Interacting Vector Boson Research Articles

An Investigation into Properties for (_66^156)Dy Isotope Using IBM-1 and IVBM Model

Abstract: The (_66^156)Dy isotopes in the O (6) region were investigated. The positive ground-state band of (_66^156)Dy nuclei was calculated using the interacting boson model ‎(IBM-1) and the interacting vector boson model (IVBM). The negative parity band energies of the above isotope were calculated using (IVBM) only. We plotted the ratios ((E(I+2))/(〖E(2〗_1^+)), (E(I+2))/(E(I)),r(((I+2))/I)) and the E-GOS curve as a function of the spin (I) to investigate the properties of the yrast band. Accordingly, the best-fit values of the parameters were used to construct the Hamiltonian, and the electromagnetic transition probability B(E2) of this nucleus was determined. Theoretical energy levels of dysprosium-156 isotope with a neutron number N = 90 and spin parity up to 〖30〗_1^+ were obtained using the MATLAB-20 simulation program. A comparison of these calculated energy levels with the corresponding experimentally measured ones shows a good agreement. The results also ‎draw our attention to the fact that the nucleus of interest deforms and exhibits gamma-instability ‎properties. Keywords: Dysprosium Isotopes, Even-even nuclei, Interacting Boson Model-1, Interacting Vector Boson Model, Negative parity, Yrast band. Abbreviations and Acronyms, IBM: Interacting Boson Model, IVBM: Interacting Vector Boson Model, U(5): Spherical limit, SU(3): Axially deformed shape limit O(6): γ-unstable limit, SP(12; R): the non-compact symplectic group.

The Evolution of 174Yb, 176Hf, 178W and 180Os Isotones

The characteristics of 174Yb, 176Hf, 178W, and 180Os isotones are determined, followed by the calculation of their energy states. The first energy states 𝐸21+ and the ratios of the second excited energy states to the first excited energy states𝑅4/2 = 𝐸41 +/𝐸21+ provide primary information regarding the characteristics of the nuclei at low levels. To know the properties of high-energy states of nuclei, the behavior of the ground states band (GSB) studied by determine the back-bending curves which may occur and determine the change in the moment of inertia 2𝜗/ℏ2 and the rotation energy of gamma emitted at different states 2𝜔2, the E-GOS curve which study the gamma energy emitted from each state 𝐸𝐵🁡nd the behavior of the successive energy states in comparison with those states close to them 𝑟 (𝐼+2🀩 are drawn and studied. The relationship between GSB and NPB (the negative parity band) which give the odd staggering ∆𝐼 = 1 curve of each nucleus have been studied and determine the probability of change of the property of 174Yb, 176Hf, 178W, 180Os isotones. We used all of the information from the previous study to calculate the energy states of GSB using the appropriate equations for the different limits of the interacting boson model IBM-1. The interacting vector boson model IVBM was also utilized to compute the GSB and NPB of the isotones 174Yb, 176Hf, 178W, 180Os. A modification of IVBM was introduced to improve the results of calculations.

Standard model EFT effects in vector-boson scattering at the LHC

The assumption that the Standard Model is an Effective Field Theory (SM EFT) of a more fundamental theory at a higher, than electroweak, energy scale, implies a growth of cross-sections for electroweak Vector Boson Scattering (VBS) processes signalling the appearance of a resonance (or resonances) nearby that scale. In this article, we investigate in detail SM EFT effects from dimension-6 operators in VBS with like-sign-$W$ production in fully leptonic decay modes at the High Luminosity LHC (HL-LHC). We find that these effects are important for a handful of operators, most notably for the operator composed of three $SU(2)$ field strength tensors responsible for strong transversely polarized vector boson interactions. Current global fits on Wilson-coefficients allow for a signal immediately permissive at the HL-LHC if not accessible at the current LHC-dataset.

