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

A Moving Mesh Method for Porous Medium Equation by the Onsager Variational Principle

In this paper, we introduce a new approach to solving the porous medium equation using a moving mesh finite element method that leverages the Onsager variational principle as an approximation tool. Both the continuous and discrete problems are formulated based on the Onsager principle. The energy dissipation structure is maintained in the semi-discrete and fully implicit discrete schemes. We also develop a fully decoupled explicit scheme by which only a few linear equations are solved sequentially in each time step. The numerical schemes exhibit an optimal convergence rate when the initial mesh is appropriately selected to ensure accurate approximation of the initial data. Furthermore, the method naturally captures the waiting time phenomena without requiring any manual intervention

Measurement of the high energy γ\gamma-rays from heavy ion reactions using \v{C}erenkov detector

The energetic bremsstrahlung photons up to 100 MeV produced in heavy ion collisions can be used as a sensitive probe to the short range correlation in atomic nuclei. The energy of the $\gamma$-rays can be measured by collecting the \v{C}erenkov light in medium induced by the fast electrons generated in Compton scattering or electromagnetic shower of the incident $\gamma$ ray. Two types of detectors, based on pure water and lead glass as the sensitive material respectively, are designed for the above purpose. The $\gamma$ response and optical photon propagation in detectors have been simulated based on the electromagnetic and optical processes in Geant4. The inherent energy resolution of $0.022+0.51/E_{\gamma}^{1/2}$ for water and $0.002+0.45/E_{\gamma}^{1/2}$ for lead glass are obtained. The geometry size of lead glass and water are optimized at $30\times 30 \times 30$ cm$^3$ and $60\times 60 \times 120$ cm$^3$, respectively, for detecting high energy $\gamma$-rays at 160 MeV. Hough transform method has been applied to reconstruct the direction of the incident $\gamma$-rays, giving the ability to distinguish experimentally the high-energy $\gamma$ rays produced in the reactions on the target from the random background cosmic ray muons