Vertex Coupling Research Articles

The theoretical study of pp¯→Λ¯Ση\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p\\bar{p}\\rightarrow \\bar{\\Lambda }\\Sigma \\eta $$\\end{document} reaction

We study the production of hyperon resonances in the pp¯→Λ¯Ση\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p\\bar{p}\\rightarrow \\bar{\\Lambda }\\Sigma \\eta $$\\end{document} reaction within an effective Lagrangian approach. The model includes the production of Σ(1750)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma (1750)$$\\end{document} and Λ(1670)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda (1670)$$\\end{document} in the intermediate state excited by the K and K∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K^*$$\\end{document} meson exchanges between the initial proton and antiproton. Due to the large coupling of Σ(1750)Ση\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma (1750)\\Sigma \\eta $$\\end{document} vertex, Σ(1750)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma (1750)$$\\end{document} is found a significant contribution near the threshold in this reaction. We provide total and differential cross section predictions for the reaction and discuss the possible influence of Σ(1750)Ση\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma (1750)\\Sigma \\eta $$\\end{document} vertex coupling and model parameters, which will be useful in future experimental studies. This reaction can provide a platform for studying the features of Σ(1750)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma (1750)$$\\end{document} resonance, especially the coupling to Ση\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma \\eta $$\\end{document} channel.

Vertex coupling interpolation in quantum chain graphs

We analyze the band spectrum of the periodic quantum graph in the form of a chain of rings connected by line segments with the vertex coupling which violates the time reversal invariance, interpolating between the δ coupling and the one determined by a simple circulant matrix. We find that flat bands are generically absent and that the negative spectrum is nonempty even for interpolation with a non-attractive δ coupling; we also determine the high-energy asymptotic behavior of the bands.

Cairo lattice with time-reversal non-invariant vertex couplings

We analyze the spectrum of a periodic quantum graph of the Cairo lattice form. The used vertex coupling violates the time reversal invariance and its high-energy behavior depends on the vertex degree parity; in the considered example both odd and even parities are involved. The presence of the former implies that the spectrum is dominated by gaps. In addition, we discuss two modifications of the model in which this is not the case, the zero limit of the length parameter in the coupling, and the sign switch of the coupling matrix at the vertices of degree three; while different they both yield the same probability that a randomly chosen positive energy lies in the spectrum.

Magnetic square lattice with vertex coupling of a preferred orientation

We analyze a square lattice graph in a magnetic field assuming that the vertex coupling is of a particular type violating the time reversal invariance. Calculating the spectrum numerically for rational values of the flux per plaquette we show how the two effects compete; at the high energies it is the magnetic field which dominates restoring asymptotically the familiar Hofstadter’s butterfly pattern.

On two-body and three-body spin correlations in leptonic toverline{t}Z production and anomalous couplings at the LHC

We study the anomalous toverline{t}Z couplings in the toverline{t}Z production in leptonic final state at the 13 TeV LHC. We use the polarizations of top quarks and Z boson, two-body and three-body spin correlations among the top quarks and Z boson, and the cross section to probe the anomalous couplings. We estimate one parameter and simultaneous limits on the couplings of the effective vertex as well as the effective operators for a set of luminosities 150 fb−1, 300 fb−1, 1000 fb−1, and 3000 fb−1. The polarizations and the spin correlations are found to be helpful on top of the cross section to better constrain the anomalous couplings.

Bulk locality and gauge invariance for boundary-bilocal cubic correlators in higher-spin gravity

We consider type-A higher-spin gravity in 4 dimensions, holographically dual to a free O(N) vector model. In this theory, the cubic correlators of higher-spin boundary currents are reproduced in the bulk by the Sleight-Taronna cubic vertex. We extend these cubic correlators from local boundary currents to bilocal boundary operators, which contain the tower of local currents in their Taylor expansion. In the bulk, these boundary bilocals are represented by linearized Didenko-Vasiliev (DV) “black holes”. We argue that the cubic correlators are still described by local bulk structures, which include a new vertex coupling two higher-spin fields to the “worldline” of a DV solution. As an illustration of the general argument, we analyze numerically the correlator of two local scalars and one bilocal. We also prove a gauge-invariance property of the Sleight-Taronna vertex outside its original range of applicability: in the absence of sources, it is invariant not just within transverse-traceless gauge, but rather in general traceless gauge, which in particular includes the DV solution away from its “worldline”.

Vertex corrections due to the triangle singularity mechanism in the light axial vector meson couplings to K*K¯+ c.c.

The light axial vector mesons can couple to $K^*\bar{K}+c.c.$ in an $S$ wave at the tree level. Due to the near-threshold $S$-wave interactions the couplings can be affected by the final state interactions. It is of peculiar interest that the pion exchange between $K^*\bar{K}+c.c.$ can go through a triangle diagram which is within the kinematics of the triangle singularity (TS). This mechanism will introduce energy dependence and a $D$-wave amplitude to the vertex couplings. Hence, it should be necessary to investigate the role played by the $K^*\bar{K}+c.c.$ threshold in order to have a better understanding of the light axial vector spectrum.

