Stabilizing the axion and a natural solution to the mu problem of supersymmetry

The axion solution to the strong CP problem makes use of a global Peccei-Quinn (PQ) U(1) symmetry which is susceptible to violations from quantum gravitational effects. We show explicitly how discrete gauge symmetries can protect the axion from such violations. PQ symmetry emerges as an accidental global symmetry from discrete gauge symmetries which are subgroups of the anomalous U(1) of string origin. We also show how the Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) axion model provides a natural solution to mu problem of supersymmetry as mu ~ M_{SUSY} ~ M^2_{PQ}/M_{Pl}.Comment: REVTex4, 4 pages. Talk presented on SUSY 2003. To appear in the Proceedings of SUSY 2003, held at the University of Arizona, Tucson, AZ, 5-10 June 2003. (Replaced version with references added.

An efficient algorithm to test forcibly-biconnectedness of graphical degree sequences

We present an algorithm to test whether a given graphical degree sequence is forcibly biconnected or not and prove its correctness. The worst case run time complexity of the algorithm is shown to be exponential but still much better than the previous basic algorithm presented in \cite{Wang2018}. We show through experimental evaluations that the algorithm is efficient on average. We also adapt Ruskey et al's classic algorithm to enumerate zero-free graphical degree sequences of length $n$ and Barnes and Savage's classic algorithm to enumerate graphical partitions of an even integer $n$ by incorporating our testing algorithm into theirs and then obtain some enumerative results about forcibly biconnected graphical degree sequences of given length $n$ and forcibly biconnected graphical partitions of given even integer $n$. Based on these enumerative results we make some conjectures such as: when $n$ is large, (1) the proportion of forcibly biconnected graphical degree sequences of length $n$ among all zero-free graphical degree sequences of length $n$ is asymptotically a constant between 0 and 1; (2) the proportion of forcibly biconnected graphical partitions of even $n$ among all forcibly connected graphical partitions of $n$ is asymptotically 0.Comment: 17 pages, 1 figure. arXiv admin note: text overlap with arXiv:1803.0067

Dixmier Trace for Toeplitz Operators on Symmetric Domains

For Toeplitz operators on bounded symmetric domains of arbitrary rank, we define a Hilbert quotient module corresponding to partitions of length $1$ and prove that it belongs to the Macaev class ${\mathcal{L}}^{n,\infty}$. We next obtain an explicit formula for the Dixmier trace of Toeplitz commutators in terms of the underlying boundary geometry

An Analytical Formulation of Power System Oscillation Frequency

This letter proposes an analytical approach to formulate the power system oscillation frequency under a large disturbance. A fact is revealed that the oscillation frequency is only the function of the oscillation amplitude when the system's model and operating condition are fixed. Case studies also show that this function is damping-insensitive and could be applied to an inter-area model of a multi-machine power system.Comment: 2 page

An Improved Algorithm for Counting Graphical Degree Sequences

We present an improved version of a previous efficient algorithm that computes the number $D(n)$ of zero-free graphical degree sequences of length $n$. A main ingredient of the improvement lies in a more efficient way to compute the function $P(N,k,l,s)$ of Barnes and Savage. We further show that the algorithm can be easily adapted to compute the $D(i)$ values for all $i\le n$ in a single run. Theoretical analysis shows that the new algorithm to compute all $D(i)$ values for $i\le n$ is a constant times faster than the previous algorithm to compute a single $D(n)$. Experimental evaluations show that the constant of improvement is about 10. We also perform simulations to estimate the asymptotic order of $D(n)$ by generating uniform random samples from the set of $E(n)$ integer partitions of fixed length $n$ with even sum and largest part less than $n$ and computing the proportion of them that are graphical degree sequences. The known numerical results of $D(n)$ for $n\le 290$ together with the known bounds of $D(n)$ and simulation results allow us to make an informed guess about its unknown asymptotic order. The techniques for the improved algorithm can be applied to compute other similar functions that count the number of graphical degree sequences of various classes of graphs of order $n$ and that all involve the function $P(N,k,l,s)$.Comment: 16 page

