Anomalous magnetic and weak magnetic dipole moments of the τ\tau lepton in the simplest little Higgs model

We obtain analytical expressions, both in terms of parametric integrals and Passarino-Veltman scalar functions, for the one-loop contributions to the anomalous weak magnetic dipole moment (AWMDM) of a charged lepton in the framework of the simplest little Higgs model (SLHM). Our results are general and can be useful to compute the weak properties of a charged lepton in other extensions of the standard model (SM). As a by-product we obtain generic contributions to the anomalous magnetic dipole moment (AMDM), which agree with previous results. We then study numerically the potential contributions from this model to the $\tau$ lepton AMDM and AWMDM for values of the parameter space consistent with current experimental data. It is found that they depend mainly on the energy scale $f$ at which the global symmetry is broken and the $t_\beta$ parameter, whereas there is little sensitivity to a mild change in the values of other parameters of the model. While the $\tau$ AMDM is of the order of $10^{-9}$, the real (imaginary) part of its AWMDM is of the order of $10^{-9}$ ($10^{-10}$). These values seem to be out of the reach of the expected experimental sensitivity of future experiments.Comment: 23 pages, 11 figures, new analysis and References adde

Combinatorics of lattice paths with and without spikes

We derive a series of results on random walks on a d-dimensional hypercubic lattice (lattice paths). We introduce the notions of terse and simple paths corresponding to the path having no backtracking parts (spikes). These paths label equivalence classes which allow a rearrangement of the sum over paths. The basic combinatorial quantities of this construction are given. These formulas are useful when performing strong coupling (hopping parameter) expansions of lattice models. Some applications are described.Comment: Latex. 25 page

Large NN reduction with the Twisted Eguchi-Kawai model

We examine the breaking of $Z_N$ symmetry recently reported for the Twisted Eguchi-Kawai model (TEK). We analyse the origin of this behaviour and propose simple modifications of twist and lattice action that could avoid the problem. Our results show no sign of symmetry breaking and allow us to obtain values of the large $N$ infinite volume string tension in agreement with extrapolations from results based upon straightforward methods.Comment: latex file 14 pages, 4 figure

Two-loop critical mass for Wilson fermions

We have redone a recent two-loop computation of the critical mass for Wilson fermions in lattice QCD by evaluating Feynman integrals with the coordinate-space method. We present the results for different types of infrared regularization. We confirm both the previous numerical estimates and the power of the coordinate-space method whenever high accuracy is needed.Comment: 13 LaTeX2e pages, 2 ps figures include

Letrozole treatment of pubertal female mice results in activational effects on reproduction, metabolism and the gut microbiome.

Polycystic ovary syndrome (PCOS) is a common endocrine disorder in reproductive-aged women that is comprised of two out of the following three features: hyperandrogenism, oligo- or amenorrhea, or polycystic ovaries. In addition to infertility, many women with PCOS have metabolic dysregulation that increases the risk of developing type 2 diabetes, hypertension, and non-alcoholic fatty liver disease. Changes in the gut microbiome are associated with PCOS and gut microbes may be involved in the pathology of this disorder. Since PCOS often manifests in the early reproductive years, puberty is considered to be a critical time period for the development of PCOS. Exposure to sex steroid hormones during development results in permanent, organizational effects, while activational effects are transient and require the continued presence of the hormone. Androgens exert organizational effects during prenatal or early post-natal development, but it is unclear whether androgen excess results in organizational or activational effects during puberty. We recently developed a letrozole-induced PCOS mouse model that recapitulates both reproductive and metabolic phenotypes of PCOS. In this study, we investigated whether letrozole treatment of pubertal female mice exerts organizational or activational effects on host physiology and the gut microbiome. Two months after letrozole removal, we observed recovery of reproductive and metabolic parameters, as well as diversity and composition of the gut microbiome, indicating that letrozole treatment of female mice during puberty resulted in predominantly activational effects. These results suggest that if exposure to excess androgens during puberty leads to the development of PCOS, reduction of androgen levels during this time may improve reproductive and metabolic phenotypes in women with PCOS. These results also imply that continuous letrozole exposure is required to model PCOS in pubertal female mice since letrozole exerts activational rather than organizational effects during puberty

Non-Abelian Vortices on the Torus

We study periodic arrays of non-Abelian vortices in an $SU(N) \times U(1)$ gauge theory with $N_f$ flavors of fundamental matter multiplets. We carefully discuss the corresponding twisted boundary conditions on the torus and propose an ansatz to solve the first order Bogomolnyi equations which we find by looking to a bound of the energy. We solve the equations numerically and construct explicit vortex solutions