Magnetic ring chains with vertex coupling of a preferred orientation

We discuss spectral properties of a periodic quantum graph consisting of an array of rings coupled either tightly or loosely through connecting links, assuming that the vertex coupling is manifestly non-invariant with respect to the time reversal and a homogeneous magnetic field perpendicular to the graph plane is present. It is shown that the vertex parity determines the spectral behavior at high energies and the Band–Berkolaiko universality holds whenever the edges are incommensurate. The magnetic field influences the probability that an energy belongs to the spectrum in the tight-chain case, and also it can turn some spectral bands into infinitely degenerate eigenvalues.

Kagome network with vertex coupling of a preferred orientation

We investigate spectral properties of periodic quantum graphs in the form of a kagome or a triangular lattice in the situation when the condition matching the wave functions at lattice vertices is chosen of a particular form violating the time-reversal invariance. The positive spectrum consists of an infinite number of bands, some of which may be flat; the negative one has at most three and two bands, respectively. The kagome lattice example shows that even in graphs with such an uncommon vertex coupling, spectral universality may hold: if its edges are incommensurate, the probability that a randomly chosen positive number is contained in the spectrum is ≈0.639.

Spectrum of periodic chain graphs with time-reversal non-invariant vertex coupling

We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly non-invariant with respect to time reversal. We discuss, in particular, the high-energy behavior of such systems and the limiting situations when one of the edges in the elementary cell of such a graph shrinks to zero. The spectrum depends on the topology and geometry of the graph. The probability that an energy belongs to the spectrum takes three different values reflecting the vertex parities and mirror symmetry, and the band patterns are influenced by commensurability of graph edge lengths.

Probing anomalous quartic gamma gamma gamma gamma couplings in light-by-light collisions at the CLIC

The anomalous quartic neutral couplings of the gamma gamma gamma gamma vertex in a polarized light-by-light scattering of the Compton backscattered photons at the CLIC are examined. Both differential and total cross sections are calculated for e^+e^- collision energies 1500 GeV and 3000 GeV. The helicity of the initial electron beams is taken to be pm ,0.8. The unpolarized and SM cross sections for the same values of helicities are also estimated. The 95% C.L. exclusion limits on two anomalous photon couplings zeta _1 and zeta _2 are calculated. The best bounds on these couplings are found to be 6.85 times 10^{-16} text { GeV}^{-4} and 1.43 times 10^{-15} text { GeV}^{-4}, respectively. The results are compared with the exclusion bounds obtained previously for the LHC and HL-LHC. It is shown that the light-by-light scattering at the CLIC, especially the polarized, has a greater potential to search for the anomalous quartic neutral couplings of the gamma gamma gamma gamma vertex.

Many-body effects in third harmonic generation of graphene

The low-energy (intraband) range of the third harmonic generation of graphene in the terahertz regime is governed by the damping terms induced by the interactions. A controlled many-body description of the scattering processes is thus a compelling and desirable requirement. In this paper, using a Kadanoff-Baym approach, we systematically investigate the impact of many-body interaction on the third-harmonic generation (THG) of graphene, taking elastic impurity scattering as a benchmark example. We predict the onset in the mixed inter-intraband regime of novel incoherent features driven by the interaction at four- and five-photon transition frequencies in the third-harmonic optical conductivity with a spectral weight proportional to the scattering rate.We show also that, in spite of the complex many-body physics, the purely intraband term governing the limit $\omega \to 0$ resembles the constraints of the phenomenological model. We ascribe this agreement to the fulfilling of the conservation laws enforced by the conserving approach. The overlap with novel incoherent features and the impact of many-body driven multi-photon vertex couplings limit however severely the validity of phenomenological description.

Quantum Graphs with Vertices Violating the Time Reversal Symmetry

We discuss quantum graphs with the vertex coupling which violates the time-reversal invariance. For a simple type of this coupling in which the violation is in a sense maximum one we show that it leads to spectral properties determined in the high-energy regime by the graph topology. We illustrate this effect on examples which involve lattice graphs and loop arrays as well as finite graphs associated with Platonic solids. We also show that transport properties of such graphs may differ in the graph bulk and at the edges.

