Kaon semi-leptonic form factor at zero momentum transfer in finite volume

Using Chiral Perturbation Theory, we obtain the kaon semi-leptonic vector form factor in finite volume at a generic momentum transfer, $q^2$, up to one loop order. At first we confirm the lattice observation that the contribution of the heavy Pseudo-Goldstone boson in the finite volume corrections at zero momentum transfer is unimportant. We then evaluate the form factor at $q^2=0$ numerically and compare our results with the present lattice data. It turns out that our ChPT results are comparable with the lattice data to some extend. The formula for the finite volume corrections obtained for the form factor at momentum transfer $q^2$, provides a tool for lattice data in order to extrapolate at large lattice size.Comment: 19 pages, 3 figures: matches published version, comparisons made with more lattice dat

DAMPE Electron-Positron Excess in Leptophilic Z′Z' model

Recently the DArk Matter Particle Explorer (DAMPE) has reported an excess in the electron-positron flux of the cosmic rays which is interpreted as a dark matter particle with the mass about $1.5$ TeV. We come up with a leptophilic $Z'$ scenario including a Dirac fermion dark matter candidate which beside explaining the observed DAMPE excess, is able to pass various experimental/observational constraints including the relic density value from the WMAP/Planck, the invisible Higgs decay bound at the LHC, the LEP bounds in electron-positron scattering, the muon anomalous magnetic moment constraint, Fermi-LAT data, and finally the direct detection experiment limits from the XENON1t/LUX. By computing the electron-positron flux produced from a dark matter with the mass about $1.5$ TeV we show that the model predicts the peak observed by the DAMPE.Comment: 18 pages, 7 figures, matches with the published versio

Graphs with few matching roots

We determine all graphs whose matching polynomials have at most five distinct zeros. As a consequence, we find new families of graphs which are determined by their matching polynomial.Comment: 14 pages, 7 figures, 1 appendix table. Final version. Some typos are fixe