Calculation Of Matrix Elements Research Articles

Measurement of the cross section for mathrm{t}overline{mathrm{t}} production with additional jets and b jets in pp collisions at sqrt{s} = 13 TeV

Measurements of the cross section for the production of top quark pairs in association with a pair of jets from bottom quarks left({sigma}_{mathrm{t}overline{mathrm{t}}mathrm{b}overline{mathrm{b}}}right) and in association with a pair of jets from quarks of any flavor or gluons left({sigma}_{mathrm{t}overline{mathrm{t}}mathrm{jj}}right) and their ratio are presented. The data were collected in proton-proton collisions at a center-of-mass energy of 13 TeV by the CMS experiment at the LHC in 2016 and correspond to an integrated luminosity of 35.9 fb−1. The measurements are performed in a fiducial phase space and extrapolated to the full phase space, separately for the dilepton and lepton+jets channels, where lepton corresponds to either an electron or a muon. The results of the measurements in the fiducial phase space for the dilepton and lepton+jets channels, respectively, are {sigma}_{mathrm{t}overline{mathrm{t}}mathrm{jj}} = 2.36±0.02 (stat)±0.20 (syst) pb and 31.0±0.2 (stat)±2.9 (syst) pb, and for the cross section ratio 0.017 ± 0.001 (stat) ± 0.001 (syst) and 0.020 ± 0.001 (stat) ± 0.001 (syst). The values of {sigma}_{mathrm{t}overline{mathrm{t}}mathrm{b}overline{mathrm{b}}} are determined from the product of the {sigma}_{mathrm{t}overline{mathrm{t}}mathrm{jj}} and the cross section ratio, obtaining, respectively, 0.040±0.002 (stat)±0.005 (syst) pb and 0.62±0.03 (stat)±0.07 (syst) pb. These measurements are the most precise to date and are consistent, within the uncertainties, with the standard model expectations obtained using a matrix element calculation at next-to-leading order in quantum chromodynamics matched to a parton shower.

Study of H2O Polarizability Based on Data on Rovibrational Line Shifts by Buffer Gas Pressure

The study of the vibrational dependence of H2O polarizability α is based on the comparison of experimental and calculated line shifts induced by argon, nitrogen, and air pressure in different H2O vibrational bands. The dependence of α on the internal coordinate θ, which describes large-amplitude bending vibration in the molecule, is expressed by a power series. The coefficients of the power series were selected so as to ensure the best agreement between the calculated matrix elements 〈ψn|α(θ)|ψn〉 and the polarizability values α(n) derived from the analysis of experimental H2O absorption line shifts in nν2 vibrational bands by nitrogen, oxygen, air, and argon pressure. The rotational contributions in the effective H2O polarizability are calculated and discussed. The α(θ) representation found is compared with ab initio calculations.

Two-dimensional electron bound hole photoluminescence in GaAs in perpendicular magnetic fields

The photoluminescence of quasi two-dimensional (2D) electrons in modulation doped AlxGa1 − xAs-GaAs single heterostructure recombining with bound holes was studied at liquid helium temperatures in magnetic fields up to 9 T. Luminescence contributions from the ground and a weakly populated first excited 2D subband were observed as well as bulk-like contributions from the GaAs buffer. The 2D subband and the bulk signals are linked and oscillate with the magnetic field strength. It is not the filling factor that rules but the alignment of the two subband Landau-ladders paired with intersubband scattering that drives an oscillatory behavior of the subband populations. Asymmetric Landau-level transition line shapes indicate a perturbed 2D electron system. We performed a detailed analyses of Landau-level dependent line strengths, positions and half widths and compared the experiment with calculations of subband energies and transition matrix elements. The total electron density is not fixed in our experiment but decreases with magnetic field strength. This might indicate that the 2D system exchanges electrons with a reservoir and/or that the correlation between radiative and nonradiative recombination channels vary strongly with the magnetic field strength.

