Vertex Coupling Research Articles

Quantum graphs with vertices of a preferred orientation

Motivated by a recent application of quantum graphs to model the anomalous Hall effect we discuss quantum graphs the vertices of which exhibit a preferred orientation. We describe an example of such a vertex coupling and analyze the corresponding band spectra of lattices with square and hexagonal elementary cells showing that they depend heavily on the network topology, in particular, on the degrees of the vertices involved.

Periodic quantum graphs from the Bethe–Sommerfeld perspective

The paper is concerned with the number of open gaps in spectra of periodic quantum graphs. The well-known conjecture by Bethe and Sommerfeld (1933) says that the number of open spectral gaps for a system periodic in more than one direction is finite. To date, its validity is established for numerous systems, however, it is known that quantum graphs do not comply with this law as their spectra have typically infinitely many gaps, or no gaps at all. These facts gave rise to the question about the existence of quantum graphs with the ‘Bethe–Sommerfeld property’, that is, featuring a nonzero finite number of gaps in the spectrum. In this paper we prove that the said property is impossible for graphs with vertex couplings which are either scale-invariant or associated to scale-invariant ones in a particular way. On the other hand, we demonstrate that quantum graphs with a finite number of open gaps do indeed exist. We illustrate this phenomenon on an example of a rectangular lattice with a δ coupling at the vertices and a suitable irrational ratio of the edges. Our result allows one to find explicitly a quantum graph with any prescribed exact number of gaps, which is the first such example to date.

A QCD sum rules calculation of the ηcD⁎D and [formula omitted] form factors and strong coupling constants

We use the QCD sum rules for the three point correlation functions to compute the strong coupling constants of the meson vertices ηcD⁎D and ηcDs⁎Ds. We consider perturbative and non-perturbative contributions, working up to dimension five on the OPE. The vertices were studied considering that each one of its three mesons are off-shell alternately. The vertex coupling constant is evaluated through the extrapolation of the three different form factors. The results obtained for the coupling constants are gηcD⁎D=5.23−1.38+1.80 and gηcDs⁎Ds=5.55−1.55+1.29.

Quantum graphs with the Bethe-Sommerfeld property

In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have gaps arbitrarily high in the spectrum. This property of graph Hamiltonians, being generic in a sense, inspires the question about the existence of graphs with a finite and nonzero number of spectral gaps. We show that the answer depends on the vertex couplings together with commensurability of the graph edges. A finite and nonzero number of gaps is excluded for graphs with scale invariant couplings; on the other hand, we demonstrate that graphs featuring a finite nonzero number of gaps do exist, illustrating the claim on the example of a rectangular lattice with a suitably tuned $\delta$-coupling at the vertices.

Measurement of the W boson polarisation in tbar{t} events from pp collisions at sqrt{s} = 8 TeV in the lepton\xa0+\xa0jets channel with ATLAS

This paper presents a measurement of the polarisation of W bosons from tbar{t} decays, reconstructed in events with one high-p_{text{ T }} lepton and at least four jets. Data from pp collisions at the LHC were collected at sqrt{s} = 8 TeV and correspond to an integrated luminosity of 20.2 fb^{-1}. The angle theta ^{*} between the b-quark from the top quark decay and a direct W boson decay product in the W boson rest frame is sensitive to the W boson polarisation. Two different W decay products are used as polarisation analysers: the charged lepton and the down-type quark for the leptonically and hadronically decaying W boson, respectively. The most precise measurement of the W boson polarisation via the distribution of cos {theta ^{*}} is obtained using the leptonic analyser and events in which at least two of the jets are tagged as b-quark jets. The fitted fractions of longitudinal, left- and right-handed polarisation states are F_{mathrm {0}}=~0.709~pm ~{0.019}, F_{mathrm {L}}=~0.299~pm ~{0.015} and F_{mathrm {R}}=~-0.008~pm ~{0.014}, and are the most precisely measured W boson polarisation fractions to date. Limits on anomalous couplings of the Wtb vertex are set.

Pseudo-orbit approach to trajectories of resonances in quantum graphs with general vertex coupling: Fermi rule and high-energy asymptotics

The aim of the paper is to investigate resonances in quantum graphs with a general self-adjoint coupling in the vertices and their trajectories with respect to varying edge lengths. We derive formulae determining the Taylor expansion of the resonance pole position up to the second order, which represent, in particular, a counterpart to the Fermi rule derived recently by Lee and Zworski for graphs with the standard coupling. Furthermore, we discuss the asymptotic behavior of the resonances in the high-energy regime in the situation where the leads are attached through δ or δs′ conditions, and we prove that in the case of δs′ coupling the resonances approach to the real axis with the increasing real parts as O((Rek)−2).