Nuclear Gamma-soft Character in ¹²⁸Ba

We report the properties of gamma soft O(6) of 128Ba isotones with neutron N = 72 using Interacting Vector Boson Model (IVBM), interacting Boson Model (IBM-1), Bohr-Mottelson Model (BM), and Doma-El-Gendy (D-G) relation. The first energy level ( ) and ratio have been investigated which show that 128Ba has gamma-soft character. The curves Eγ/Vs.J of E-GOS of even 128Ba nucleus were compared with the standard curves of vibrational, gamma soft and rotational limits. The staggering factors were studied of available measured data of 128Ba nucleus. The yrast levels of this isotope are calculated by the model of VBMI, IBM-1, BM and D-G and they were compared by measured data. The negative parity band of 128Ba was calculated by IVBM and BM model and compared with experimental values.

Characteristics of Energy States and their Calculation Using IBM-1 and IVBM of Isotones 180HF, 182W, 184Os, 186Pt

The positive ground-state band (GSB) of isotones for N = 108 has been calculated using the Interacting Bosons Model (IBM-1), and Interacting Vector Boson Model (IVBM), while the negative-parity band (NPB) of , has been calculated using the (IVBM). since (IBM-1) have different calculation according to the characteristics of each nucleus, these characteristics were identified using different method, Plotting the relation of the moment of inertia ( ) against the rotational frequency of the emitted photons ( ) during nuclear transition between different energy states were determined, The calculation shows that nucleus do not have any back-bending effect which indicates that its characteristics have not changed, While have a back-bending which indicate that a change in their characteristics. Also using the relation between different excited states energies to their preceding values, one can determine the characteristic of each nucleus which shows a rotational characteristics for nucleus, while have transitional characteristics between the two vibrational and rotational challenges, To get to know the characteristics of the nucleus more accurately the relation of the gamma energy over spin ( ) as a function of the spin (I) E-GOS was drown, the calculation showed pure rotational characteristic for nucleus, While the nuclei have gamma soft O(6) characteristic, When staggering phenomena between (NPB) and (GSB) has been studied, The contour plot show that nucleus did not reach zero value which refer to the constancy of their characteristics.

Nuclear Structure and Energy Levels of 158Er, 160Yb and 162Hf Isotones

The properties of even-even158Er, 160Yb and 162Hf isotones are studied and its energy states calculated. To identify the properties of each isotone, the values of the first excited states and the ratio of the second to the first excited states were adopted. The phenomenon of back-bending, the E-GOS curve and the odd-even staggering were studied. Examining the algebraic structure of the Bohr model (BM) clarified the relationship with the interacting vector boson model (IVBM) and the interacting boson model (IBM) which it has related solvable limits and corresponding dynamical symmetries. BM, IVBM and IBM were used to calculate the energy states for each isotone and compared with the experimental data. The results showed that the BM and IVBM are more comfort than the calculation of IBM-1. The contour plots of the potential energy surface (PES) to the IBM Hamiltonian for Er–Hf with N = 90 have been obtained using the intrinsic coherent state and evolve from deformed shapes to γ- unstable with decreasing the boson number.

Measurements of production cross sections of WZ and same-sign WW boson pairs in association with two jets in proton-proton collisions at [formula omitted

Measurements of production cross sections of WZ and same-sign WW boson pairs in association with two jets in proton-proton collisions at s=13TeV at the LHC are reported. The data sample corresponds to an integrated luminosity of 137fb−1, collected with the CMS detector during 2016–2018. The measurements are performed in the leptonic decay modes ▪ and ▪, where ℓ,ℓ′=e, ▪. Differential fiducial cross sections as functions of the invariant masses of the jet and charged lepton pairs, as well as of the leading-lepton transverse momentum, are measured for W±W± production and are consistent with the standard model predictions. The dependence of differential cross sections on the invariant mass of the jet pair is also measured for WZ production. An observation of electroweak production of WZ boson pairs is reported with an observed (expected) significance of 6.8 (5.3) standard deviations. Constraints are obtained on the structure of quartic vector boson interactions in the framework of effective field theory.

