Reanalyzing Pentaquark Θ^＋（1540） in Framework of QCD Sum Rules Approach with Direct Instantons

In this article, we study the pentaquark state Θ＋（1540） with a （scalar） diquark-（pseudoscalar） diquarkantiquark type interpolating current in the framework of the QCD sum rules approach by including the contributions from the direct instantons. The numerical results indicate that the contributions from the direct instantons are very small and can be safely neglected.

Higgs-like(pseudo)scalars in AdS_(4),marginal and irrelevant deformations in CFT_(3),and instantons on S^(3)

Employing a 4-form ansatz of 11-dimensional supergravity over a non-dynamical AdS_(4)×S^(7)/Z_(k)background and setting the internal space as an S1 Hopf fibration on CP3,we obtain a consistent truncation.The(pseudo)scalars,in the resulting scalar equations in Euclidean AdS_(4)space,may be considered to arise from(anti)M-branes wrapping around the internal directions in the(Wick-rotated)skew-whiffed M2-brane background(as the resulting theory is for anti-M2-branes),thus realizing the modes after swapping the three fundamental representations 8_(s),8_(c),and 8_(v) of SO(8).Taking the backreaction on the external and internal spaces,we obtain the massless and massive modes,corresponding to exactly marginal and marginally irrelevant deformations on the boundary CFT3,respectively.Subsequently,we obtain a closed solution for the bulk equation and compute its correction with respect to the background action.Next,considering the Higgs-like(breathing)mode m^(2)=18,having all supersymmetries as well as parity and scale-invariance broken,solving the associated bulk equation with mathematical methods,specifically the Adomian decomposition method,and analyzing the behavior near the boundary of the solutions,we realize the boundary duals in the SU(4)×U(1)-singlet sectors of the ABJM model.Then,introducing the new dual deformationΔ_(+)=3,6 operators made of bi-fundamental scalars,fermions,and U(1)gauge fields,we obtain the SO(4)-invariant solutions as small instantons on a three-sphere with the radius at infinity,which correspond to collapsing bulk bubbles leading to big-crunch singularities.

Exact construction of noncommutative instantons

We discuss the Atiyah-Drinfeld-Hitchin-Manin （ADHM） construc- tion of U（N） instantons in noncommutative （NC） space and give some exact instanton solutions for various noncommutative settings. We also present a new formula which is crucial to show an origin of the instanton number for U（1） and to prove the one-to-one correspondence between moduli spaces of the noncommutative instantons and the ADHM data.

Testing B-violating signatures from exotic instantons in future colliders

We discuss possible implications of exotic stringy instantons for baryon-violating signatures in future colliders. In particular, we discuss high-energy quark collisions and A- transitions. In principle, the A-A process can be probed by high-luminosity electron-positron colliders. However, we find that an extremely high luminosity is needed in order to provide a （somewhat） stringent bound compared to the current data on NN→ππ,KK. On the other hand, （exotic） instanton-induced six-quark interactions can be tested in near future high-energy colliders beyond LHC, at energies around 20-100 TeV. The Super proton-proton Collider （SppC） would be capable of such measurement given the proposed energy level of 50-90 TeV. Comparison with other channels is made. In particular, we show the compatibility of our model with neutron-antineutron and NN→ππ, KK bounds.

Stabilization and Consistency for Subtracted and Unsubtracted QCD Sum Rules for 0^＋＋ Scalar Glueball

Based on a semi-classical expansion for quantum chromodynamics in the instanton liquid background, the correlation function of the 0^＋＋ scalar glueball current is calculated. Besides the pure classical and quantum contributions, the contributions arising from the interactions between the classical instanton fields and quantum gluon ones come into play. It turns out that the latter contributions have a great role not only in making the stabilization of the subtracted and unsubtracted Laplace-transformed QCD sum rules for 0^＋＋ scalar glueball, but also in bring back the consistency between the two related sum rules, or equivalently between the QCD asymptotic expression and low energy theorem. The result for the scalar glueball mass is predicted to be mG= 1.35 GeV.

Analysis of X（1576） as a Tetraquark State with the QCD Sum Rules

We take the viewpoint that X（1576） is the tetraquark state which consists of a scalar diquark and an antiscalar-diquark in relative P-wave, and calculate its mass in the framework of the QCD sum rule approach. The numerical value of the mass mx= （1.66 =k 0.14） GeV is consistent with the experimental data. There might be some tetraquark components in the vector meson X（1576）.

Ground State Meson Spectrum in a Relativistic Model with Instanton Induced Interaction

The mass spectrum of the S-wave mesons is considered in the frame work of relativistic harmonic model （RHM）. The full Hamiltonian used in the investigation has the Lorentz scalar plus a vector harmonic-oscillator potential, the confined-one-gluon-exchange potential （COGEP） and the instanton-induced quark-antiquak interaction （Ⅲ）. A good description of the mass spectrum is obtained. The respective role of Ⅲ and COGEP in the S-wave meson spectrum is discussed.

