Generalised Jantzen filtration of Lie superalgebras I.

A Jantzen type filtration for generalised Verma modules of Lie superalgebras is introduced. In the case of type I Lie superalgebras, it is shown that the generalised Jantzen filtration for any Kac module is the unique Loewy filtration, and the decomposition numbers of the layers of the filtration are determined by the coefficients of inverse Kazhdan–Lusztig polynomials. Furthermore, the length of the Jantzen filtration for any Kac module is determined explicitly in terms of the degree of atypicality of the highest weight. These results are applied to obtain a detailed description of the submodule lattices of Kac modules

Extra boson mix with Z boson explaining the mass of W boson

We explore the possibility of explaining the W mass with an extra gauge boson mixing with the Z boson at tree level. Extra boson mixing with Z boson will change the expression of Z boson mass, thus altering the W boson mass. We explore two models in this work. We find that in the Derivative Portal Dark Matter model, there are parameters space which can give the observed W boson mass. And in the U(1) extension model, the kinetic mixing between extra boson and B boson can also predict the observed W boson mass. Both model indicate an extra vector boson with best fit mass around 120 GeV.Comment: 12 pages, 3 figure

Microvascular autologous submandibular gland transplantation in severe cases of keratoconjunctivitis sicca

Dry eye syndrome is a relatively common disease of the tears and ocular surfaces that results in discomfort, visual disturbance, and tear film instability with possible damage to the ocular surfaces. Microvascular submandibular gland (SMG) transfer offers a surgical alternative for a permanent autologous substitution of tears using the basal secretion of a transplanted SMG. Long-term follow-up reveals that this technique is a lasting and effective solution for patients with severe dry eye syndrome. The uncomfortable symptoms were relieved, and the frequency of use of pharmaceutical tear substitutes was reduced. Objective examination showed significant improvement in tear film and some features of ocular surface such as breakup time of tear film and corneal staining. Patients may suffer from obstruction of Wharton's duct or epiphora after surgery. Activation of secretion-related receptors could improve the early hypofunction of the denervated SMG and prevent the duct obstruction. Reduction surgery, partial SMG transplantation, uses of atropine gel or Botulinum toxin A could be the choices of treatment for epiphora.PubMed0153

Testing weakest force with coldest spot

Ultra-cold atom experiment in space with microgravity allows for realization of dilute atomic-gas Bose-Einstein condensate (BEC) with macroscopically large occupation number and significantly long condensate lifetime, which allows for a precise measurement on the shape oscillation frequency by calibrating itself over numerous oscillation periods. In this paper, we propose to measure the Newtonian gravitational constant via ultra-cold atom BEC with shape oscillation, although it is experimentally challenging. We also make a preliminary perspective on constraining the modified Newtonian potential such as the power-law potential, Yukawa interaction, and fat graviton. A resolution of frequency measurement of $(1-100)\,\mathrm{nHz}$ at most for the occupation number $10^9$, just one order above experimentally achievable number $N\sim10^6-10^8$, is feasible to constrain the modified Newtonian potential with Yukawa interaction greatly beyond the current exclusion limits.Comment: v1, 10 pages, 3 figures; v2, references added, discussion extended for enlarged parameter space of Yukawa interaction, version accepted by EPJ

Nano-Hertz gravitational waves from collapsing domain walls associated with freeze-in dark matter in light of pulsar timing array observations

Evidence for a stochastic gravitational wave background in the nHz frequency band is recently reported by four pulsar timing array collaborations NANOGrav, EPTA, CPTA, and PPTA. It can be interpreted by gravitational waves from collapsing domain walls in the early universe. We assume such domain walls arising from the spontaneous breaking of a $Z_2$ symmetry in a scalar field theory, where a tiny $Z_2$-violating potential is required to make domain walls unstable. We propose that this $Z_2$-violating potential is radiatively induced by a feeble Yukawa coupling between the scalar field and a fermion field, which is also responsible for dark matter production via the freeze-in mechanism. Combining the pulsar timing array data and the observed dark matter relic density, we find that the model parameters can be narrowed down to small ranges.Comment: 18 pages, 6 figure

Hamiltonian type Lie bialgebras

We first prove that, for any generalized Hamiltonian type Lie algebra $L$, the first cohomology group $H^1(L,L \otimes L)$ is trivial. We then show that all Lie bialgebra structures on $L$ are triangular.Comment: LaTeX, 16 page