Small Improvement to the Kolmogorov-Smirnov Test

The Kolmogorov-Smirnov (K-S) test is widely used as a goodness-of-fit test. This thesis consists of two parts to describe ways to improve the classical K-S test in both 1-dimensional and 2-dimensional data. The first part is about how to improve the accuracy of the classical K-S goodness-of-fit test in 1-dimensional data. We replace the p-values estimated by the asymptotic distribution with near-exact p-values. In the second part, we propose two new methods to increase power of the widely used 2-dimensional two-sample Fasano and Franceschini test. Simulation studies show the new methods are significantly more powerful than the Fasano and Franceschini’s test

The naturalness in the BLMSSM and B-LSSM

In order to interpret the Higgs mass and its decays more naturally, we hope to intrude the BLMSSM and B-LSSM. In the both models, the right-handed neutrino superfields are introduced to better explain the neutrino mass problems. In addition, there are other superfields considered to make these models more natural than MSSM. In this paper, the method of $\chi^2$ analyses will be adopted in the BLMSSM and B-LSSM to calculate the Higgs mass, Higgs decays and muon $g-2$. With the fine-tuning in the region $0.67\%-2.5\%$ and $0.67\%-5\%$, we can obtain the reasonable theoretical values that are in accordance with the experimental results respectively in the BLMSSM and B-LSSM. Meanwhile, the best-fitted benchmark points in the BLMSSM and B-LSSM will be acquired at minimal $(\chi^{BL}_{min})^2 = 2.34736$ and $(\chi^{B-L}_{min})^2 = 2.47754$, respectively

Phenomenological discriminations of the Yukawa interactions in two-Higgs doublet models with Z2Z_2 symmetry

There are four types of two-Higgs doublet models under a discrete $Z_2$ symmetry imposed to avoid tree-level flavour-changing neutral current, i.e. type-I, type-II, type-X and type-Y models. We investigate the possibility to discriminate the four models in the light of the flavour physics data, including $B_s-\bar B_s$ mixing, $B_{s,d} \to \mu^+ \mu^-$, $B\to \tau\nu$ and $\bar B \to X_s \gamma$ decays, the recent LHC Higgs data, the direct search for charged Higgs at LEP, and the constraints from perturbative unitarity and vacuum stability. After deriving the combined constraints on the Yukawa interaction parameters, we have shown that the correlation between the mass eigenstate rate asymmetry $A_{\Delta\Gamma}$ of $B_{s} \to \mu^+ \mu^-$ and the ratio $R={\cal B}(B_{s} \to \mu^+ \mu^-)_{exp}/ {\cal B}(B_{s} \to \mu^+ \mu^-)_{SM}$ could be sensitive probe to discriminate the four models with future precise measurements of the observables in the $B_{s} \to \mu^+ \mu^-$ decay at LHCb.Comment: 29 pages, 4 tables, 11 figures. v3: minor corrections included, matches published version in EPJ