Local Isometric immersions of pseudo-spherical surfaces and evolution equations

The class of differential equations describing pseudo-spherical surfaces, first introduced by Chern and Tenenblat [3], is characterized by the property that to each solution of a differential equation, within the class, there corresponds a 2-dimensional Riemannian metric of curvature equal to $-1$. The class of differential equations describing pseudo-spherical surfaces carries close ties to the property of complete integrability, as manifested by the existence of infinite hierarchies of conservation laws and associated linear problems. As such, it contains many important known examples of integrable equations, like the sine-Gordon, Liouville and KdV equations. It also gives rise to many new families of integrable equations. The question we address in this paper concerns the local isometric immersion of pseudo-spherical surfaces in ${\bf E}^{3}$ from the perspective of the differential equations that give rise to the metrics. Indeed, a classical theorem in the differential geometry of surfaces states that any pseudo-spherical surface can be locally isometrically immersed in ${\bf E}^{3}$. In the case of the sine-Gordon equation, one can derive an expression for the second fundamental form of the immersion that depends only on a jet of finite order of the solution of the pde. A natural question is to know if this remarkable property extends to equations other than the sine-Gordon equation within the class of differential equations describing pseudo-spherical surfaces. In an earlier paper [11], we have shown that this property fails to hold for all other second order equations, except for those belonging to a very special class of evolution equations. In the present paper, we consider a class of evolution equations for $u(x,t)$ of order $k\geq 3$ describing pseudo-spherical surfaces. We show that whenever an isometric immersion in ${\bf E}^3$ exists, depending on a jet of finite order of $u$, then the coefficients of the second fundamental forms are functions of the independent variables $x$ and $t$ only.Comment: Fields Institute Communications, 2015, Hamiltonian PDEs and Applications, pp.N

Search for leptophobic Z ' bosons decaying into four-lepton final states in proton-proton collisions at root s=8 TeV

Peer reviewe

Search for black holes and other new phenomena in high-multiplicity final states in proton-proton collisions at root s=13 TeV

Peer reviewe

Measurements of differential production cross sections for a Z boson in association with jets in pp collisions at root s=8 TeV

Peer reviewe

Search for high-mass diphoton resonances in proton-proton collisions at 13 TeV and combination with 8 TeV search

Peer reviewe

Search for heavy resonances decaying into a vector boson and a Higgs boson in final states with charged leptons, neutrinos, and b quarks

Peer reviewe

Search for neutral resonances decaying into a Z boson and a pair of b jets or τ leptons

A search is performed for a new resonance decaying into a lighter resonance and a Z boson. Two channels are studied, targeting the decay of the lighter resonance into either a pair of oppositely charged τ leptons or a bb‾ pair. The Z boson is identified via its decays to electrons or muons. The search exploits data collected by the CMS experiment at a centre-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 19.8 fb −1 . No significant deviations are observed from the standard model expectation and limits are set on production cross sections and parameters of two-Higgs-doublet models

Search for a low-mass pseudoscalar Higgs boson produced in association with a bb⁻ pair in pp collisions at √s=8 TeV

A search is reported for a light pseudoscalar Higgs boson decaying to a pair of tau leptons, produced in association with a b (b) over bar pair, in the context of two-Higgs-doublet models. The results are based on pp collision data at a centre-of-mass energy of 8 TeV collected by the CMS experiment at the LHC and corresponding to an integrated luminosity of 19.7 fb(-1). Pseudoscalar boson masses between 25 and 80 GeV are probed. No evidence for a pseudoscalar boson is found and upper limits are set on the product of cross section and branching fraction to tau pairs between 7 and 39 pb at the 95% confidence level. This excludes pseudoscalar A bosons with masses between 25 and 80 GeV, with SM-like Higgs boson negative couplings to down-type fermions, produced in association with bb pairs, in Type II, two-Higgs-doublet models. (C) 2016 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommonnorg/licensesiby/4.01)

Phenomenological MSSM interpretation of CMS searches in pp collisions at √s=7 and 8 TeV

Searches for new physics by the CMS collaboration are interpreted in the framework of the phenomenological minimal supersymmetric standard model (pMSSM). The data samples used in this study were collected at root s = 7 and 8 TeV and have integrated luminosities of 5.0 fb(-1) and 19.5 fb(-1), respectively. A global Bayesian analysis is performed, incorporating results from a broad range of CMS supersymmetry searches, as well as constraints from other experiments. Because the pMSSM incorporates several well-motivated assumptions that reduce the 120 parameters of the MSSM to just 19 parameters defined at the electroweak scale, it is possible to assess the results of the study in a relatively straightforward way. Approximately half of the model points in a potentially accessible subspace of the pMSSM are excluded, including all pMSSM model points with a gluino mass below 500 GeV, as well as models with a squark mass less than 300 GeV. Models with chargino and neutralino masses below 200 GeV are disfavored, but no mass range of model points can be ruled out based on the analyses considered. The nonexcluded regions in the pMSSM parameter space are characterized in terms of physical processes and key observables, and implications for future searches are discussed

Forward-backward asymmetry of Drell-Yan lepton pairs in pp collisions at root s=8 TeV

Peer reviewe