Dirichlet uniformly well-approximated numbers

Fix an irrational number $\theta$. For a real number $\tau >0$, consider the numbers $y$ satisfying that for all large number $Q$, there exists an integer $1\leq n\leq Q$, such that $\|n\theta-y\|<Q^{-\tau}$, where $\|\cdot\|$ is the distance of a real number to its nearest integer. These numbers are called Dirichlet uniformly well-approximated numbers. For any $\tau>0$, the Haussdorff dimension of the set of these numbers is obtained and is shown to depend on the Diophantine property of $\theta$. It is also proved that with respect to $\tau$, the only possible discontinuous point of the Hausdorff dimension is $\tau=1$.Comment: 35 page

Scalar resonance at 750 GeV as composite of heavy vector-like fermions

We study a model of scalars which includes both the SM Higgs and a scalar singlet as composites of heavy vector-like fermions. The vector-like fermions are bounded by the super-strong four-fermion interactions. The scalar singlet decays to SM vector bosons through loop of heavy vector-like fermions. We show that the surprisingly large production cross section of di-photon events at 750 GeV resonance and the odd decay properties can all be explained. This model serves as a good model for both SM Higgs and a scalar resonance at 750 GeV.Comment: 12 pages, no figure, references updated, version for publicatio

LHC Phenomenology of the Type II Seesaw Mechanism: Observability of Neutral Scalars in the Nondegenerate Case

This is a sequel to our previous work on LHC phenomenology of the type II seesaw model in the nondegenerate case. In this work, we further study the pair and associated production of the neutral scalars H^0/A^0. We restrict ourselves to the so-called negative scenario characterized by the mass order M_{H^{\pm\pm}}>M_{H^\pm}>M_{H^0/A^0}, in which the H^0/A^0 production receives significant enhancement from cascade decays of the charged scalars H^{\pm\pm},~H^\pm. We consider three important signal channels---b\bar{b}\gamma\gamma, b\bar{b}\tau^+\tau^-, $b\bar{b}\ell^+\ell^-\cancel{E}_T$---and perform detailed simulations. We find that at the 14 TeV LHC with an integrated luminosity of 3000/fb, a 5\sigma mass reach of 151, 150, and 180 GeV, respectively, is possible in the three channels from the pure Drell-Yan H^0A^0 production, while the cascade-decay-enhanced H^0/A^0 production can push the mass limit further to 164, 177, and 200 GeV. The neutral scalars in the negative scenario are thus accessible at LHC run II.Comment: v1: 32 pages, 17 figures, 3 tables. v2: added 2 refs (2nd in [61] and [66]), revised Acknowledgments, and corrected grammatical errors according to proofs; no other change

LHC Phenomenology of Type II Seesaw: Nondegenerate Case

In this paper, we thoroughly investigate the LHC phenomenology of the type II seesaw mechanism for neutrino masses in the nondegenerate case where the triplet scalars of various charge ($H^{\pm\pm}, H^\pm, H^0, A^0$) have different masses. Compared with the degenerate case, the cascade decays of scalars lead to many new, interesting signal channels. In the positive scenario where $M_{H^{\pm\pm}}<M_{H^\pm}<M_{H^0/A^0}$, the four-lepton signal is still the most promising discovery channel for the doubly-charged scalars $H^{\pm\pm}$. The five-lepton signal is crucial to probe the mass spectrum of the scalars, for which, for example, a $5\sigma$ reach at 14 TeV LHC for $M_{H^{\pm}}=430 GeV$ with $M_{H^{\pm\pm}}=400 GeV$ requires an integrated luminosity of 76/fb. And the six-lepton signal can be used to probe the neutral scalars $H^0/A^0$, which are usually hard to detect in the degenerate case. In the negative scenario where $M_{H^{\pm\pm}}>M_{H^\pm}>M_{H^0/A^0}$, the detection of $H^{\pm\pm}$ is more challenging, when the cascade decay $H^{\pm\pm}\to H^{\pm}W^{\pm*}$ is dominant. The most important channel is the associated $H^{\pm}H^0/A^0$ production in the final state $\ell^\pm\cancel{E}_Tb\bar{b}b\bar{b}$, which requires a luminosity of 109/fb for a $5\sigma$ discovery, while the final state $\ell^\pm\cancel{E}_Tb\bar{b}\tau^+\tau^-$ is less promising. Moreover, the associated $H^0A^0$ production can give same signals as the standard model Higgs pair production. With a much larger cross section, the $H^0A^0$ production in the final state $b\bar{b}\tau^+\tau^-$ could reach $3\sigma$ significance at 14 TeV LHC with a luminosity of 300/fb. In summary, with an integrated luminosity of order 500/fb, the triplet scalars can be fully reconstructed at 14 TeV LHC in the negative scenario.Comment: 41 pages, 20 figures, 7 tables. Version 2 accepted by PRD. 41 pages, 18 figures. Main changes are, (1) rewording in secs III and IV, removing 2 figs and quoting ref [34]; (2) a paragraph added before eq (10) to clarify constraints from electroweak precision data; (3) a paper added to ref [11]. No changes in result

