Lateral critical Casimir force in 2D Ising strip with inhomogeneous walls

We analyze the lateral critical Casimir force acting between two planar, chemically inhomogeneous walls confining an infinite 2D Ising strip of width $M$. The inhomogeneity of each of the walls has size $N_1$; they are shifted by the distance $L$ along the strip. Using the exact diagonalization of the transfer matrix, we calculate the lateral critical Casimir force and discuss its properties, in particular its scaling close to the 2D bulk critical point, as a function of temperature, surface magnetic field, and the geometric parameters $M$, $N_1$, $L$. We determine the magnetization profiles which display the formation of the bridge joining the inhomogeneities on the walls and establish the relation between the characteristic properties of the lateral Casimir force and magnetization morphologies. We check numerically that breaking of the bridge is related to the inflection point of the lateral force.Comment: 5 pages, 6 figure

Lateral critical Casimir force in two-dimensional inhomogeneous Ising strip. Exact results

We consider two-dimensional Ising strip bounded by two planar, inhomogeneous walls. The inhomogeneity of each wall is modeled by a magnetic field acting on surface spins. It is equal to $+h_1$ except for a group of $N_1$ sites where it is equal to $-h_1$. The inhomogeneities of the upper and lower wall are shifted with respect to each other by a lateral distance $L$. Using exact diagonalization of the transfer matrix, we study both the lateral and normal critical Casimir forces as well as magnetization profiles for a wide range of temperatures and system parameters. The lateral critical Casimir force tends to reduce the shift between the inhomogeneities, and the excess normal force is attractive. Upon increasing the shift $L$ we observe, depending on the temperature, three different scenarios of breaking of the capillary bridge of negative magnetization connecting the inhomogeneities of the walls across the strip. As long as there exists a capillary bridge in the system, the magnitude of the excess total critical Casimir force is almost constant, with its direction depending on $L$. By investigating the bridge morphologies we have found a relation between the point at which the bridge breaks and the inflection point of the force. We provide a simple argument that some of the properties reported here should also hold for a whole range of different models of the strip with the same type of inhomogeneity

Light neutral CP-even Higgs boson within Next-to-Minimal Supersymmetric Standard model (NMSSM) at the Large Hadron electron Collider (LHeC)

We analyze the prospects of observing the light CP-even neutral Higgs bosons ($h_1$) in their decays into $b \bar b$ quarks, in the neutral and charged current production processes $e h_1 q$ and $\nu h_1 q$ at the upcoming LHeC, with $\sqrt s \approx 1.296$ TeV. Assuming that the intermediate Higgs boson ($h_2$) is Standard Model (SM)-like, we study the Higgs production within the framework of NMSSM. We consider the constraints from Dark-matter, Sparticle masses, and the Higgs boson data. The signal in our analysis can be classified as three jets, with electron (missing energy)coming from the neutral (charged) current interaction. We demand that the number of b-tagged jets in the central rapidity region be greater or equal to two. The remaining jet is tagged in the forward regions. With this forward jet and two $b$-tagged jets in the central region, we reconstructed three jets invariant masses. Applying some lower limits on these invariant masses turns out to be an essential criterion to enhance the signal--to--background rates, with slightly different sets of kinematical selections in the two different channels. We consider almost all reducible and irreducible SM background processes. We find that the non-SM like Higgs boson, $h_1$, would be accessible in some of the NMSSM benchmark points, at approximately 0.4$\sigma$ (2.5$\sigma$) level in the $e$+3j channel up to Higgs boson masses of 75 GeV and in the $E\!\!\!\!/_T$+3j channel could be discovered with 1.7$\sigma$ (2.4$\sigma$) level up to Higgs boson masses of 88 GeV with 100 fb$^{-1}$ of data in a simple cut-based (with optimization) selection. With ten times more data accumulation at the end of the LHeC run and using optimization, one can have 5$\sigma$ discovery in the electron (missing energy) channel up to 85 (more than 90) GeV.Comment: 38 pages, 27 figures, version to be appeared in Phys.Rev.