A more general form of lump solution,lumpoff,and instanton/rogue wave solutions of a reduced (3+1)-dimensional nonlinear evolution equation

In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution to the special case for z=x.Furthermore,a more general form of lump solution of the equation is found which possesses seven arbitrary parameters and four constraint conditions.By cutting the lump by the induced soliton(s),lumpoff and instanton/rogue wave solutions are also constructed by the more general form of lump solution.

Study of Vacuum Structure by Low-Lying Eigenmodes of Overlap-Dirac Operator

APE smearing and overlap-Dirac operator are combined to filter vacuum configurations. The structures of vacuum are studied by low-lying eigenmodes of the overlap-Dirac operator, which exhibits that instanton liquid model can be used.

Instanton Effects on Gluon Propagator

Gluon propagator is investigated for pure Yang-Mills SU(3) gauge theory in field-strength approach. It isfound that instantohs provide a homogeneous solid-like medium background which generates finite nonzero momentumgluon propagator and gluon receives effective mass.

The intermittent excitation of geodesic acoustic mode by resonant Instanton of electron drift wave envelope in L-mode discharge near tokamak edge

There are two distinct phases in the evolution of drift wave envelope in the presence of zonal flow.A long-lived standing wave phase,which we call the Caviton,and a short-lived traveling wave phase(in radial direction) we call the Instanton.Several abrupt phenomena observed in tokamaks,such as intermittent excitation of geodesic acoustic mode(GAM) shown in this paper,could be attributed to the sudden and fast radial motion of Instanton.The composite drift wave-zonal flow system evolves at the two well-separate scales:the micro-scale and the meso-scale.The eigenmode equation of the model defines the zero-order(micro-scale) variation;it is solved by making use of the two-dimensional(2 D) weakly asymmetric ballooning theory(WABT),a theory suitable for modes localized to rational surface like drift waves,and then refined by shifted inverse power method,an iterative finite difference method.The next order is the equation of electron drift wave(EDW) envelope(containing group velocity of EDW) which is modulated by the zonal flow generated by Reynolds stress of EDW.This equation is coupled to the zonal flow equation,and numerically solved in spatiotemporal representation;the results are displayed in self-explanatory graphs.One observes a strong correlation between the Caviton-Instanton transition and the zero-crossing of radial group velocity of EDW.The calculation brings out the defining characteristics of the Instanton:it begins as a linear traveling wave right after the transition.Then,it evolves to a nonlinear stage with increasing frequency all the way to 20 kHz.The modulation to Reynolds stress in zonal flow equation brought in by the nonlinear Instanton will cause resonant excitation to GAM.The intermittency is shown due to the random phase mixing between multiple central rational surfaces in the reaction region.

Study of Topological Structure of Vacuum by Lattice QCD

Overlap fermions and improved 5Li cooling are compared, which exhibits that these two filter methods can produce similar structures. Then the overlap fermions and improved 5Li cooling are combined to calculate the topological charge and identify the structure of the vacuum. The results are consistent with instanton liquid model .

Matone's Relation of N = 2 Super Yang-Mills and Spectrum of Toda Chain

In N = 2 super Yang-Mills theory, the Matone＇s relation relates instanton corrections of the prepotential to instanton corrections of scMar field condensation （Trφ2）. This relation has been proved to hold for Omega deformed theories too, using localization method. In this paper, we first give a case study supporting the relation, which does not rely on the localization technique. Especially, we show that the magnetic expansion also satisfies a relation of Matone＇s type. Then we discuss implication of the relation for proposed Nekrasov-Shatashvili scheme. the spectrum of periodic Toda chain, in the context of recentlyproposed Nekrasov-Shatashvili scheme.

Light D wave meson spectrum in a relativistic harmonic model with instanton induced interaction

The mass spectrum of the D wave mesons is considered in the frame work of relativistic harmonic model (RHM). The full Hamiltonian used in the investigation has the Lorentz scalar plus a vector harmonic-oscillator potential, the confined-one-gluon-exchange potential (COGEP) and the instanton-induced quark-antiquark interaction (III). A good agreement between calculated D wave meson masses with experimental D wave meson masses is obtained. The respective role of III and COGEP in the D wave meson spectrum is discussed.