Dynamical Symmetries in Shell and Collective Models of Nuclear Structure

The dynamical symmetries in the algebraic shell model and the collective Interacting Vector Boson Model (IVBM) realized in terms of fermion and boson creation and annihilation operators are investigated. The obtained analytic eigen-energies in both models are compared with the experimental ones and the strengths of the corresponding terms of the model Hamiltonians are evaluated in both cases. In the algebraic realization of the Pairing plus Quadrupole Shell Model the correlations and transition between the quadrupole and pairing phases—dynamical symmetries are investigated in application to nuclear systems in the first few light shells. In the symplectic extension of the IVBM the spectra of heavy even-even nuclei with transitional between rotational and vibrational character is well reproduced. The algebraic connections between dynamical symmetries of the nuclear collective spectra and the ordering of the low-lying states with fixed angular momentum permits a reasonable and experimentally proved prediction of the position of the 0+ band heads of the collective bands. The models based on dynamical symmetries give an elegant and simple way to describe the complex spectra of nuclei with different shapes.

Measurement of the cross section for electroweak production of a Z boson, a photon and two jets in proton-proton collisions at sqrt{mathrm{s}} = 13 TeV and constraints on anomalous quartic couplings

A measurement is presented of the cross section for electroweak production of a Z boson and a photon in association with two jets (Zγjj) in proton-proton collisions. The Z boson candidates are selected through their decay into a pair of electrons or muons. The process of interest, electroweak Zγjj production, is isolated by selecting events with a large dijet mass and a large pseudorapidity gap between the two jets. The measurement is based on data collected at the CMS experiment at sqrt{s} = 13 TeV, corresponding to an integrated luminosity of 35.9 fb−1. The observed significance of the signal is 3.9 standard deviations, where a significance of 5.2 standard deviations is expected in the standard model. These results are combined with published results by CMS at sqrt{s} = 8 TeV, which leads to observed and expected respective significances of 4.7 and 5.5 standard deviations. From the 13 TeV data, a value is obtained for the signal strength of electroweak Zγjj production and bounds are given on quartic vector boson interactions in the framework of dimension-eight effective field theory operators.

Properties of some Nuclei with Mass Number A=140

The positive ground-state band (GSB) of isobars was calculated using the Bohr – Mottelson (BM) model, interacting vector boson model (IVBM), and interacting boson model (IBM-1), while the negative-parity band (NPB) of was calculated using the BM model and IVBM. To determine the properties of the ground-state band, the back-bending curve, the E-GOS curve (Eγ/I), the ratio (r(I +2)/I) and the staggering have been plotted as a function of the spin (I). The contour plots show that all nuclei under consideration have complicate properties.

Towards the higher point holographic momentum space amplitudes. Part II. Gravitons

In this follow up paper, we calculate higher point tree level graviton Witten diagrams in AdS4 via bulk perturbation theory. We show that by rearranging the bulk to bulk graviton propagators, the calculations effectively reduce to the computation of a scalar factor. Analogous to the amplitudes for vector boson interactions we computed in the previous paper, scalar factors for the graviton exchange diagrams also become relatively simple when written in momentum space. We explicitly calculate higher point correlators and discuss how this momentum space formalism makes flat space and collinear limits simpler.

Search for anomalous electroweak production of vector boson pairs in association with two jets in proton-proton collisions at 13 TeV

A search for anomalous electroweak production of WW, WZ, and ZZ boson pairs in association with two jets in proton-proton collisions at s=13TeV at the LHC is reported. The data sample corresponds to an integrated luminosity of 35.9fb−1 collected with the CMS detector. Events are selected by requiring two jets with large rapidity separation and invariant mass, one or two leptons (electrons or muons), and a W or Z boson decaying hadronically. No excess of events with respect to the standard model background predictions is observed and constraints on the structure of quartic vector boson interactions in the framework of dimension-8 effective field theory operators are reported. Stringent limits on parameters of the effective field theory operators are obtained. The observed 95% confidence level limits for the S0, M0, and T0 operators are −2.7<fS0/Λ4<2.7, −1.0<fM0/Λ4<1.0, and −0.17<fT0/Λ4<0.16, in units of TeV−4. Constraints are also reported on the product of the cross section and branching fraction for vector boson fusion production of charged Higgs bosons as a function of mass from 600 to 2000 GeV. The results are interpreted in the context of the Georgi–Machacek model.

