Discretized normal approximation by Stein's method

We prove a general theorem to bound the total variation distance between the distribution of an integer valued random variable of interest and an appropriate discretized normal distribution. We apply the theorem to 2-runs in a sequence of i.i.d. Bernoulli random variables, the number of vertices with a given degree in the Erd\"{o}s-R\'{e}nyi random graph, and the uniform multinomial occupancy model.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ527 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

A multivariate CLT for bounded decomposable random vectors with the best known rate

We prove a multivariate central limit theorem with explicit error bound on a non-smooth function distance for sums of bounded decomposable $d$-dimensional random vectors. The decomposition structure is similar to that of Barbour, Karo\'nski and Ruci\'nski (1989) and is more general than the local dependence structure considered in Chen and Shao (2004). The error bound is of the order $d^{\frac{1}{4}} n^{-\frac{1}{2}}$, where $d$ is the dimension and $n$ is the number of summands. The dependence on $d$, namely $d^{\frac{1}{4}}$, is the best known dependence even for sums of independent and identically distributed random vectors, and the dependence on $n$, namely $n^{-\frac{1}{2}}$, is optimal. We apply our main result to a random graph example.Comment: 12 page

Study of the heavy CP-even Higgs with mass 125 GeV in two-Higgs-doublet models at the LHC and ILC

We assume that the 125 GeV Higgs discovered at the LHC is the heavy CP-even Higgs of the two-Higgs-doublet models, and examine the parameter space in the Type-I, Type-II, Lepton-specific and Flipped models allowed by the latest Higgs signal data, the relevant experimental and theoretical constraints. Further, we show the projected limits on $\tan\beta$, $\sin(\beta-\alpha)$, $Hf\bar{f}$ and $HVV$ couplings from the future measurements of the 125 GeV Higgs at the LHC and ILC, including the LHC with integrated luminosity of 300 fb$^{-1}$ (LHC-300 fb$^{-1}$) and 3000 fb$^{-1}$ (LHC-3000 fb$^{-1}$) as well as the ILC at $\sqrt{s}=250$ GeV (ILC-250 GeV), $\sqrt{s}=500$ GeV (ILC-500 GeV) and $\sqrt{s}=1000$ GeV (ILC-1000 GeV). Assuming that the future Higgs signal data have no deviation from the SM expectation, the LHC-300 fb$^{-1}$, LHC-3000 fb$^{-1}$ and ILC-1000 GeV can exclude the wrong-sign Yukawa coupling regions of the Type-II, Flipped and Lepton-specific models at the $2\sigma$ level, respectively. The future experiments at the LHC and ILC will constrain the Higgs couplings to be very close to SM values, especially for the $HVV$ coupling.Comment: 22 pages, 3 tables, 6 figures. Version accepted for publication in JHE

A simplified 2HDM with a scalar dark matter and the galactic center gamma-ray excess

Due to the strong constrain from the LUX experiment, the scalar portal dark matter can not generally explain a gamma-ray excess in the galactic center by the annihilation of dark matter into $b\bar{b}$. With the motivation of eliminating the tension, we add a scalar dark matter to the aligned two-Higgs-doublet model, and focus on a simplified scenario, which has two main characteristics: (i) The heavy CP-even Higgs is the discovered 125 GeV Higgs boson, which has the same couplings to the gauge bosons and fermions as the SM Higgs. (ii) Only the light CP-even Higgs mediates the dark matter interactions with SM particles, which has no couplings to $WW$ and $ZZ$, but the independent couplings to the up-type quarks, down-type quarks and charged leptons. We find that the tension between $_{SS\to b\bar{b}}$ and the constraint from LUX induced by the scalar portal dark matter can go away for the isospin-violating dark matter-nucleon coupling with $-1.0< f^n/f^p<0.7$, and the constraints from the Higgs search experiments and the relic density of Planck are also satisfied.Comment: 12 pages, 3 figures, 1 table; reference adde