The nonlinear field equation of the three-point correlation function of galaxies

Based on the field theory of density fluctuation under Newtonian gravity, we obtain analytically the nonlinear equation of 3-pt correlation function $\zeta$ of galaxies in a homogeneous, isotropic, static universe. The density fluctuations have been kept up to second order. By the Fry-Peebles ansatz and the Groth-Peebles ansatz, the equation of $\zeta$ becomes closed and differs from the Gaussian approximate equation. Using the boundary condition inferred from the data of SDSS, we obtain the solution $\zeta(r, u, \theta)$ at fixed $u=2$, which exhibits a shallow $U$-shape along the angle $\theta$ and, nevertheless, decreases monotonously along the radial $r$. We show its difference with the Gaussian solution. As a direct criterion of non-Gaussianity, the reduced $Q(r, u, \theta)$ deviates from the Gaussianity plane $Q=1$, exhibits a deeper $U$-shape along $\theta$ and varies weakly along $r$, agreeing with the observed data.Comment: 11 pages, 6 figure

Leptophilic dark matter in gauged U(1)Le−LμU(1)_{L_e-L_\mu} model in light of DAMPE cosmic ray e++e−e^+ + e^- excess

Motivated by the very recent cosmic-ray electron+positron excess observed by DAMPE collaboration, we investigate a Dirac fermion dark matter (DM) in the gauged $L_e - L_\mu$ model. DM interacts with the electron and muon via the $U(1)_{e-\mu}$ gauge boson $Z^{'}$. The model can explain the DAMPE data well. Although a non-zero DM-nucleon cross section is only generated at one loop level and there is a partial cancellation between $Z^{'}ee$ and $Z^{'}\mu\mu$ couplings, we find that a large portion of $Z^{'}$ mass is ruled out from direct DM detection limit leaving the allowed $Z^{'}$ mass to be close to two times of the DM mass. Implications for $pp \to Z^{'} \to 2\ell$ and $pp \to 2\ell + Z^{'}$ , and muon $g-2$ anomaly are also studied.Comment: Discussions added, version accepted by EPJ

Vacuum stability in stau-neutralino coannihilation in MSSM

The stau-neutralino coannihilation provides a feasible way to accommodate the observed cosmological dark matter (DM) relic density in the minimal supersymmetric standard model (MSSM). In such a coannihilation mechanism the stau mass usually has an upper bound since its annihilation rate becomes small with the increase of DM mass. Inspired by this observation, we examine the upper limit of stau mass in the parameter space with a large mixing of staus. We find that the stau pair may dominantly annihilate into dibosons and hence the upper bound on the stau mass ($\sim400$ GeV) obtained from the $f\bar{f}$ final states can be relaxed. Imposing the DM relic density constraint and requiring a long lifetime of the present vacuum, we find that the lighter stau mass can be as heavy as about 1.4 TeV for the stau maximum mixing. However, if requiring the present vacuum to survive during the thermal history of the universe, this mass limit will reduce to about 0.9 TeV. We also discuss the complementarity of vacuum stability and direct detections in probing this stau coannihilation scenario.Comment: 12 pages, 6 figure

Probing GeV-scale MSSM neutralino dark matter in collider and direct detection experiments

Given the recent constraints from the dark matter (DM) direct detections, we examine a light GeV-scale (2-30 GeV) neutralino DM in the alignment limit of the Minimal Supersymmetric Standard Model (MSSM). In this limit without decoupling, the heavy CP-even scalar $H$ plays the role of the Standard Model (SM) Higgs boson while the other scalar $h$ can be rather light so that the DM can annihilate through the $h$ resonance or into a pair of $h$ to achieve the observed relic density. With the current collider and cosmological constraints, we find that such a light neutralino DM above 6 GeV can be excluded by the XENON-1T (2017) limits while the survivied parameter space below 6 GeV can be fully covered by the future germanium-based light dark matter detections (such as CDEX), by the Higgs coupling precison measurements or by the production process $e^+e^- \to hA$ at an electron-positron collider (Higgs factory).Comment: 15 pages, 5 figures. Discussions and references added, version accepted by PL

PTab: Using the Pre-trained Language Model for Modeling Tabular Data

Tabular data is the foundation of the information age and has been extensively studied. Recent studies show that neural-based models are effective in learning contextual representation for tabular data. The learning of an effective contextual representation requires meaningful features and a large amount of data. However, current methods often fail to properly learn a contextual representation from the features without semantic information. In addition, it's intractable to enlarge the training set through mixed tabular datasets due to the difference between datasets. To address these problems, we propose a novel framework PTab, using the Pre-trained language model to model Tabular data. PTab learns a contextual representation of tabular data through a three-stage processing: Modality Transformation(MT), Masked-Language Fine-tuning(MF), and Classification Fine-tuning(CF). We initialize our model with a pre-trained Model (PTM) which contains semantic information learned from the large-scale language data. Consequently, contextual representation can be learned effectively during the fine-tuning stages. In addition, we can naturally mix the textualized tabular data to enlarge the training set to further improve representation learning. We evaluate PTab on eight popular tabular classification datasets. Experimental results show that our method has achieved a better average AUC score in supervised settings compared to the state-of-the-art baselines(e.g. XGBoost), and outperforms counterpart methods under semi-supervised settings. We present visualization results that show PTab has well instance-based interpretability

Simplified TeV leptophilic dark matter in light of DAMPE data

Using a simplified framework, we attempt to explain the recent DAMPE cosmic $e^+ + e^-$ flux excess by leptophilic Dirac fermion dark matter (LDM). The scalar ($\Phi_0$) and vector ($\Phi_1$) mediator fields connecting LDM and Standard Model particles are discussed. Under constraints of DM relic density, gamma-rays, cosmic-rays and Cosmic Microwave Background (CMB), we find that the couplings $P \otimes S$, $P \otimes P$, $V \otimes A$ and $V \otimes V$ can produce the right bump in $e^+ + e^-$ flux for a DM mass around 1.5 TeV with a natural thermal annihilation cross-section $\sim 3 \times 10^{-26} cm^3/s$ today. Among them, $V \otimes V$ coupling is tightly constrained by PandaX-II data (although LDM-nucleus scattering appears at one-loop level) and the surviving samples appear in the resonant region, $m_{\Phi_1} \simeq 2m_{\chi}$. We also study the related collider signatures, such as dilepton production $pp \to \Phi_1 \to \ell^+\ell^-$, and muon $g-2$ anomaly. Finally, we present a possible $U(1)_X$ realization for such leptophilic dark matter.Comment: discussions added, version accepted by JHE