Simulating hard photon production with Whizard

One of the important goals of the proposed future hbox {e}^{+}hbox {e}^{-} collider experiments is the search for dark matter particles using different experimental approaches. The most general search approach is based on the mono-photon signature, which is expected when production of the invisible final state is accompanied by a hard photon from initial state radiation. Analysis of the energy spectrum and angular distributions of those photons can shed light on the nature of dark matter and its interactions. Therefore, it is crucial to be able to simulate the signal and background samples in a uniform framework, to avoid possible systematic biases. The Whizard program is a flexible tool, which is widely used by hbox {e}^{+}hbox {e}^{-} collaborations for simulation of many different “new physics” scenarios. We propose the procedure of merging the matrix element calculations with the lepton ISR structure function implemented in Whizard. It allows us to reliably simulate the mono-photon events, including the two main Standard Model background processes: radiative neutrino pair production and radiative Bhabha scattering. We demonstrate that cross sections and kinematic distributions of mono-photon in neutrino pair-production events agree with corresponding predictions of the mathcal{KK} MC, a Monte Carlo generator providing perturbative predictions for SM and QED processes, which has been widely used in the analysis of LEP data.

Finite-size effects in cylindrical topological insulators

We present a theoretical study of a nanowire made of a three-dimensional topological insulator. The bulk topological insulator is described by a continuum-model Hamiltonian, and the cylindrical-nanowire geometry is modelled by a hard-wall boundary condition. We provide the secular equation for the eigenergies of the systems (both for bulk and surface states) and the analytical form of the energy eigenfunctions. We describe how the surface states of the cylinder are modified by finite-size effects. In particular, we provide a 1/R expansion for the energy of the surface states up to second order. The knowledge of the analytical form for the wavefunctions enables the computation of matrix elements of any single-particle operators. In particular, we compute the matrix elements of the optical dipole operator, which describe optical absorption and emission, treating intra- and inter-band transition on the same footing. Selection rules for optical transitions require conservation of linear momentum parallel to the nanowire axis, and a change of 0 or ±1 in the total-angular-momentum projection parallel to the nanowire axis. The magnitude of the optical-transition matrix elements is strongly affected by the finite radius of the nanowire.

Quantum thermalization and Virasoro symmetry

We initiate a systematic study of high energy matrix elements of local operators in 2D CFT. Knowledge of these is required in order to determine whether the generalized eigenstate thermalization hypothesis (ETH) can hold in such theories. Most high energy states are high level Virasoro descendants, and by employing an oscillator representation of the Virasoro algebra we develop an efficient method for computing matrix elements of primary operators in such states. In parameter regimes where we expect (e.g. from AdS/CFT intuition) thermalization to occur, we observe striking patterns in the matrix elements: diagonal matrix elements are smoothly varying and off-diagonal elements, while nonzero, are power-law suppressed compared to the diagonal elements. We discuss the implications of these universal properties of 2D CFTs in regard to their compatibility with generalized ETH.

Exact Green's function approach to RKKY interactions

The Green's function~(GF) of two localized magnetic moments embedded in the electron gas is calculated exactly. The electrons are treated in the effective mass approximation and the magnetic moments are coupled with electrons by a delta-like~$s-d$ interaction. The resulting GF is obtained by the exact summation of the Born series using a generalization of the method developed by Slater-Koster and Ziman to non-commuting spin operators with the use of the Woodbury identities. The exact GF crucially depends on the value of the one-electron GF at the origin, denoted as~$g_0$. The Born series is convergent only if~$g_0$ is finite, which holds for electrons in parabolic energy bands in~$1D$, but not in~$2D$ and~$3D$. In the general case, the exact GF includes nonlinear combination of localized spins operators. A method of calculating matrix elements of these operators is given. For spins~$S_a=S_b = 1/2$ the exact GF is expressed as a linear combination of components of~$\hS_a, \hS_b$, and the exact range function~${\cal J}(r)$ is obtained as a double integral over analytical expression. For electron energy~$E=0$ and~$J g_0/2 = 2$ or~$J g_0/2=-2/3$ the range function and GF are singular. Poles of GF occur in the vicinities of singularity points and the resulting energies of bound states are calculated. There are three regimes of~$J$. For small $J$ the range function resembles RKKY one: it has the same period~$\pi/k_F$, the same decay character and a slightly different amplitude, usually within a few percent. This regime occurs for most frequently in the nature. For~$|J|$ comparable to~$|g_0|^{-1}$ the exact range function differs qualitatively from RKKY one,. For large $|J|$ the exact range function oscillates with the same period and power-like decay as the usual RKKY function but it has much lower amplitude decaying with growing~$|J|$.

