WEYL TYPE THEOREMS FOR ALGEBRIACALLY CLASS pp-wA(s,t)wA(s,t) OPERATORS

In this paper, we study Weyl type theorems for $f(T)$, where $T$ is algebraically class $p$-$wA(s, t)$ operator with $0 < p \leq 1$ and $0 < s, t, s + t \leq 1$ and $f$ is an analytic function defined on an open neighborhood of the spectrum of $T$. Also we show that if $A , B^{*} \in B(\mathcal{H})$ are class $p$-$wA(s, t)$ operators with $0 < p \leq 1$ and $0 < s, t, s + t \leq 1$,then generalized Weyl's theorem , a-Weyl's theorem, property $(w)$, property $(gw)$ and generalized a-Weyl's theorem holds for $f(d_{AB})$ for every $f \in H(\sigma(d_{AB})$, where $d_{AB}$ denote the generalized derivation $\delta_{AB}:B(\mathcal{H})\rightarrow B(\mathcal{H})$ defined by $\delta_{AB}(X)=AX-XB$ or the elementary operator $\Delta_{AB}:B(\mathcal{H})\rightarrow B(\mathcal{H})$ defined by $\Delta_{AB}(X)=AXB-X$

Generalized Fuglede-Putnam Theorem and mm-quasi-class A(k)A(k) operators

For a bounded linear operator $T$ acting on acomplex infinite dimensional Hilbert space \h, we say that $T$is $m$-quasi-class $A(k)$ operator for $k>0$ and $m$ is apositive integer (abbreviation T\in\QAkm) if$T^{*m}\left((T^*|T|^{2k}T)^{\frac{1}{k+1}}-|T|^2\right)T^m\geq0.$ The famous {\it Fuglede-Putnam theorem} asserts that: the operator equation$AX=XB$ implies $A^*X=XB^*$ when $A$ and $B$ are normal operators.In this paper, we prove that if T\in \QAkm and $S^*$ isan operator of class $A(k)$ for $k>0$. Then $TX=XS$, where X\in\bh is an injective with dense range implies $XT^*=S^*X$

Interacting Modified Variable Chaplygin Gas in Non-flat Universe

A unified model of dark energy and matter is presented using the modified variable Chaplygin gas for interacting dark energy in a non-flat universe. The two entities interact with each other non-gravitationally which involves a coupling constant. Due to dynamic interaction, the variation in this constant arises that henceforth changes the equations of state of these quantities. We have derived the effective equations of state corresponding to matter and dark energy in this interacting model. Moreover, the case of phantom energy is deduced by putting constraints on the parameters involved.Comment: 9 pages; Accepted for publication in European Physical Journal

Memorial Viewpoint for Joop van Lenthe

Contains fulltext : 283769.pdf (Publisher’s version ) (Closed access

Measurement of the cross section for isolated-photon plus jet production in pp collisions at √s=13 TeV using the ATLAS detector

The dynamics of isolated-photon production in association with a jet in proton–proton collisions at a centre-of-mass energy of 13 TeV are studied with the ATLAS detector at the LHC using a dataset with an integrated luminosity of 3.2 fb−1. Photons are required to have transverse energies above 125 GeV. Jets are identified using the anti- algorithm with radius parameter and required to have transverse momenta above 100 GeV. Measurements of isolated-photon plus jet cross sections are presented as functions of the leading-photon transverse energy, the leading-jet transverse momentum, the azimuthal angular separation between the photon and the jet, the photon–jet invariant mass and the scattering angle in the photon–jet centre-of-mass system. Tree-level plus parton-shower predictions from Sherpa and Pythia as well as next-to-leading-order QCD predictions from Jetphox and Sherpa are compared to the measurements

A search for resonances decaying into a Higgs boson and a new particle X in the XH → qqbb final state with the ATLAS detector