Search for Anomalous Quartic ZZγγ Couplings in Photon-Photon Collisions

The self-couplings of the electroweak gauge bosons are completely specified by the non-Abelian gauge nature of the Standard Model (SM). The direct study of these couplings provides a significant opportunity to test the validity of the SM and the existence of new physics beyond the SM up to the high energy scale. For this reason, we investigate the potential of the processes γγ→ZZ, e-γ→e-γ⁎γ→e-ZZ, and e+e-→e+γ⁎γ⁎e-→e+ZZe- to examine the anomalous quartic couplings of ZZγγ vertex at the Compact Linear Collider (CLIC) with center-of-mass energy 3 TeV. We calculate 95% confidence level sensitivities on the dimension-8 parameters with various values of the integrated luminosity. We show that the best bounds on the anomalous fM2/Λ4, fM3/Λ4, fT0/Λ4, and fT9/Λ4 couplings arising from γγ→ZZ process among those three processes at center-of-mass energy of 3 TeV and integrated luminosity of Lint=2000 fb−1 are found to be [-3.30;3.30]×10-3 TeV−4, [-1.20;1.20]×10-2 TeV−4, [-3.40;3.40]×10-3 TeV−4, and [-1.80;1.80]×10-3 TeV−4, respectively.

Longitudinal top polarisation measurement and anomalous Wtb coupling

Kinematical distributions of decay products of the top quark carry information on the polarisation of the top as well as on any possible new physics in the decay of the top quark. We construct observables in the form of asymmetries in the kinematical distributions to probe their effects. Charged-lepton angular distributions in the decay are insensitive to anomalous couplings to leading order. Hence these can be a robust probe of top polarisation. However, these are difficult to measure in the case of highly boosted top quarks as compared to energy distributions of decay products. These are then sensitive, in general, to both top polarisation and top anomalous couplings. We compare various asymmetries for their sensitivities to the longitudinal polarisation of the top quark as well as to possible new physics in the Wtb vertex, paying special attention to the case of highly boosted top quarks. We perform a chi(2) analysis to determine the regions in the plane of longitudinal polarisation of the top quark and the couplings of the Wtb vertex constrained by different combinations of the asymmetries. Moreover, we find that the use of observables sensitive to the longitudinal top polarisation can add to the sensitivity to which the Wtb vertex can be probed.

Spectra of magnetic chain graphs: coupling constant perturbations

We analyze spectral properties of a quantum graph in the form of a ring chain with a δ coupling in the vertices exposed to a homogeneous magnetic field perpendicular to the graph plane. We find the band spectrum in the case when the chain exhibits a translational symmetry and study the discrete spectrum in the gaps resulting from changing a finite number of vertex coupling constants. In particular, we discuss in detail some examples such as perturbations of one or two vertices, weak perturbation asymptotics, and a pair of distant perturbations.

Approximations of Quantum-Graph Vertex Couplings by Singularly Scaled Rank-One Operators

We investigate approximations of the vertex coupling on a star-shaped graph by families of operators with singularly scaled rank-one interactions. We find a family of vertex couplings, generalizing the $\delta'$-interaction on the line, and show that with a suitable choice of the parameters they can be approximated in this way in the norm-resolvent sense. We also analyze spectral properties of the involved operators and demonstrate convergence of the corresponding on-shell scattering matrices.

Quantum Graph Vertices with Minimal Number of Passbands

We study a set of scattering matrices of quantum graphs containing minimal number of passbands, i.e., maximal number of zero elements. The cases of even and odd vertex degree are considered. Using a solution of inverse scattering problem, we reconstruct boundary conditions of scale-invariant vertex couplings. Potential-controlled universal flat filtering properties are found for considered types of vertex couplings. Obtained boundary conditions are approximated by simple graphs carrying only $\delta$ potentials and inner magnetic field.

Quantum-graph vertex couplings: some old and new approximations

In 1986 P. Seba in the classic paper considered one-dimensional pseudo-Hamiltonians containing the first derivative of the Dirac delta function. Although the paper contained some inaccuracy, it was one of the starting points in approximating one-dimension self-adjoint couplings. In the present paper we develop the above results to the case of quantum systems with complex geometry.

Some Abstract Wegner Estimates with Applications

We prove some abstract Wegner bounds for random self-adjoint operators. Applications include elementary proofs of Wegner estimates for discrete and continuous Anderson Hamiltonians with possibly sparse potentials, as well as Wegner bounds for quantum graphs with random edge length or random vertex coupling. We allow the coupling constants describing the randomness to be correlated and to have quite general distributions.