Calculation of the neutrinoless double- β decay matrix element within the realistic shell model

We approach the calculation of the nuclear matrix element of the neutrinoless double-beta decay process, considering the light-neutrino-exchange channel, by way of the realistic shell model. To this end, we start from a realistic nucleon-nucleon potential and then derive the effective shell-model Hamiltonian and neutrinoless double-beta decay operator within the many-body perturbation theory. We focus on investigating the perturbative properties of the effective shell-model operator of such a decay process, aiming to establish the degree of reliability of our predictions. The contributions of the so-called short-range correlations and of the correction of Pauli-principle violations to the effective shell-model operator, the latter introduced in many-valence nucleon systems, are also taken into account. The subjects of our study are a few candidates to the neutrinoless double-beta decay detection, in a mass interval ranging from A=48 up to A=136, whose spin- and spin-isospin-dependent decay properties we have studied in previous works. Our results will be finally compared with shell-model calculations for the same set of nuclei.

Reduced Common Molecular Orbital Basis for Nonorthogonal Configuration Interaction.

Electron and charge transfers are part of many vital processes in nature and technology. Ab initio descriptions of these processes provide useful insights that can be utilized for applications. A combination of the embedded cluster material model and nonorthogonal configuration interaction (NOCI), in which the cluster wave functions are expanded in many-electron basis functions (MEBFs) consisting of spin-adapted, antisymmetrized products of multiconfigurational wave functions of fragments (which are usually molecules) in the cluster, appears to provide a compromise between accuracy and calculation time. Additional advantages of this NOCI–Fragments approach are the chemically convenient interpretation of the wave function in terms of molecular states, and the direct accessibility of electronic coupling between diabatic states to describe energy and electron transfer processes. Bottlenecks in this method are the large number of two-electron integrals that have to be handled for the calculation of an electronic coupling matrix element and the enormous number of matrix elements over determinant pairs that have to be evaluated for the calculation of one matrix element between the MEBFs. We show here how we created a reduced common molecular orbital basis that is utilized to significantly reduce the number of two-electron integrals that need to be handled. The results obtained with this basis do not show any loss of accuracy in relevant quantities like electronic couplings and vertical excitation energies. We also show a significant reduction in computation time without loss in accuracy when matrix elements over determinant pairs with small weights are neglected in the NOCI. These improvements in the methodology render NOCI–Fragments to be also applicable to treat clusters of larger molecular systems with larger atomic basis sets and larger active spaces, as the computation time becomes dependent on the number of occupied orbitals and less dependent on the size of the active space.

One of the approaches for the analytical description of the interaction of an elastic wheel with a solid surface