Relaxation time for the alignment between the spin of a finite-mass quark or antiquark and the thermal vorticity in relativistic heavy-ion collisions

We study the relaxation time required for the alignment between the spin of a finite-mass quark/antiquark and the thermal vorticity, at finite temperature and baryon chemical potential, in the context of relativistic heavy-ion collisions. The relaxation time is computed as the inverse of the total reaction rate that in turn is obtained from the imaginary part of the quark/antiquark self-energy. We model the interaction between spin and thermal vorticity within the medium by means of a vertex coupling quarks and thermal gluons that, for a uniform temperature, is proportional to the global angular velocity and inversely proportional to the temperature. We use realistic estimates for the angular velocities for different collision energies and show that the effect of the quark mass is to reduce the relaxation times as compared to the massless quark case. Using these relaxation times we estimate the intrinsic quark and antiquark polarizations produced by the thermal vorticity. We conclude by pointing out that, in spite of the former being larger than the latter, it is still possible to understand recent results from the STAR Beam Energy Scan when accounting for the fact that only a portion of quarks/antiquarks come from the denser and thus thermalized region in the collision.

Ring chains with vertex coupling of a preferred orientation

We consider a family of Schrödinger operators supported by a periodic chain of loops connected either tightly or loosely through connecting links of the length [Formula: see text] with the vertex coupling which is non-invariant with respect to the time reversal. The spectral behavior of the model illustrates that the high-energy behavior of such vertices is determined by the vertex parity. The positive spectrum of the tightly connected chain covers the entire halfline while the one of the loose chain is dominated by gaps. In addition, there is a negative spectrum consisting of an infinitely degenerate eigenvalue in the former case, and of one or two absolutely continuous bands in the latter. Furthermore, we discuss the limit [Formula: see text] and show that while the spectrum converges as a set to that of the tight chain, as it should in view of a result by Berkolaiko, Latushkin, and Sukhtaiev, this limit is rather non-uniform.

Topological bulk-edge effects in quantum graph transport

We examine quantum transport in periodic quantum graphs with a vertex coupling non-invariant with respect to time reversal. It is shown that the graph topology may play a decisive role in the conductivity properties illustrating this claim with two examples. In the first, the transport is possible at high energies in the bulk only being suppressed at the sample edges, while in the second one the situation is opposite, the transport is possible at the edge only.

Spectral asymptotics of the Laplacian on Platonic solids graphs

We investigate the high-energy eigenvalue asymptotics of quantum graphs consisting of the vertices and edges of the five Platonic solids considering two different types of the vertex coupling. One is the standard δ-condition and the other is the preferred-orientation one introduced in the work by Exner and Tater [Phys. Lett. A 382, 283–287 (2018)]. The aim is to provide another illustration of the fact that the asymptotic properties of the latter coupling are determined by the vertex parity by showing that the octahedron graph differs in this respect from the other four for which the edges at high energies effectively disconnect and the spectrum approaches the one of the Dirichlet Laplacian on an interval.

Shape of proton and the pion cloud

Proton-proton differential and total cross sections provide information on the energy dependence of proton shape and size. We show that the deviation from exponential behavior of the diffraction cone observed near $t=-0.1$ GeV$^2$, (so-called break), both at the ISR and the LHC follows from the $t$-channel two-pion loop contributions, imposed by unitarity. By using a simple Regge-pole model, we extrapolate the "break" from the ISR energy region to that of the LHC. This allows us to answer two important questions: 1) To what extent is the "break" observed recently at the LHC a "recurrence" of that seen at the ISR (universality)? 2) What is the relative weight of two-pion effect to the vertex coupling (Regge residue) compared to expanding size (pomeron propagator) in producing the "break"? We find that the effect comes both from the Regge residue (proton-pomeron coupling) and from the Regge propagator. A detail analyses of their balance, including the correlation between the relevant parameters is presented.

A family of quantum graph vertex couplings interpolating between different symmetries

The paper discusses quantum graphs with a vertex coupling which interpolates between the common one of the δ type and a coupling introduced recently by two of the authors which exhibits a preferred orientation. Describing the interpolation family in terms of circulant matrices, we analyze the spectral and scattering property of such vertices, and investigate the band spectrum of the corresponding square lattice graph.

Spectral enclosures for non-self-adjoint extensions of symmetric operators

The spectral properties of non-self-adjoint extensions A[B] of a symmetric operator in a Hilbert space are studied with the help of ordinary and quasi boundary triples and the corresponding Weyl functions. These extensions are given in terms of abstract boundary conditions involving an (in general non-symmetric) boundary operator B. In the abstract part of this paper, sufficient conditions for sectoriality and m-sectoriality as well as sufficient conditions for A[B] to have a non-empty resolvent set are provided in terms of the parameter B and the Weyl function. Special attention is paid to Weyl functions that decay along the negative real line or inside some sector in the complex plane, and spectral enclosures for A[B] are proved in this situation. The abstract results are applied to elliptic differential operators with local and non-local Robin boundary conditions on unbounded domains, to Schrödinger operators with δ-potentials of complex strengths supported on unbounded hypersurfaces or infinitely many points on the real line, and to quantum graphs with non-self-adjoint vertex couplings.