Cancellation of divergences in unitary gauge calculation of H→γγH \to \gamma \gamma process via one W loop, and application

Following the thread of R. Gastmans, S. L. Wu and T. T. Wu, the calculation in the unitary gauge for the $H \to \gamma \gamma$ process via one W loop is repeated, without the specific choice of the independent integrated loop momentum at the beginning. We start from the 'original' definition of each Feynman diagram, and show that the 4-momentum conservation and the Ward identity of the W-W-photon vertex can guarantee the cancellation of all terms among the Feynman diagrams which are to be integrated to give divergences higher than logarithmic. The remaining terms are to the most logarithmically divergent, hence is independent from the set of integrated loop momentum. This way of doing calculation is applied to $H \to \gamma Z$ process via one W loop in the unitary gauge, the divergences proportional to $M_Z^2/M^3$ including quadratic ones are all cancelled, and terms proportional to $M_Z^2/M^3$ are shown to be zero. The way of dealing with the quadratic divergences proportional to $M_Z^2/M^3$ in $H \to \gamma Z$ has subtle implication on the employment on the Feynman rules especially when those rules can lead to high level divergences. So calculation without integration on all the $\delta$ functions until have to is a more proper or maybe necessary way of the employment of the Feynman rules.Comment: 1 figure, 34 pages (updated

Different critical points of chiral and deconfinement phase transitions in (2+1)-dimensional fermion-gauge interacting model

Based on the truncated Dyson-Schwinger equations for fermion and massive boson propagators in QED$_3$, the fermion chiral condensate and the mass singularities of the fermion propagator via the Schwinger function are investigated. It is shown that the critical point of chiral phase transition is apparently different from that of deconfinement phase transition and in Nambu phase the fermion is confined only for small gauge boson mass.Comment: 5 Pages and 3 figure

Fourth generation Majorana neutrino, dark matter and Higgs physics

We consider extensions of the standard model with fourth generation fermions (SM4) in which extra symmetries are introduced such that the transitions between the fourth generation fermions and the ones in the first three generations are forbidden. In these models, the stringent lower bounds on the masses of fourth generation quarks from direct searches are relaxed, and the lightest fourth neutrino is allowed to be stable and light enough to trigger the Higgs boson invisible decay. In addition, the fourth Majorana neutrino can be a subdominant but highly detectable dark matter component. We perform a global analysis of the current LHC data on the Higgs production and decay in this type of SM4. The results show that the mass of the lightest fourth Majorana neutrino is confined in the range $\sim 41-59$ GeV. Within the allowed parameter space, the predicted effective cross-section for spin-independent DM-nucleus scattering is $\sim 3\times 10^{-48}-6\times 10^{-46} \text{cm}^{2}$, which is close to the current Xenon100 upper limit and is within the reach of the Xenon1T experiment in the near future. The predicted spin-dependent cross sections can also reach $\sim 8\times 10^{-40}\text{cm}^{2}$.Comment: arXiv admin note: substantial text overlap with arXiv:1110.293