The design of branched transmissions of multi-axle vehicles, multistage steering systems and automated workflow control systems requires their preliminary dynamic calculation. These calculations are based on mathematical models of structural elements corresponding to the modern level of development of system theory, i.e. taking into account dynamic interrelations between the system links. The aim of the work is to build a mathematical model of the automobile wheeled propulsor intended for use in the dynamic model of the “car-road” system or models of separate automobile systems. The approach to mathematical modeling of the automobile wheeled propulsor is offered, consisting in its description by methods of the control theory as an element of dynamic system. The method of construction and analysis of the complete system of equations of kinematic bonds superimposed in the contact zone on the movement of points of the external surface of the tire of linear elastic wheel at its perturbed rectilinear rolling on a solid uneven support surface is developed. The method of construction of a transfer matrix of automobile linear elastic wheel at which its structure practically does not depend on features of the settlement scheme of the tyres is developed too in this study. The method of obtaining the tire characteristics necessary for the calculation of the transfer matrix elements by the generalized method of successive approximations, which gives the qualitatively correct results in zero approximation, is proposed. The method of qualitative theoretical analysis of the features of rectilinear stationary rolling of the automobile wheel is given in this paper. The results allow to carry out researches and calculations of dynamic characteristics of automobile systems, units and assemblies directly interacting with the wheel; they can serve as a basis for further improvement of mathematical models of automobile ruts by methods of system theory.

Automated predictions from polarized matrix elements

The anticipated experimental resolution and data cache of the High Luminosity Large Hadron Collider will enable precision investigations of polarization in multiboson processes. This includes, for the first time, vector boson scattering. To facilitate such studies, we report the automation of polarized matrix element computations in the publicly available Monte Carlo tool suite, MadGraph5_aMC@NLO. This enables scattering and decay simulations involving helicity-polarized asymptotic or intermediate states, preserving both spin-correlation and off-shell effects. As demonstrations of the method, we investigate the leading order production and decay of polarized weak gauge bosons in the process ppto {jjW}_{lambda}^{+}{W}_{lambda prime}^{-} , with helicity eigenstates (λ, λ′) defined in various reference frames. We consider the Standard Model at both mathcal{O} (α4) and mathcal{O} (α2 {alpha}_s^2 ) as well as a benchmark composite Higgs scenario. We report good agreement with polarization studies based on the On-Shell Projection (OSP) technique. Future capabilities are discussed.

Variational Quantum Fidelity Estimation

Computing quantum state fidelity will be important to verify and characterize states prepared on a quantum computer. In this work, we propose novel lower and upper bounds for the fidelityF(ρ,σ)based on the ``truncated fidelity''F(ρm,σ), which is evaluated for a stateρmobtained by projectingρonto itsm-largest eigenvalues. Our bounds can be refined, i.e., they tighten monotonically withm. To compute our bounds, we introduce a hybrid quantum-classical algorithm, called Variational Quantum Fidelity Estimation, that involves three steps: (1) variationally diagonalizeρ, (2) compute matrix elements ofσin the eigenbasis ofρ, and (3) combine these matrix elements to compute our bounds. Our algorithm is aimed at the case whereσis arbitrary andρis low rank, which we call low-rank fidelity estimation, and we prove that no classical algorithm can efficiently solve this problem under reasonable assumptions. Finally, we demonstrate that our bounds can detect quantum phase transitions and are often tighter than previously known computable bounds for realistic situations.

Measurement of the cross section for $\text{t}\bar{\text{t}}$ production with additional jets and b jets in pp collisions at $\sqrt{s}=$ 13 TeV