The collective Properties of Even-Even164-174 W Isotopes

Ground states bands (GSB) and negative parity band (NPB) of isotopes have been calculated. Bohr-Mottelson (BM), Interacting boson approximation-1(IBM-1) and Interacting vector boson model (IVBM) were used for this purpose. The principal excited state ( ) and the proportion of the second to the primary excited state provide primary information about the properties of the nucleus. The ratio of the gamma energy, over spin of each state as a function of the angular momentum (E-GOS), has been assessed to decide the ground states property of each nucleus. The ratio of energies of ( ) and ( ), states as a function of the angular momentum , have been attracted to decide numerically the properties of the ground states band of all states and all nuclei. The staggering between octupole band and ground state band is found to display a beat pattern as a function of angular momentum . The methods which were used, showed the transitional U(5)-O(6) properties of , the general properties that U(5)-O(6)-SU(3) of , and the transitional properties O(6)-SU(3) of ; while showed the SU(3) properties.

Investigation of energy staggering effects in Thorium isotopes in framework of interacting vector Boson model

The energies of the positive parity ground state band with Lπ=0+,2+,4+,… and the negative parity octupole band with Lπ=1−,3−,5−,… in normally deformed Thorium (Th) even-even nuclei are described in the framework of the rotational limit of the symplectic interacting vector boson model (IVBM) based on the algebra of Sp(12,R) group. The experimental data best fit to adopt the best model parameters are determined by utilizing a simulated search program in order to achieve minimum root mean square deviation between the experimental and calculated excitation energies. The agreement between experimental and calculated energies is very good. The odd-even ΔL=1 staggering effects between ground and octupole bands are investigating by calculating staggering index depending on the dipole transitions linking the two bands and the quadruple transitions within each band. Also the presence of ΔL=2 energy staggering (commonly called ΔL=4 bifurcation) in ground state band of 232Th has been investigated, by calculating staggering index representing the finite difference approximation to the forth order derivative of the quadruple transition energies at a given spin.

Critical Point of the 152Sm, 154Gd, and 156Dy Isotones

The even—even rare-earth nuclei in U(5)—SU(3) region at neutron number (N) = 90, have been systematically studied using the Bohr—Mottelson Model (BM), Interacting Vector Boson Model (IVBM), and Interacting Boson Model (IBM). The positive ground-state band (GSB) of 152Sm, 154Gd, and 156Dy nuclei has been calculated by using BM, IVBM, and IBM, while the negative-parity band (NPB) of those nuclei are calculated by BM and IVBM only. To determine the intermediate structure, the ratio (r(I + 2)/I) and E-GOS curve (E-Gamma Over Spin) as a function of the spin (I) have been drawn. In the IBM, the calculated reduced B(E2) transition probabilities of the GSB in the 152Sm, 154Gd, and 156Dy nuclei are analyzed and compared to the prediction of vibrational U(5) and rotational SU(3) limits. In the Sm—Dy nuclei with N = 90, the U(5)—SU(3) IBM potential energy surfaces (PES’s) are analyzed and evolve from spherical to deformed shapes with increasing the boson number. The critical phase transition points are identified in the space of model parameters and 152Sm,154Gd, and 156Dy nuclei have been found to be close to critical points.

Description of Energy Levels for 84,86,96,98Sr Isotopes

The positive ground-state band (GSB) of 84,86,96,98Sr has been calculated using the Bohr–Mottelson (BM) model, interacting vector boson model (IVBM), and interacting boson model (IBM-1), while the negative-parity band (NPB) of 84,86,96,98Sr has been calculated using the BM model and IVBM. IBM-1 has been used to calculate the energy of the gamma and beta bands. To determine the properties of the ground-state band, the ratio (r(I +2)/I) and the E-GOScurve (Eγ/I) have been plotted as a function of the spin (I). The potential energy surface (PES) has been calculated using IBM-1. The contour plots of the PESs show that 84,86,96Sr nuclei have vibrational properties and 98Sr has rotational characteristics.

