Atmospheric Chemistry for Astrophysicists: A Self-consistent Formalism and Analytical Solutions for Arbitrary C/O

We present a self-consistent formalism for computing and understanding the atmospheric chemistry of exoplanets from the viewpoint of an astrophysicist. Starting from the first law of thermodynamics, we demonstrate that the van't Hoff equation (which describes the equilibrium constant), Arrhenius equation (which describes the rate coefficients) and procedures associated with the Gibbs free energy (minimisation, rescaling) have a common physical and mathematical origin. We address an ambiguity associated with the equilibrium constant, which is used to relate the forward and reverse rate coefficients, and restate its two definitions. By necessity, one of the equilibrium constants must be dimensionless and equate to an exponential function involving the Gibbs free energy, while the other is a ratio of rate coefficients and must therefore possess physical units. We demonstrate that the Arrhenius equation takes on a functional form that is more general than previously stated without recourse to tagging on ad hoc functional forms. Finally, we derive analytical models of chemical systems, in equilibrium, with carbon, hydrogen and oxygen. We include acetylene and are able to reproduce several key trends, versus temperature and carbon-to-oxygen ratio, published in the literature. The rich variety of behavior that mixing ratios exhibit as a function of the carbon-to-oxygen ratio is merely the outcome of stoichiometric book-keeping and not the direct consequence of temperature or pressure variations.Comment: Accepted by ApJ. 9 pages, 4 figure

Explanation of the ATLAS Z-peaked excess by squark pair production in the NMSSM

The ATLAS collaboration recently reported a $3\sigma$ excess in the leptonic-$Z+jets+E_{T}^{miss}$ channel. We intend to interpret this excess by squark pair production in the Next-to-Minimal Supersymmetric Standard Model (NMSSM). The decay chain we employ is $\tilde{q} \to q \tilde{\chi}_2^0 \to q \tilde{\chi}_1^0 Z$, where $\tilde{\chi}_1^0$ and $\tilde{\chi}_2^0$ denote the lightest and the next-to-lightest neutralinos with singlino and bino as their dominant components respectively. Our simulations indicate that after considering the constraints from the ATLAS searches for $jets + E_{T}^{miss}$ signal the central value of the excess can be obtained for $m_{\tilde{q}} \lesssim 1.2 {\rm TeV}$, and if the constraint from the CMS on-$Z$ search is further considered, more than 10 signal events are still attainable for $m_{\tilde{q}} \lesssim 750 {\rm GeV}$. Compared with the interpretation by gluino pair production, the squark explanation allows for a significantly wider range of $m_{\tilde{q}}$ as well as a less compressed SUSY mass spectrum. We also show that the squark explanation will be readily tested at the initial stage of the 14 TeV LHC.Comment: 19 pages, 4 figure

Explanation of the ATLAS Z-peaked excess in the NMSSM

Recently the ATLAS collaboration reported a $3\sigma$ excess in the leptonic-$Z+jets+E_{T}^{miss}$ channel. This may be interpreted in the Next-to-Minimal Supersymmetric Standard Model (NMSSM) by gluino pair production with the decay chain $\tilde{g} \to q \bar{q} \tilde{\chi}_2^0 \to q \bar{q} Z \tilde{\chi}_1^0$, where $\tilde{\chi}_1^0$ and $\tilde{\chi}_2^0$ denote the lightest and the next-to-lightest neutralinos with singlino and bino as their dominant components respectively. After exploring the relevant parameter space of the NMSSM by considering the constraints from the ATLAS searches for $jets + E_{T}^{miss}$ signals, we conclude that the NMSSM is able to explain the excess at $1 \sigma$ level with the number of the signal events reaching its measured central value in optimal cases, and the best explanation comes from a compressed spectrum such as $m_{\tilde{g}} \simeq 650 {\rm GeV}$, $m_{\tilde{\chi}_2^0} \simeq 565 {\rm GeV}$ and $m_{\tilde{\chi}_1^0} \simeq 465 {\rm GeV}$. We also check the consistency of the ATLAS results with the null result of the CMS on-$Z$ search. We find that under the CMS limits at $95\%$ C.L., the event number of the ATLAS on-$Z$ signal can still reach 11 in our scenario, which is about $1.2 \sigma$ away from the measured central value.Comment: 18 pages, 2 figure