Measurements of the cross section for the production of top quark pairs in association with a pair of jets from bottom quarks $ \left({\sigma}_{\mathrm{t}\overline{\mathrm{t}}\mathrm{b}\overline{\mathrm{b}}}\right) $ and in association with a pair of jets from quarks of any flavor or gluons $ \left({\sigma}_{\mathrm{t}\overline{\mathrm{t}}\mathrm{jj}}\right) $ and their ratio are presented. The data were collected in proton-proton collisions at a center-of-mass energy of 13 TeV by the CMS experiment at the LHC in 2016 and correspond to an integrated luminosity of 35.9 fb$^{−1}$. The measurements are performed in a fiducial phase space and extrapolated to the full phase space, separately for the dilepton and lepton+jets channels, where lepton corresponds to either an electron or a muon. The results of the measurements in the fiducial phase space for the dilepton and lepton+jets channels, respectively, are $ {\sigma}_{\mathrm{t}\overline{\mathrm{t}}\mathrm{jj}} $ = 2.36±0.02 (stat)±0.20 (syst) pb and 31.0±0.2 (stat)±2.9 (syst) pb, and for the cross section ratio 0.017 ± 0.001 (stat) ± 0.001 (syst) and 0.020 ± 0.001 (stat) ± 0.001 (syst). The values of $ {\sigma}_{\mathrm{t}\overline{\mathrm{t}}\mathrm{b}\overline{\mathrm{b}}} $ are determined from the product of the $ {\sigma}_{\mathrm{t}\overline{\mathrm{t}}\mathrm{jj}} $ and the cross section ratio, obtaining, respectively, 0.040±0.002 (stat)±0.005 (syst) pb and 0.62±0.03 (stat)±0.07 (syst) pb. These measurements are the most precise to date and are consistent, within the uncertainties, with the standard model expectations obtained using a matrix element calculation at next-to-leading order in quantum chromodynamics matched to a parton shower.[graphic not available: see fulltext]

Ab initio Calculations of the Lowest $$^{1}\Sigma _{g}^{ + }$$ States of the Na2 Dimer

The ground and 10 lowest excited $$^{1}\Sigma _{g}^{ + }$$ adiabatic electronic states of the Na2 dimer are calculated using the pseudopotential method. The use of the basis [7s6p5d4f] of atomic orbitals makes it possible to extend the range of available internuclear distances up to 1.7–50 A. It is found that the theoretical values of the Te and De constants are in a good agreement with the experimental ones. Herein you will find the sample calculations of the radial non-adiabatic coupling matrix elements enable to transform the basis of the adiabatic states to quasidiabatic one. It is found also that the Le Roy modified radius scales down the left boundary of an asymptotic range for the electronic state with the (3s + 5p) dissociation limit and for the higher states.

Lattice QCD Matrix Elements for the B_{s}^{0}-B[over ¯]_{s}^{0} Width Difference beyond Leading Order.

Predicting the B_{s}^{0}-B[over ¯]_{s}^{0} width difference ΔΓ_{s} relies on the heavy quark expansion and on hadronic matrix elements of ΔB=2 operators. We present the first lattice QCD results for matrix elements of the dimension-7 operators R_{2,3} and linear combinations R[over ˜]_{2,3} using nonrelativistic QCD for the bottom quark and a highly improved staggered quark (HISQ) action for the strange quark. Computations use MILC Collaboration ensembles of gauge field configurations with 2+1+1 flavors of sea quarks with the HISQ discretization, including lattices with physically light up or down quark masses. We discuss features unique to calculating matrix elements of these operators and analyze uncertainties from series truncation, discretization, and quark mass dependence. Finally we report the first standard model determination of ΔΓ_{s} using lattice QCD results for all hadronic matrix elements through O(1/m_{b}). The main result of our calculations yields the 1/m_{b} contribution ΔΓ_{1/m_{b}}=-0.022(10) ps^{-1}. Adding this to the leading order contribution, the standard model prediction is ΔΓ_{s}=0.092(14) ps^{-1}.

Neutrinoless double beta decay theory

Within left-right symmetric model a generalization of the Majorana neutrino mass for the case of light and and heavy neutrinos is introduced and analyzed. Further, current status of calculation of the neutrinoless double beta decay matrix elements is shortly reviewed. An important connection between them and matrix element of double Gamow-Teller operator is established. A new way of fixing quenching of axial-vector coupling constant gA is presented.

