, we introduce their decomposition and prove it by the Atkinson Factorization in Rota-Baxter algebra. We then give some applications of this decomposition in the study of divergent integrals and multiple zeta values.Comment: 39 pages. To appear in "Automorphic Forms and Langlands Program

Muon g-2 Anomaly confronted with the higgs global data in the Left-Right Twin Higgs Models

We will examine the Left-Right Twin Higgs(LRTH) Models as a solution of muon g-2 anomaly with the background of the Higgs global fit data. In the calculation, the joint constrains from the theory, the precision electroweak data, the 125 GeV Higgs data, the leptonic flavor changing decay \mu \to e\gamma decays, and the constraints m_{\nu_R}>m_T>m_{W_H} are all considered. And with the small mass of the \phi^0, the direct searches from the $h\to \phi^0\phi^0$ channels can impose stringent upper limits on Br(h\to \phi^0\phi^0) and can reduce the allowed region of m_{\phi^0} and f. It is concluded that the muon g-2 anomaly can be explained in the region of 200 GeV \leq M\leq 500 GeV, 700 GeV \leq f\leq 1100 GeV, 13 GeV \leq m_{\phi^0}\leq 55 GeV, 100 GeV \leq m_{\phi^\pm}\leq 900 GeV, and m_{\nu_R}\geq 15 TeV after imposing all the constraints mentioned above.Comment: 18 pages, 4 figures, some typos modifie