Schauder-type estimates for higher-order parabolic SPDEs

In this paper we consider the Cauchy problem for $2m$-order stochastic partial differential equations of parabolic type in a class of stochastic Hoelder spaces. The Hoelder estimates of solutions and their spatial derivatives up to order $2m$ are obtained, based on which the existence and uniqueness of solution is proved. An interesting finding of this paper is that the regularity of solutions relies on a coercivity condition that differs when $m$ is odd or even: the condition for odd $m$ coincides with the standard parabolicity condition in the literature for higher-order stochastic partial differential equations, while for even $m$ it depends on the integrability index $p$. The sharpness of the new-found coercivity condition is demonstrated by an example

From rules to runs: A dynamic epistemic take on imperfect information games

In the literature of game theory, the information sets of extensive form games have different interpretations, which may lead to confusions and paradoxical cases. We argue that the problem lies in the mix-up of two interpretations of the extensive form game structures: game rules or game runs which do not always coincide. In this paper, we try to separate and connect these two views by proposing a dynamic epistemic framework in which we can compute the runs step by step from the game rules plus the given assumptions of the players. We propose a modal logic to describe players' knowledge and its change during the plays, and provide a complete axiomatization. We also show that, under certain conditions, the mix-up of the rules and the runs is not harmful due to the structural similarity of the two.Comment: draft of a paper accepted by Studies in Logic (published by Sun Yat-Sen University

Smoothing methods comparison for CMB E- and B-mode separation

The anisotropies of the B-mode polarization in the cosmic microwave background radiation play a crucial role for the study of the very early Universe. However, in the real observation, the mixture of the E-mode and B-mode can be caused by the partial sky surveys, which must be separated before applied to the cosmological explanation. The separation method developed by Smith (\citealt{PhysRevD.74.083002}) has been widely adopted, where the edge of the top-hat mask should be smoothed to avoid the numerical errors. In this paper, we compare three different smoothing methods, and investigate the leakage residuals of the E-B mixture. We find that, if the less information loss is needed and the smaller region is smoothed in the analysis, the \textit{sin}- and \textit{cos}-smoothing methods are better. However, if we need a clean constructed B-mode map, the larger region around the mask edge should be smoothed. In this case, the \textit{Gaussian}-smoothing method becomes much better. In addition, we find that the leakage caused by the numerical errors in the \textit{Gaussian}-smoothing method mostly concentrates on two bands, which is quite easy to be reduced for the further E-B separations.Comment: 14 pages, 7 figures, RAA accepte

Probe CPCP-violating HγγH\gamma\gamma coupling through interferometry

The diphoton invariant mass distribution of interference between $gg\to H \to \gamma\gamma$ and $gg\to \gamma\gamma$ is almost antisymmetric around the Higgs mass $M_H$. We propose a new observable $A_{\text{int}}$ to quantify this effect, which is a ratio of a sign-reversed integral around $M_H$ ( e.g. \int^{M_H}_{M_H-5~\mbox{GeV}} -\int_{M_H}^{M_H+5~\mbox{GeV}}) and the cross section of the Higgs signal. We study $A_{\text{int}}$ both in Standard Model (SM) and new physics with various $CP$-violating $H\gamma\gamma$ couplings. The $A_{\text{int}}$ in SM could reach a value of $10\%$, while for $CP$-violating $H\gamma\gamma$ couplings $A_{\text{int}}$ could range from $10\%$ to $-10\%$, which is probable to be detected in HL-LHC experiment. The $A_{\text{int}}$ with both $CP$-violating $H\gamma\gamma$ and $Hgg$ couplings are also studied and its value range is further extended.Comment: 8 pages, 7 figures, to be published in Chinese Physics

Is polarization effect visible in leptonic SUSY searches?

On-shell effective theory approach has been widely used in search of various supersymmetric signals, in particular, gluino/squark pairs with long cascade decay chains in which complete matrix element calculations may encounter over-20 dimensional integrations. On the other hand, leptons from polarized chargino decays may show significant boost or anti-boost effect in some scenarios and simulation without polarization information may underestimate or overestimate the lepton $p_{T}$ cut efficiencies in the first place. We study the polarization effects in supersymmetry searches of multi-jets plus leptons final states. We find it justifiable for first two generations to only use on-shell effective theories. While for measurements related to third generation squarks, for instance, polarization effect of charginos from stop may reduce the lepton $p_{T}$ cut efficiencies in cross section measurements by $25\%$ when slepton contributions dominate in chargino decay or $W$ are on-shell. The signal is then underestimated if only on-shell effective theory approach is taken in simulation of signal and the real bound on squark/gluino should be more stringent.Comment: 12 pages, 4 figure