Emergence of conformal symmetry in quantum spin chains: Antiperiodic boundary conditions and supersymmetry

Universal properties of a critical quantum spin chain are encoded in the underlying conformal field theory (CFT). This underlying CFT is fully characterized by its conformal data. We propose a method to extract the conformal data from a critical quantum spin chain with both periodic and anti-periodic boundary conditions (PBC and APBC) based on low-energy eigenstates, generalizing previous work on spin chains with only PBC. First, scaling dimensions and conformal spins are extracted from the energies and momenta of the eigenstates. Second, the Koo-Saleur formula of lattice Virasoro generators is generalized to APBC and used to identify conformal towers. Third, local operators and string operators on the lattice are identified with CFT operators with PBC and APBC, respectively. Finally, operator product expansion coefficients are extracted by computing matrix elements of lattice primary operators in the low-energy subspaces with PBC and APBC. To go beyond exact diagonalization, tensor network methods based on periodic uniform matrix product states are used. We illustrate our approach with critical and tricritical Ising quantum spin chains. In the latter case, we propose lattice operators that correspond to supervirasoro generators and verify their action on low-energy eigenstates. In this way we explore the emergence of superconformal symmetry in the quantum spin chain.

Quadrupolar interactions between acceptor pairs in p -doped semiconductors

We consider the interaction between acceptor pairs in doped semiconductors in the limit of large inter-acceptor separation relevant for low doping densities. Modeling individual acceptors via the spherical model of Baldereschi and Lipari, we calculate matrix elements of the quadrupole tensor between the four degenerate ground states and show that the acceptor has a nonzero quadrupole moment. As a result, the dominant contribution to the large-separation acceptor-acceptor interaction comes from direct (charge-density) terms rather than exchange terms. The quadrupole is the leading nonzero moment, so the electric quadrupole-quadrupole interaction dominates for large separation. We calculate the matrix elements of the quadrupole-quadrupole interaction Hamiltonian in a product-state basis and diagonalize, obtaining a closed-form expression for the energies and degeneracies of the sixteen-state energy spectrum. All dependence on material parameters enters via an overall prefactor, resulting in surprisingly simple and universal results. This simplicity is due, in part, to a mathematical happenstance, the nontrivial vanishing of a particular Wigner 6-j symbol. Results are relevant to the control of two-qubit interactions in quantum computing implementations based on acceptor spins, as well as calculations of the thermodynamic properties of insulating p-type semiconductors.

Consistent large-scale shell-model analysis of the two-neutrino ββ and single β branchings in 48Ca and 96Zr

Two-neutrino double-beta-decay matrix elements M2ν and single beta-decay branching ratios were calculated for 48Ca and 96Zr in the interacting nuclear shell model using large single-particle valence spaces with well-tested two-body Hamiltonians. For 48Ca the matrix element M2ν=0.0511 is obtained, which is 5.5% smaller than the previously reported value of 0.0539. For 96Zr this work reports the first large-scale shell-model calculation of the nuclear matrix element, yielding a value M2ν=0.0747 with extreme single-state dominance. These matrix elements, combined with the available ββ-decay half-life data, yield effective values of the weak axial coupling which in turn are used to produce in a consistent way the β-decay branching ratios of (7.5±2.8)% for 48Ca and (18.4±0.09)% for 96Zr. These are larger than obtained in previous studies, implying that the detection of the β-decay branches could be possible in dedicated experiments sometime in the (near) future.

A Full Quantum Eigensolver for Quantum Chemistry Simulations.

Quantum simulation of quantum chemistry is one of the most compelling applications of quantum computing. It is of particular importance in areas ranging from materials science, biochemistry, and condensed matter physics. Here, we propose a full quantum eigensolver (FQE) algorithm to calculate the molecular ground energies and electronic structures using quantum gradient descent. Compared to existing classical-quantum hybrid methods such as variational quantum eigensolver (VQE), our method removes the classical optimizer and performs all the calculations on a quantum computer with faster convergence. The gradient descent iteration depth has a favorable complexity that is logarithmically dependent on the system size and inverse of the precision. Moreover, the FQE can be further simplified by exploiting a perturbation theory for the calculations of intermediate matrix elements and obtaining results with a precision that satisfies the requirement of chemistry application. The full quantum eigensolver can be implemented on a near-term quantum computer. With the rapid development of quantum computing hardware, the FQE provides an efficient and powerful tool to solve quantum chemistry problems.