Lithium Quantum Consciousness

Conscious agency is considered to be founded upon a quantum state of mind . An original synthesis, called “Lithium Quantum Consciousness” (LQC), proposes that this quantum state utilises lithium-6 (spin-1) qutrit nuclear magnetic resonance (NMR) quantum information processing (QIP) in the connectome (brain-graph). In parallel to the connectome’s processing of physiological controls, perception, cognition and intelligence via quantum electrodynamics (QED), the connectome also functions via its dynamic algebraic topology as a unitary transceiver antenna laced with lithium-6 nuclei which are spin-entangled with each other and with the environmental vortical gluon field via quantum chromodynamics (QCD). This unitary antenna (connectome) bestows the self its unity of consciousness within an intertwined-history multi-agent environment. An equivalence is proposed between Whitehead’s occasions of experience and topological spacetime instantons in the vortical gluon field. Topological spacetime instantons pervade the vortical gluon field in a quantum information network of vortex interactions, herein termed the “instanton-net”, or “Instanet” [sic]. The fermionic isotope lithium-6 has a very low nuclear binding energy and the smallest non-zero nuclear electric quadrupole moment of any stable nucleus making it susceptible to quantum chromodynamic (QCD) interaction with the vortical gluon field and ideal for spin-1 qutrit NMR-QIP. The compact spherical atomic orbital of lithium provides ideal rotational freedom inside tetrahedral water cages in organo6Li+(H2O)4 within which the lithium nucleus rapidly tumbles for NMR motional narrowing and long decoherence times. Nuclear spin-entanglement, among water-caged lithium-6 nuclei in the connectome, is a spin-1 qutrit NMR-QIP resource for conscious agency. By contrast, similar tetrahedral xenon cages in organo6Li+Xe4 excimers are postulated to decohere the connectome’s NMR-QIP due to xenon’s NMR signal being extremely sensitive to its molecular environment. By way of this quantum neurochemistry, lithium is an effective psychiatric medication for enhancing mood and xenon is an effective anaesthetic.

Super Gaussian enhancers in the Schwinger mechanism

We study the Schwinger mechanism in the presence of an additional uniformly oriented,weak super Gaussian of integer order 4 N+2.Using the worldline approach,we determine the relevant critical points to compute the leading order exponential factor analytically.We show that increasing the parameter N gives rise to a strong dynamical enhancement.For N=2,this effect turns out to be larger compared to a weak contribution of the Sauter type.For higher orders,specifically,for the rectangular barrier limit,i.e.N→∞,we approach the Lorentzian case as an upper bound.Although the mentioned backgrounds significantly differ in Minkowski spacetime,we show that the found coincidence applies due to identical reflection points in the Euclidean instanton plane.In addition,we also treat the background in perturbation theory following recent ideas.By doing so,we show that the parameter N determines whether the weak contribution behaves perturbatively or nonperturbatively with respect to the field strength ratio,and,hence,reveals an interesting dependence on the background shape.In particular,we show that for backgrounds,for which higher orders in the field strength ratio turn out to be relevant,a proposed integral condition is not fulfilled.In view of these findings,the latter may serve as an indicator for the necessity for higher-order contributions.

Properties of Charmonium States in a Phenomenological Approach

We investigate the spectrum and decay rates of charmonium states within the framework of the non relativistic quark model by employing a Coulomb like potential from the perturbative one gluon exchange and the linear confining potential along with the potential derived from instanton vacuum to account for the hyperfine mass splitting of charmonium states in variational approach. We predict radiative E1, M1, two-photon, lepton and two-gluon decay rates of low lying charmonium states. An overall agreement is obtained with the experimental masses and decay widths.We have estimated the branching ratio of two gluons decaying into light hadrons.

instanton quantum tunneling Jacobi elliptic functions Lamé functions

Under condition of four potential fields, equations of motion and fluctuations in imaginary time are utilized to analytically derive the basic and fluctuating periodic instantons. It is shown that the basic instantons satisfy the elliptic or simple pendulum equations and their solutions are Jacobi elliptic functions, and fluctuating periodic instantons satisfy the Lam′e equation and their solutions are Lame functions. These results indicate that there exists the common solution family for different potential fields which are called the super-symmetry family.

Constrained instanton and black hole creation

A gravitational instanton is considered as the seed for the creation of a universe. However, there exist too few instantons. To include many interesting phenomena in the framework of quantum cosmology, the concept of constrained gravitational instanton is inevitable. In this paper we show how a primordial black hole is created from a constrained instanton. The quantum creation of a generic black hole in the closed or open background is completely resolved. The relation of the creation scenario with gravitational thermodynamics and topology is discussed.

Entropy and equilibrium property of QCD-instanton induced final state in deep-inelastic scattering

The scaling and additivity properties of Rényi entropy in rapidity space of the instanton final state （IFS） and current jet identified by the r-sorting method from the QCDINS Monte Carlo event sample are studied. Asymptotic scaling of the Rényi entropy H2 is observed for the IFS while H2 for the current jet jtends to saturation with decreasing phase space scale. Furthermore, it is found that the additivity of H2 holds well for the IFS in narrow rapidity windows at different positions. These results indicate that the IFS produced in the instanton-induced process of deep inelastic scattering has reached local equilibrium.