A search for heavy resonances decaying into a Higgs boson (H) and a new particle (X) is reported, utilizing 36.1 fb−1 of proton–proton collision data at collected during 2015 and 2016 with the ATLAS detector at the CERN Large Hadron Collider. The particle X is assumed to decay to a pair of light quarks, and the fully hadronic final state is analysed. The search considers the regime of high XH resonance masses, where the X and H bosons are both highly Lorentz-boosted and are each reconstructed using a single jet with large radius parameter. A two-dimensional phase space of XH mass versus X mass is scanned for evidence of a signal, over a range of XH resonance mass values between 1 TeV and 4 TeV, and for X particles with masses from 50 GeV to 1000 GeV. All search results are consistent with the expectations for the background due to Standard Model processes, and 95% CL upper limits are set, as a function of XH and X masses, on the production cross-section of the resonance

Combination of searches for Higgs boson pairs in pp collisions at \sqrts = 13 TeV with the ATLAS detector

This letter presents a combination of searches for Higgs boson pair production using up to 36.1 fb(-1) of proton-proton collision data at a centre-of-mass energy root s = 13 TeV recorded with the ATLAS detector at the LHC. The combination is performed using six analyses searching for Higgs boson pairs decaying into the b (b) over barb (b) over bar, b (b) over barW(+)W(-), b (b) over bar tau(+)tau(-), W+W-W+W-, b (b) over bar gamma gamma and W+W-gamma gamma final states. Results are presented for non-resonant and resonant Higgs boson pair production modes. No statistically significant excess in data above the Standard Model predictions is found. The combined observed (expected) limit at 95% confidence level on the non-resonant Higgs boson pair production cross-section is 6.9 (10) times the predicted Standard Model cross-section. Limits are also set on the ratio (kappa(lambda)) of the Higgs boson self-coupling to its Standard Model value. This ratio is constrained at 95% confidence level in observation (expectation) to -5.0 &lt; kappa(lambda) &lt; 12.0 (-5.8 &lt; kappa(lambda) &lt; 12.0). In addition, limits are set on the production of narrow scalar resonances and spin-2 Kaluza-Klein Randall-Sundrum gravitons. Exclusion regions are also provided in the parameter space of the habemus Minimal Supersymmetric Standard Model and the Electroweak Singlet Model. For complete list of authors see http://dx.doi.org/10.1016/j.physletb.2019.135103</p

Searches for lepton-flavour-violating decays of the Higgs boson in s=13\sqrt{s}=13 TeV pp\mathit{pp} collisions with the ATLAS detector

This Letter presents direct searches for lepton flavour violation in Higgs boson decays, H → eτ and H → μτ , performed with the ATLAS detector at the LHC. The searches are based on a data sample of proton–proton collisions at a centre-of-mass energy √s = 13 TeV, corresponding to an integrated luminosity of 36.1 fb−1. No significant excess is observed above the expected background from Standard Model processes. The observed (median expected) 95% confidence-level upper limits on the leptonflavour-violating branching ratios are 0.47% (0.34+0.13−0.10%) and 0.28% (0.37+0.14−0.10%) for H → eτ and H → μτ , respectively.publishedVersio

Search for flavour-changing neutral currents in processes with one top quark and a photon using 81 fb⁻¹ of pp collisions at \sqrts = 13 TeV with the ATLAS experiment

A search for flavour-changing neutral current (FCNC) events via the coupling of a top quark, a photon, and an up or charm quark is presented using 81 fb−1 of proton–proton collision data taken at a centre-of-mass energy of 13 TeV with the ATLAS detector at the LHC. Events with a photon, an electron or muon, a b-tagged jet, and missing transverse momentum are selected. A neural network based on kinematic variables differentiates between events from signal and background processes. The data are consistent with the background-only hypothesis, and limits are set on the strength of the tqγ coupling in an effective field theory. These are also interpreted as 95% CL upper limits on the cross section for FCNC tγ production via a left-handed (right-handed) tuγ coupling of 36 fb (78 fb) and on the branching ratio for t→γu of 2.8×10−5 (6.1×10−5). In addition, they are interpreted as 95% CL upper limits on the cross section for FCNC tγ production via a left-handed (right-handed) tcγ coupling of 40 fb (33 fb) and on the branching ratio for t→γc of 22×10−5 (18×10−5). © 2019 The Author(s