Second Stop and Sbottom Searches with a Stealth Stop

The top squarks (stops) may be the most wanted particles after the Higgs boson discovery. The searches for the lightest stop have put strong constraints on its mass. However, there is still a search gap in the low mass region if the spectrum of the stop and the lightest neutralino is compressed. In that case, it may be easier to look for the second stop since naturalness requires both stops to be close to the weak scale. The current experimental searches for the second stop are based on the simplified model approach with the decay modes $\tilde{t}_2 \to \tilde{t}_1 Z$ and $\tilde{t}_2 \to \tilde{t}_1 h$. However, in a realistic supersymmetric spectrum there is always a sbottom lighter than the second stop, hence the decay patterns are usually more complicated than the simplified model assumptions. In particular, there are often large branching ratios of the decays $\tilde{t}_2 \to \tilde{b}_1 W$ and $\tilde{b}_1 \to \tilde{t}_1 W$ as long as they are open. The decay chains can be even more complex if there are intermediate states of additional charginos and neutralinos in the decays. By studying several MSSM benchmark models at the 14 TeV LHC, we point out the importance of the multi-$W$ final states in the second stop and the sbottom searches, such as the same-sign dilepton and multilepton signals, aside from the traditional search modes. The observed same-sign dilepton excesses at LHC Run 1 and Run 2 may be explained by some of our benchmark models. We also suggest that the vector boson tagging and a new kinematic variable may help to suppress the backgrounds and increase the signal significance for some search channels. Due to the complex decay patterns and lack of the dominant decay channels, the best reaches likely require a combination of various search channels at the LHC for the second stop and the lightest sbottom.Comment: 46 pages, 9 figures, updated experimental constraints and benchmark points after the ICHEP2016 data, published in JHE

Constraining the Compressed Top Squark and Chargino along the W Corridor

Studying superpartner production together with a hard initial state radiation (ISR) jet has been a useful strategy for searches of supersymmetry with a compressed spectrum at the Large Hadron Collider (LHC). In the case of the top squark (stop), the ratio of the missing transverse momentum from the lightest neutralinos and the ISR momentum, defined as $\bar{R}_M$, turns out to be an effective variable to distinguish the signal from the backgrounds. It has helped to exclude the stop mass below 590 GeV along the top corridor where $m_{\tilde{t}} - m_{\tilde{\chi}_1^0} \approx m_t$. On the other hand, the current experimental limit is still rather weak in the $W$ corridor where $m_{\tilde{t}} - m_{\tilde{\chi}_1^0} \approx m_W +m_b$. In this work we extend this strategy to the parameter region around the $W$ corridor by considering the one lepton final state. In this case the kinematic constraints are insufficient to completely determine the neutrino momentum which is required to calculate $\bar{R}_M$. However, the minimum value of $\bar{R}_M$ consistent with the kinematic constraints still provides a useful discriminating variable, allowing the exclusion reach of the stop mass to be extended to $\sim 550$ GeV based on the current 36 fb$^{-1}$ LHC data. The same method can also be applied to the chargino search with $m_{\tilde{\chi}_1^\pm} -m_{\tilde{\chi}_1^0} \approx m_W$ because the analysis does not rely on $b$ jets. If no excess is present in the current data, a chargino mass of 300 GeV along the $W$ corridor can be excluded, beyond the limit obtained from the multilepton search.Comment: 29 pages,8 figure

On the B-twisted topological sigma model and Calabi-Yau geometry

We provide a rigorous perturbative quantization of the B-twisted topological sigma model via a first order quantum field theory on derived mapping space in the formal neighborhood of constant maps. We prove that the first Chern class of the target manifold is the obstruction to the quantization via Batalin-Vilkovisky formalism. When the first Chern class vanishes, i.e. on Calabi-Yau manifolds, the factorization algebra of observables gives rise to the expected topological correlation functions in the B-model. We explain a twisting procedure to generalize to the Landau-Ginzburg case, and show that the resulting topological correlations coincide with Vafa's residue formula.Comment: 73 pages. Comments welcom

Implicit Asymptotic Preserving Method for Linear Transport Equations

The computation of the radiative transfer equation is expensive mainly due to two stiff terms: the transport term and the collision operator. The stiffness in the former comes from the fact that particles (such as photons) travels at the speed of light, while that in the latter is due to the strong scattering in the diffusive regime. We study the fully implicit scheme for this equation to account for the stiffness. The main challenge in the implicit treatment is the coupling between the spacial and velocity coordinates that requires the large size of the to-be-inverted matrix, which is also ill-conditioned and not necessarily symmetric. Our main idea is to utilize the spectral structure of the ill-conditioned matrix to construct a pre-conditioner, which, along with an exquisite split of the spatial and angular dependence, significantly improve the condition number and allows matrix-free treatment. We also design a fast solver to compute this pre-conditioner explicitly in advance. Meanwhile, we reformulate the system via an even-odd parity, which results in a symmetric and positive definite matrix that can be inverted using conjugate gradient method. This idea can also be implemented to the original non-symmetric system whose inversion is solved by GMRES. A qualitative comparison with the conventional methods, including Krylov iterative method pre-conditioned with diffusive synthetic acceleration and asymptotic preserving scheme via even-odd decomposition, is also discussed