Observation of Electroweak Production of Same-Sign W Boson Pairs in the Two Jet and Two Same-Sign Lepton Final State in Proton-Proton Collisions at sqrt[s]=13 TeV.

The first observation of electroweak production of same-sign W boson pairs in proton-proton collisions is reported. The data sample corresponds to an integrated luminosity of 35.9 fb^{-1} collected at a center-of-mass energy of 13TeV with the CMS detector at the LHC. Events are selected by requiring exactly two leptons (electrons or muons) of the same charge, moderate missing transverse momentum, and two jets with a large rapidity separation and a large dijet mass. The observed significance of the signal is 5.5 standard deviations, where a significance of 5.7 standard deviations is expected based on the standard model. The ratio of measured event yields to that expected from the standard model at leading order is 0.90±0.22. A cross section measurement in a fiducial region is reported. Bounds are given on the structure of quartic vector boson interactions in the framework of dimension-8 effective field theory operators and on the production of doubly charged Higgs bosons.

Theoretical description of the deformation properties for 154–164Gd isotopes

The 154–164Gd isotopes in SU(3) region were investigated. For these nuclei, the positive ground-state band of 154–164Gd has been calculated using Bohr–Mottelson Model, Interacting Vector Boson Model and Interacting Boson Model, while the negative-parity band of 154–164Gd has been calculated using Bohr–Mottelson Model and Interacting Vector Boson Model only. To determine the property of the ground-state band, the ratio (r(I+2)/I) and E-GOS curve (Eγ/I) as a function of the spin (I) have been drawn. The reduced transition probabilities B(E2) of these nuclei were calculated. The results were compared with the experimental data and the previous calculations. It is shown that there is a good agreement between the results found and especially with the experimental ones. The potential energy surface (PES) has been calculated within the framework using interacting boson model (IBM-1). The contour plot of the potential energy surfaces shows that the interested nuclei are deformed and have rotational characters.

Investigation of Energy Levels and Electromagnetic Transitions for Yb–Pt Nuclei with N=108 Using IBM, IVBM, and BMM

The interacting boson and vector boson models, as well as the Bohr–Mottelson one, are employed to describe the energy levels and electromagnetic transitions of the 178Yb–186Pt (N = 108) nuclei. For the purpose of determining the evolution of the ground state, both r((I + 2)/I) and E-GOS ratios have been calculated as functions of the spin I. Based on the interacting vector boson model and Bohr–Mottelson model, the negative-parity and GSB bands have been calculated, while the interacting boson model is only employed to calculate GSB, y, and b. The interacting boson model is also used to calculate the reduced transition probabilities B(E2). The obtained findings show a very well agreement with experimentally obtained results elsewhere. We also used the intrinsic coherent state to obtain the potential energy surfaces. These results indicate that these nuclei have a rotational property SU(3), while 186Pt has property O(6).

Microscopic description of the even-even 140-148Ba isotopes using BM, IBM and IVBM

A description of the even-even Ba isotopes for A = 140 to 148 in framework of Bohr-Mottelson model, interacting boson model and interacting vector boson model are carried out. The E-GOS curve (E $\gamma$ /I and the ratio between the energies of the (I + 2) and (I) states (r(I + 2)/I) as a function of the spin (I have been drawn to determine the property of the ground-state band. The positive ground-state band of 140-148Ba has been calculated using Bohr-Mottelson model, interacting boson model and interacting vector boson model, while the negative-parity band of 140-148Ba has been calculated using Bohr-Mottelson model and interacting vector boson model only. The reduced transition probabilities B(E2) of these nuclei were calculated. The parameters of the best fit to the measured data are determined. The potential energy surfaces (PESs) to the IBM Hamiltonian have been obtained using the intrinsic coherent state.