Approximations of quantum-graph vertex couplings by singularly scaled potentials

We investigate the limit properties of a family of Schrödinger operators of the form acting on n-edge star graphs with the Kirchhoff interface conditions at the vertex. Here the real-valued potential Q has compact support and λ( · ) is analytic around ε = 0 with λ(0) = 1. We show that if the operator has a zero-energy resonance of order m for ε = 1 and λ(1) = 1, in the limit ε → 0 one obtains the Laplacian with a vertex coupling depending on parameters. We prove the norm-resolvent convergence as well as the convergence of the corresponding on-shell scattering matrices. The obtained vertex couplings are of scale-invariant type provided λ′(0) = 0; otherwise the scattering matrix depends on energy and the scaled potential becomes asymptotically opaque in the low-energy limit.

Anomalous Higgs couplings at the LHeC

The discovery of Higgs boson plays a crucial role in understanding the electroweak symmetry breaking sector. From now on, solving the dynamics of this sector needs precision measurements of the couplings of the Higgs boson to the Standard Model particles. In this work, we investigate the constrains on the anomalous HWW and HWWγ couplings, described by the dimension-six operators in the effective Lagrangian, in a high energy envisaged ep collider which is called Large Hadron electron Collider (LHeC). We obtained the 95% confidence level limits on the couplings of anomalous HWW and HWWγ vertex, with the design luminosity of 10 fb−1 and electron beam energy of 140 GeV, through ep→νH+X, γp→WH+X and eγ→WHν processes by considering the new physics energy scale to be Λ=1 TeV. The sensitivity of the LHeC to the new physics scale is also briefly discussed.

ZZγandZγγanomalous couplings inγpcollision at the LHC

We study the sensitivity of anomalous $ZZ\gamma$ and $Z\gamma\gamma$ vertex couplings $h_3^{\gamma,Z}$ and $h_4^{\gamma,Z}$, which would be powerful sign of new physics, via the subprocess $\gamma q\to Z q$ of the main reaction $pp\to p\gamma p\to Z q X$ at the LHC. We calculated limits on these couplings at 95% confidence level for various values of integrated luminosity. It is shown that the $pp\to p\gamma p\to Z q X$ reaction provides one order of magnitude improvement in the couplings $h_4^{\gamma,Z}$ compared to the current experimental limits obtained in events dominated by $Z\gamma$ production from the LHC and Tevatron.

A General Approximation of Quantum Graph Vertex Couplings by Scaled Schrödinger Operators on Thin Branched Manifolds

We demonstrate that any self-adjoint coupling in a quantum graph vertex can be approximated by a family of magnetic Schroedinger operators on a tubular network built over the graph. If such a manifold has a boundary, Neumann conditions are imposed at it. The procedure involves a local change of graph topology in the vicinity of the vertex; the approximation scheme constructed on the graph is subsequently `lifted' to the manifold. For the corresponding operator a norm-resolvent convergence is proved, with the natural identification map, as the tube diameters tend to zero.

Quantum graph as a quantum spectral filter

We study the transmission of a quantum particle along a straight input–output line to which a graph Γ is attached at a point. In the point of contact we impose a singularity represented by a certain properly chosen scale-invariant coupling with a coupling parameter α. We show that the probability of transmission along the line as a function of the particle energy tends to the indicator function of the energy spectrum of Γ as α → ∞. This effect can be used for a spectral analysis of the given graph Γ. Its applications include a control of a transmission along the line and spectral filtering. The result is illustrated with an example where Γ is a loop exposed to a magnetic field. Two more quantum devices are designed using other special scale-invariant vertex couplings. They can serve as a band-stop filter and as a spectral separator, respectively.

Anomalous top magnetic couplings

The real and imaginary parts of the one-loop electroweak contributions to the left and right tensorial anomalous couplings of the tbW vertex in the Standard Model (SM) are computed.

Measurement of the W boson polarization in top quark decays with the ATLAS detector

Abstract This paper presents measurements of the polarization of W bosons in top quark decays, derived from $ t\overline t $ events with missing transverse momentum, one charged lepton and at least four jets, or two charged leptons and at least two jets. Data from pp collisions at a centre-of-mass energy of 7 TeV were collected with the ATLAS experiment at the LHC and correspond to an integrated luminosity of 1.04 fb−1. The measured fractions of longitudinally, left- and right-handed polarization are F 0 = 0.67 ± 0.07, F L = 0.32 ± 0.04 and F R = 0.01 ± 0.05, in agreement with the Standard Model predictions. As the polarization of the W bosons in top quark decays is sensitive to the Wtb vertex Lorentz structure and couplings, the measurements were used to set limits on anomalous contributions to the Wtb couplings.