Higgs production at future e+e−e^+e^- colliders in the Georgi-Machacek model

We study how the dominant single and double SM-like Higgs ($h$) production at future $e^+e^-$ colliders is modified in the Georgi-Machacek (GM) model. On imposing theoretical, indirect and direct constraints, significant deviations of $h$-couplings from their SM values are still possible; for instance, the Higgs-gauge coupling coupling can be corrected by a factor $\kappa_{hVV}\in[0.93,1.15]$ in the allowed parameter space. For the Higgs-strahlung $e^+e^-\to hZ$ and vector boson fusion processes $e^+e^-\to h\nu\bar{\nu},~he^+e^-$, the cross section could increase by $32\%$ or decrease by $13\%$. In the case of associated production with a top quark pair $e^+e^-\to ht\bar{t}$, the cross section can be enhanced up to several times when the custodial triplet scalar $H_3^0$ is resonantly produced. In the meanwhile, the double Higgs production $e^+e^-\to hhZ~(hh\nu\bar{\nu})$ can be maximally enhanced by one order of magnitude at the resonant $H_{1,3}^0$ production. We also include exclusion limits expected from future LHC runs at higher energy and luminosity and discuss their further constraints on the relevant model parameters. We find that the GM model can result in likely measurable deviations of Higgs production from the SM at future $e^+e^-$ colliders.Comment: 31 pages, 17 figures, published in JHE

Metal contamination of soils and crops affected by the Chenzhou lead/zinc mine spill (Hunan, China)

In 1985, the collapse of the tailing dam in Chenzhou lead/zinc mine (Hunan, southern China) led to the spread of mining waste spills on the farmland along the Dong River. After the accident, an urgent soil cleaning up was carried out in some places. Seventeen years later, cereal (rice, maize, and sorghum), pulses (soybean, Adzuki bean, mung bean and peanut), vegetables (ipomoea, capsicum, taro and string bean) and the rooted soils were sampled at four sites: (1) the mining area (SZY), (2) the area still covered with the mining tailing spills (GYB), (3) the cleaned area from mining tailing spills (JTC), and (4) a background site (REF). Metal concentrations in the crops and soils were analyzed to evaluate the long-term effects of the spilled waste on the soil and the potential human exposure through food chains. The results showed that the physical–chemical properties of the soils obviously changed due to the different farming styles used by each individual farmer. Leaching effects and plant extraction of metals from some soils were quite weak. Certain soils were still heavily polluted with As, Cd, Zn, Pb and Cu. The contamination levels were in the order of GYB>SZY>JTC showing that the clean-up treatment was effective. The maximum allowable concentration (MAC) levels for Chinese agricultural soils were still highly exceeded, particularly for As and Cd (followed by Zn, Pb and Cu), with mean concentrations of 709 and 7.6 mg kg−1, respectively. These concentrations exceed the MAC levels by 24 times for As and 13 times for Cd at GYB. Generally, the edible leaves or stems of crops were more heavily contaminated than seeds or fruits. Ipomoea was the most severely contaminated crop. The concentrations of Cd and Pb were 3.30 and 76.9 mg kg−1 in ipomoea leaves at GYB, which exceeded the maximum permit levels (0.5 mg kg−1 for Cd and 9 mg kg−1 for Pb) by 6.6 and 8.5 times, respectively. Taro (+skin) could accumulate high concentrations of Zn and Cd in the edible stem, and rice and capsicum had high Cd concentration in the edible parts. However, the toxic element concentrations in maize, sorghum, Adzuki bean, soybean and mung bean remained lower than the threshold levels. The bio-accumulation factors (BAFs) of crops were in the order: Cd>Zn>Cu>Pb>As. BAF was typically lower in the edible seeds or fruits than in stems and leaves. The accumulation effect strongly depends on the crop's physiological properties, the mobility, of the metals, and the availability of metals in soils but not entirely on the total element concentrations in the soils. Even so, the estimated daily intake amount of Cu, Zn, Cd, and Pb from the crops grown in the affected three sites and arsenic at SZY and GYB exceeded the RDA (Recommended dietary allowance) levels. Subsequently, the crops grown in Chenzhou Pb/Zn mine waste affected area might have a hazardous effect on the consumer's health. This area still needs effective measures to cure the As, Cd, Pb, Zn and Cu contamination

Listen-and-Talk: Full-duplex Cognitive Radio Networks

In traditional cognitive radio networks, secondary users (SUs) typically access the spectrum of primary users (PUs) by a two-stage "listen-before-talk" (LBT) protocol, i.e., SUs sense the spectrum holes in the first stage before transmit in the second stage. In this paper, we propose a novel "listen-and-talk" (LAT) protocol with the help of the full-duplex (FD) technique that allows SUs to simultaneously sense and access the vacant spectrum. Analysis of sensing performance and SU's throughput are given for the proposed LAT protocol. And we find that due to self-interference caused by FD, increasing transmitting power of SUs does not always benefit to SU's throughput, which implies the existence of a power-throughput tradeoff. Besides, though the LAT protocol suffers from self-interference, it allows longer transmission time, while the performance of the traditional LBT protocol is limited by channel spatial correction and relatively shorter transmission period. To this end, we also present an adaptive scheme to improve SUs' throughput by switching between the LAT and LBT protocols. Numerical results are provided to verify the proposed methods and the theoretical results.Comment: in proceeding of IEEE Globecom 201

Full-duplex MAC Protocol Design and Analysis

The idea of in-band full-duplex (FD) communications revives in recent years owing to the significant progress in the self-interference cancellation and hardware design techniques, offering the potential to double spectral efficiency. The adaptations in upper layers are highly demanded in the design of FD communication systems. In this letter, we propose a novel medium access control (MAC) using FD techniques that allows transmitters to monitor the channel usage while transmitting, and backoff as soon as collision happens. Analytical saturation throughput of the FD-MAC protocol is derived with the consideration of imperfect sensing brought by residual self- interference (RSI) in the PHY layer. Both analytical and simulation results indicate that the normalized saturation throughput of the proposed FD-MAC can significantly outperforms conventional CSMA/CA under various network conditions