Interpreting the galactic center gamma-ray excess in the NMSSM

In the Next-to-Minimal Supersymmetric Standard Model (NMSSM), all singlet-dominated particles including one neutralino, one CP-odd Higgs boson and one CP-even Higgs boson can be simultaneously lighter than about 100 GeV. Consequently, dark matter (DM) in the NMSSM can annihilate into multiple final states to explain the galactic center gamma-ray excess (GCE). In this work we take into account the foreground and background uncertainties for the GCE and investigate these explanations. We carry out a sophisticated scan over the NMSSM parameter space by considering various experimental constraints such as the Higgs data, $B$-physics observables, DM relic desnity, LUX experiment and the dSphs constraints. Then for each surviving parameter point we perform a fit to the GCE spectrum by using the correlation matrix that incorporates both the statistical and systematic uncertainties of the measured excess. After examining the properties of the obtained GCE solutions, we conclude that the GCE can be well explained by the pure annihilations $\tilde{\chi}_1^0 \tilde{\chi}_1^0 \to b \bar{b}$ and $\tilde{\chi}_1^0 \tilde{\chi}_1^0 \to A_1 H_i$ with $A_1$ being the lighter singlet-dominated CP-odd Higgs boson and $H_i$ denoting the singlet-dominated CP-even Higgs boson or SM-like Higgs boson, and it can also be explained by the mixed annihilation $\tilde{\chi}_1^0 \tilde{\chi}_1^0 \to W^+ W^-, A_1 H_1$. Among these annihilation channels, $\tilde{\chi}_1^0 \tilde{\chi}_1^0 \to A_1 H_i$ can provide the best interpretation with the corresponding $p$-value reaching 0.55. We also discuss to what extent the future DM direct detection experiments can explore the GCE solutions and conclude that the XENON-1T experiment is very promising in testing nearly all the solutions.Comment: 31 pages, 7 figure

Pair Production of a 125 GeV Higgs Boson in MSSM and NMSSM at the LHC

In light of the recent LHC Higgs search data, we investigate the pair production of a SM-like Higgs boson around 125 GeV in the MSSM and NMSSM. We first scan the parameter space of each model by considering various experimental constraints, and then calculate the Higgs pair production rate in the allowed parameter space. We find that in most cases the dominant contribution to the Higgs pair production comes from the gluon fusion process and the production rate can be greatly enhanced, maximally 10 times larger than the SM prediction (even for a TeV-scale stop the production rate can still be enhanced by a factor of 1.3). We also calculate the chi-square value with the current Higgs data and find that in the most favored parameter region the production rate is enhanced by a factor of 1.45 in the MSSM, while in the NMSSM the production rate can be enhanced or suppressed (\sigma_{SUSY}/\sigma_{SM} varies from 0.7 to 2.4).Comment: 15 pages, 5 figure

The Status of RMB Financial Products of Commercial Banks in China: From the Perspective of Homogeneity

With the rapid development of commercial bank financial services in China, some problems arise in the process. This paper focuses on the widely concerned issue of homogeneity, basing on the classification of products, and takes the data from 2007 to 2013 about RMB financial products issued by 17 commercial banks as the sample to analyze the product type, minimum amount, investment period and returns of these products. Reasons for homogeneity will be discussed and recommendations in the aspects of customers, products, marketing channels and financial managers will be made to solve this problem

Interpreting the 750 GeV diphoton excess by the singlet extension of the Manohar-Wise Model

The evidence of a new scalar particle $X$ from the 750 GeV diphoton excess, and the absence of any other signal of new physics at the LHC so far suggest the existence of new colored scalars, which may be moderately light and thus can induce sizable $X g g$ and $X \gamma \gamma$ couplings without resorting to very strong interactions. Motivated by this speculation, we extend the Manohar-Wise model by adding one gauge singlet scalar field. The resulting theory then predicts one singlet dominated scalar $\phi$ as well as three kinds of color-octet scalars, which can mediate through loops the $\phi gg$ and $\phi \gamma \gamma$ interactions. After fitting the model to the diphoton data at the LHC, we find that in reasonable parameter regions the excess can be explained at $1\sigma$ level by the process $g g \to \phi \to \gamma \gamma$, and the best points predict the central value of the excess rate with $\chi_{min}^2=2.32$, which corresponds to a $p$-value of $0.68$. We also consider the constraints from various LHC Run I signals, and we conclude that, although these constraints are powerful in excluding the parameter space of the model, the best points are still experimentally allowed.Comment: 19 pages, 3 figure