Calculation Of Matrix Elements Research Articles

Neutron-proton pairing and double- β decay in the interacting boson model

Background: The interacting boson model (IBM) has been used extensively to calculate the matrix elements governing neutrinoless double-beta decay. Studies within other models indicate that a good description of neutron-proton pairing is essential for accurate calculations of those matrix elements. The usual interacting boson model is based only on like-particle pairs, however, and the extent to which it captures neutron-proton pairing is not clear. Purpose: To determine whether neutron-proton pairing should be explicitly included as neutron-proton bosons in IBM calculations of neutrinoless double-beta decay matrix elements. Method: An isospin-invariant version of the nucleon-pair shell model is applied to carry out shell-model calculations in a large space and in a collective subspace, and to define effective operators in the latter. A democratic mapping is then used to define corresponding boson operators for the IBM, with and without an isoscalar neutron-proton pair boson. Results: IBM calculations with and without the isoscalar boson are carried out for nuclei near the beginning of the $pf$ shell, with a realistic shell-model Hamiltonian and neutrinoless double-beta-decay operator as the starting point. Energy spectra and double-beta matrix elements are compared to those obtained in the underlying shell model. Conclusions: The isoscalar boson does not improve energy spectra but does improve double-beta matrix elements. To be useful at the level of precision we need, the mapping procedure must be further developed to better determine the dependence of the boson Hamiltonian and decay operator on particle number and isospin. But the benefits provided by the isoscalar boson suggest that through an appropriate combination of mappings and fitting, it would make IBM matrix elements more accurate for the heavier nuclei used in experiments.

Nuclear Matrix Elements for Tests of Local Lorentz Invariance Violation.

The nuclear matrix elements for the spin operator and the momentum quadrupole operator are important for the interpretation of precision atomic physics experiments that search for violations of local Lorentz and CPT symmetry and for new spin-dependent forces. We use the configuration-interaction nuclear shell model and self-consistent mean-field theory to calculate the momentum matrix elements for ^{21}Ne, ^{23}Na, ^{133}Cs, ^{173}Yb, and ^{201}Hg. We show that these momentum matrix are strongly suppressed by the many-body correlations, in contrast to the well-known enhancement of the spatial quadrupole nuclear matrix elements.

Automated calculation of matrix elements and physics motivated observables

The central aspect of my personal scientific activity, has focused on calculations useful for interpretation of High Energy accelerator experimental results, especially in a domain of precision tests of the Standard Model. My activities started in early 80’s, when computer support for algebraic manipulations was in its infancy. But already then it was important for my work. It brought a multitude of benefits, but at the price of some inconvenience for physics intuition. Calculations became more complex, work had to be distributed over teams of researchers and due to automatization, some aspects of the intermediate results became more difficult to identify.In my talk I will not be very exhaustive, I will present examples from my personal research only: (i) calculations of spin effects for the process e+e− → τ+τ−γ at Petra/PEP energies, calculations (with the help of the Grace system of Minami-tateya group) and phenomenology of spin amplitudes for (ii) e+e− → 4f and for (iii) e+e− → νeν̄eγγ processes, (iv) phenomenology of CP-sensitive observables for Higgs boson parity in H → τ+τ−, τ± → ν2(3)π cascade decays.

Measurement of the differential cross sections for the associated production of a W boson and jets in proton-proton collisions at s=13 TeV

A measurement of the differential cross sections for a W boson produced in association with jets in the muon decay channel is presented. The measurement is based on 13 TeV proton-proton collision data corresponding to an integrated luminosity of 2.2 inverse femtobarns, recorded by the CMS detector at the LHC. The cross sections are reported as functions of jet multiplicity, jet transverse momentum pT, jet rapidity, the scalar pT sum of the jets, and angular correlations between the muon and the jet for different jet multiplicities. The measured cross sections are in agreement with predictions that include multileg leading-order (LO) and next-to-LO matrix element calculations interfaced with parton showers, as well as a next-to-next-to-LO calculation for the W boson and one jet production.

Direct CP asymmetry in D → π−π+ and D → K−K+ in QCD-based approach

We present the first QCD-based calculation of hadronic matrix elements with penguin topology determining direct CP-violating asymmetries in D0→π−π+ and D0→K−K+ nonleptonic decays. The method is based on the QCD light-cone sum rules and does not rely on any model-inspired amplitude decomposition, instead leaning heavily on quark–hadron duality. We provide a Standard Model estimate of the direct CP-violating asymmetries in both pion and kaon modes and their difference and comment on further improvements of the presented computation.

Ferrocene Molecular Architectures Grafted on Si(111): A Theoretical Calculation of the Standard Oxidation Potentials and Electron Transfer Rate Constant.

The standard oxidation potential and the electron transfer (ET) rate constants of two silicon-based hybrid interfaces, Si(111)/organic-spacer/Ferrocene, are theoretically calculated and assessed. The dynamics of the electrochemical driven ET process is modeled in terms of the classical donor/acceptor scheme within the framework of “Marcus theory”. The ET rate constants, , are determined following calculation of the electron transfer matrix element, , together with the knowledge of the energy of the neutral and charge separated systems. The recently introduced Constrained Density Functional Theory (CDFT) method is exploited to optimize the structure and determine the energy of the charge separated species. Calculated ET rate constants are and , in the case of the short and long organic-spacer, respectively.

