A Theory of R(D∗,D)R(D^*,D) Anomaly With Right-Handed Currents

We present an ultraviolet complete theory for the $R(D^*)$ and $R(D)$ anomaly in terms of a low mass $W_R^\pm$ gauge boson of a class of left-right symmetric models. These models, which are based on the gauge symmetry $SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$, utilize vector-like fermions to generate quark and lepton masses via a universal seesaw mechanism. A parity symmetric version as well as an asymmetric version are studied. A light sterile neutrino emerges naturally in this setup, which allows for new decay modes of $B$-meson via right-handed currents. We show that these models can explain $R(D^*)$ and $R(D)$ anomaly while being consistent with LHC and LEP data as well as low energy flavor constraints arising from $K_L-K_S, B_{d,s}-\bar{B}_{d,s}$, $D-\bar{D}$ mixing, etc., but only for a limited range of the $W_R$ mass: $1.2\, (1.8)~{\rm TeV} \leq M_{W_R}\leq 3~ {\rm TeV}$ for parity asymmetric (symmetric) Yukawa sectors. The light sterile neutrinos predicted by the model may be relevant for explaining the MiniBoone and LSND neutrino oscillation results. The parity symmetric version of the model provides a simple solution to the strong CP problem without relying on the axion. It also predicts an isospin singlet top partner with a mass $M_T = (1.5-2.5)$ TeV.Comment: 43 pages, 7 figures, references added, model slightly modifie

Some properties of the range of super-Brownian motion

We consider a super-Brownian motion $X$. Its canonical measures can be studied through the path-valued process called the Brownian snake. We obtain the limiting behavior of the volume of the $\epsilon$-neighborhood for the range of the Brownian snake, and as a consequence we derive the analogous result for the range of super-Brownian motion and for the support of the integrated super-Brownian excursion. Then we prove the support of $X_t$ is capacity-equivalent to $[0,1]^2$ in $\R^d$, $d\geq 3$, and the range of $X$, as well as the support of the integrated super-Brownian excursion are capacity-equivalent to $[0,1]^4$ in $\R^d$, $d\geq 5$

Virtual Element Methods on Meshes with Small Edges or Faces

We consider a model Poisson problem in $\R^d$ ($d=2,3$) and establish error estimates for virtual element methods on polygonal or polyhedral meshes that can contain small edges ($d=2$) or small faces ($d=3$).Comment: 36 page