Two Higgs doublet models at future colliders

The two Higgs doublet model (THDM) is a simple extension of the standard model, which can provide a low energy effective description of more fundamental theories. The model contains additional Higgs bosons, and predicts rich phenomenology especially due to the variation of Yukawa interactions. Under imposing a softly broken discrete symmetry, there are four independent types of Yukawa interactions in THDMs. In this review, we briefly summarize bounds from current experimental data on THDMs and implications at future collider experiments. We pay special attention to the collider phenomenology of the Type-X (lepton specific) THDM, and also discuss recent progress for $\tan\beta$ determination in THDMs.Comment: 7 pages, 6 eps files. Talk given at Toyama International Workshop on Higgs as a Probe of New Physics 2013, Toyama, Japan, February 13-16, 201

The quadratic character of 1+\sqrt{2} and an elliptic curve

When p is congruent to 1 mod 8, we have a criterion of the quadratic character of 1+\sqrt{2}, which is related to the class number of \Q(\sqrt{-p}). In this paper, we obtain a similar criterion using an elliptic curve, which contrasts to the proof using algebraic number theory for the old one.Comment: 4 page

Primality tests for Fermat numbers and 2^(2k+1)\pm2^(k+1)+1

Robert Denomme and Gordan Savin made a primality test for Fermat numbers 2^(2^k)+1 using elliptic curves. We propose another primality test using elliptic curves for Fermat numbers and also give primality tests for integers of the form 2^(2k+1)\pm2^(k+1)+1.Comment: 11 page

Primality tests for 2^kn-1 using elliptic curves

We propose some primality tests for 2^kn-1, where k, n in Z, k>= 2 and n odd. There are several tests depending on how big n is. These tests are proved using properties of elliptic curves. Essentially, the new primality tests are the elliptic curve version of the Lucas-Lehmer-Riesel primality test. Note:An anonymous referee suggested that Benedict H. Gross already proved the same result about a primality test for Mersenne primes using elliptic curve.Comment: 8 page

On the finiteness of Carmichael numbers with Fermat factors and L=2αP2L=2^{\alpha}P^2

Let $m$ be a Carmichael number and let $L$ be the least common multiple of $p-1$, where $p$ runs over the prime factors of $m$. We determine all the Carmichael numbers $m$ with a Fermat prime factor such that $L=2^{\alpha}P^2$, where $k\in \mathbb{N}$ and $P$ is an odd prime number. There are eleven such Carmichael numbers.Comment: 42 page

On compositeness of special types of integers

In paper on a classification of Lehmer triples, Juricevic conjectured that there are infinitely many primes of special form. We disprove one of his conjectures and consider the other one.Comment: 6 page

Optimal Quantization of Signals for System Identification

In this paper, we examine the optimal quantization of signals for system identification. We deal with memoryless quantization for the output signals and derive the optimal quantization schemes. The objective functions are the errors of least squares parameter estimation subject to a constraint on the number of subsections of the quantized signals or the expectation of the optimal code length for either high or low resolution. In the high-resolution case, the optimal quantizer is found by solving Euler-Lagrange's equations and the solutions are simple functions of the probability densities of the regressor vector. In order to clarify the minute structure of the quantization, the optimal quantizer in the low resolution case is found by solving recursively a minimization of a one-dimensional rational function. The solution has the property that it is coarse near the origin of its input and becomes dense away from the origin in the usual situation. Finally the required quantity of data to decrease the total parameter estimation error, caused by quantization and noise, is discussed.Comment: 33 page

Is the Infrared Background Excess Explained by the Isotropic Zodiacal Light from the Outer Solar System?

This paper investigates whether an isotropic zodiacal light from the outer Solar system can account for the detected background excess in near-infrared. Assuming that interplanetary dust particles are distributed in a thin spherical shell at the outer Solar system (>200 AU), thermal emission from such cold (<30 K) dust in the shell has a peak at far-infrared (~100 microns). By comparing the calculated thermal emission from the dust shell with the observed background emissions at far-infrared, permissible dust amount in the outer Solar system is obtained. Even if the maximum dust amount is assumed, the isotropic zodiacal light as the reflected sunlight from the dust shell at the outer Solar system cannot explain the detected background excess at near-infrared.Comment: 6 pages, 2 figures, accepted by PAS

The number of points on an elliptic curve with square x-coordinates

Let K be a finite field. We know that a half of elements of K* is a square. So it is natural to ask how many of them appear as x-coordinate of points on an elliptic curve over K. We consider a specific class of elliptic curves over finite fields and show that a half of x-coordinate on an elliptic curve is a square. This result generalizes my old paper posted 30 Dec 2009.Comment: 2 pages, this result generalizes my old paper posted 30 Dec 2009. Comments are welcom

Lepton flavor violation in Higgs boson decays

We discuss lepton flavor violation (LFV) associated with tau leptons in the framework of the two-Higgs-doublet model. Current data for rare tau decays provide substantial upper limits on the LFV Yukawa couplings in the large $\tan\beta$ region where $\tan\beta$ is the ratio of vacuum expectation values of the two Higgs doublets. We show that measuring the LFV Higgs boson decays $h \to \tau^\pm \mu^\mp$ at future colliders can be useful to further constrain the LFV couplings especially in the relatively small $\tan\beta$ region.Comment: 3 pages, 1 figure. Proceeding for "Summer Institute 2005", August 11-18, 2005, Fuji-Yoshida, Japa