On the Number of Zeros and Poles of Dirichlet Series

This paper investigates lower bounds on the number of zeros and poles of a general Dirichlet series in a disk of radius $r$ and gives, as a consequence, an affirmative answer to an open problem of Bombieri and Perelli on the bound. Applications will also be given to Picard type theorems, global estimates on the symmetric difference of zeros, and uniqueness problems for Dirichlet series.Comment: 24 page

Response to "Reply to comment on 'Divergent and Ultrahigh Thermal Conductivity in Millimeter-Long Nanotubes'"

More than one year ago, Prof. Chih-Wei Chang and the co-authors published "Divergent and Ultrahigh Thermal Conductivity in Millimeter-Long Nanotubes" in PRL and we submitted a comment. After some while we received Prof. Chang et al.'s reply, which is almost the same as their arXiv preprint, and responded to the reply promptly. On the request of some readers, I personally post here the detailed response to "Reply to comment on 'Divergent and Ultrahigh Thermal Conductivity in Millimeter-Long Nanotubes'"

A characterization of rational functions

We give an elementary characterization of rational functions among meromorphic functions in the complex plane

Shuffle product formulas of multiple zeta values

Using the combinatorial description of shuffle product, we prove or reformulate several shuffle product formulas of multiple zeta values, including a general formula of the shuffle product of two multiple zeta values, some restricted shuffle product formulas of the product of two multiple zeta values, and a restricted shuffle product formula of the product of $n$ multiple zeta values.Comment: 28 page

WENO interpolation-based and upwind-biased schemes with free-stream preservation

Based on the understandings regarding linear upwind schemes with flux splitting to achieve free-stream preservation (Q. Li, etc. Commun. Comput. Phys., 22 (2017) 64-94), a series of WENO interpolation-based and upwind-biased nonlinear schemes are proposed in this study. By means of engagement of fluxes on midpoints, the nonlinearity of schemes is introduced through WENO interpolations, and upwind-biased features are acquired through the choice of dependent grid stencil. Regarding the third- and fifth-order versions, schemes with one and two midpoints are devised and carefully tested. With the integration of the piecewise-polynomial mapping function methods (Q. Li, etc. Commun. Comput. Phys. 18 (2015) 1417-1444), the proposed schemes are found to achieve the designed orders and free-stream preservation property. In 1-D Sod and Shu-Osher problems, all schemes succeed in yielding well predictions. In 2-D cases, the vortex preservation, supersonic inviscid flow around cylinder at M=4, Riemann problem and Shock-vortex interaction problems are tested. In each problem, two types of grids are employed, i.e. the uniformed/smooth grids and the randomized/partially-randomized grids. On the latter, the shock wave and complex flow structures are located/partially located. All schemes fulfill computations in uniformed/smooth grids with satisfactory results. On randomized grids, all schemes accomplish computations and yield reasonable results except the third-order one with two midpoints engaged fails in Riemann problem and shock-vortex interaction problem. Overall speaking, the proposed schemes manifest the capability to solve problems on grids with bad quality, and therefore indicate their potential in engineering applications

Ensemble Kalman Inversion: mean-field limit and convergence analysis

Ensemble Kalman Inversion (EKI) has been a very popular algorithm used in Bayesian inverse problems. It samples particles from a prior distribution, and introduces a motion to move the particles around in pseudo-time. As the pseudo-time goes to infinity, the method finds the minimizer of the objective function, and when the pseudo-time stops at $1$, the ensemble distribution of the particles resembles, in some sense, the posterior distribution in the linear setting. The ideas trace back further to Ensemble Kalman Filter and the associated analysis, but to today, when viewed as a sampling method, why EKI works, and in what sense with what rate the method converges is still largely unknown. In this paper, we analyze the continuous version of EKI, a coupled SDE system, and prove the mean field limit of this SDE system. In particular, we will show that 1. as the number of particles goes to infinity, the empirical measure of particles following SDE converges to the solution to a Fokker-Planck equation in Wasserstein 2-distance with an optimal rate, for both linear and weakly nonlinear case; 2. the solution to the Fokker-Planck equation reconstructs the target distribution in finite time in the linear case