Second moment of the pion distribution amplitude with the momentum smearing technique

Using the second moment of the pion distribution amplitude as an example, we investigate whether lattice calculations of matrix elements of local operators involving covariant derivatives may benefit from the recently proposed momentum smearing technique for hadronic interpolators. Comparing the momentum smearing technique to the traditional Wuppertal smearing we find—at equal computational cost—a considerable reduction of the statistical errors. The present investigation was carried out using Nf=2+1 dynamical non-perturbatively order a improved Wilson fermions on lattices of different volumes and pion masses down to 220 MeV.

Erratum to: “An optimization method for the calculation of Hamiltonian matrix elements for Josephson flux qubits”

Erratum to: “An optimization method for the calculation of Hamiltonian matrix elements for Josephson flux qubits”

Search for double β-decays of 124Xe with XENON100 & XENON1T

The rare nuclear process of two-neutrino double electron capture, where two electrons are simultaneously captured from the atomic shell, has not yet been observed for 124Xe. A detection of this decay would provide a new reference for nuclear matrix element calculations. Moreover, if a neutrinoless mode were discovered, it would prove a Majorana nature of neutrinos and would shed light on the effective neutrino mass. The XENON dark matter project, with its dual-phase xenon time projection chambers XENON100 and XENON1T, is well suited for this rare event searches with signatures in the keV-region. The search with the XENON100 detector, containing 29 g of 124Xe, is explained as well as the outlook of its successor XENON1T, which contains 2 kg of the isotope in its active volume.

Measurement of the double-β decay half-life and search for the neutrinoless double-β decay of 48Ca with the NEMO-3 detector

Neutrinoless double-β decay is a powerful probe of lepton number violating processes that may arise from Majorana terms in neutrino masses, or from supersymmetric, left-right symmetric, and other extensions of the Standard Model. Of the candidate isotopes for the observation of this process, 48Ca has the highest Qββ-value, resulting in decays with energies significantly above most naturally occurring backgrounds. The nucleus also lends itself to precise matrix element calculations within the nuclear shell model. We present the world’s best measurement of the two-neutrino double-β decay of 48Ca, obtained by the NEMO-3 collaboration using 5.25 yr of data recorded with a 6.99 g sample of isotope, yielding ≈ 150 events with a signal to background ratio larger than 3. Neutrinoless modes of double-β decay are also investigated, with no evidence of new physics. Furthermore, these results indicate that two-neutrino double-β decay would be the main source of background for similar future searches using 48Ca with significantly larger exposures.

Isotropic matrix elements of the collision integral for the Boltzmann equation

We have proposed an algorithm for constructing matrix elements of the collision integral for the nonlinear Boltzmann equation isotropic in velocities. These matrix elements have been used to start the recurrent procedure for calculating matrix elements of the velocity-nonisotropic collision integral described in our previous publication. In addition, isotropic matrix elements are of independent interest for calculating isotropic relaxation in a number of physical kinetics problems. It has been shown that the coefficients of expansion of isotropic matrix elements in Ω integrals are connected by the recurrent relations that make it possible to construct the procedure of their sequential determination.

Universal analytic form of optical matrix elements in Boron Nitride nanotubes

Because of the structure and then arrangement of Boron and Nitrogen atoms in the cylindrical form of Boron Nitride nanotubes, their optical properties strongly depend on the polarization direction of the incident light. The challenge of describing the optical properties of Boron Nitride nanotubes is mainly related to the calculation of dipole matrix elements. In this paper analytic expressions for the electric dipole matrix elements of single wall Boron Nitride nanotubes with arbitrary chirality for light polarized parallel and perpendicular to the nanotube axis have been obtained and then used to investigate the linear susceptibility of Boron Nitride nanotubes, semi-analytically.

On the Feynman-Hellmann theorem in quantum field theory and the calculation of matrix elements

The Feynman-Hellmann theorem can be derived from the long Euclidean-time limit of correlation functions determined with functional derivatives of the partition function. Using this insight, we fully develop an improved method for computing matrix elements of external currents utilizing only two-point correlation functions. Our method applies to matrix elements of any external bilinear current, including nonzero momentum transfer, flavor-changing, and two or more current insertion matrix elements. The ability to identify and control all the systematic uncertainties in the analysis of the correlation functions stems from the unique time dependence of the ground-state matrix elements and the fact that all excited states and contact terms are Euclidean-time dependent. We demonstrate the utility of our method with a calculation of the nucleon axial charge using gradient-flowed domain-wall valence quarks on the $N_f=2+1+1$ MILC highly improved staggered quark ensemble with lattice spacing and pion mass of approximately 0.15 fm and 310 MeV respectively. We show full control over excited-state systematics with the new method and obtain a value of $g_A = 1.213(26)$ with a quark-mass-dependent renormalization coefficient.

Role of the Euclidean signature in lattice calculations of quasidistributions and other nonlocal matrix elements

Lattice quantum chromodynamics (QCD) provides the only known systematic, nonperturbative method for first-principles calculations of nucleon structure. However, for quantities such as lightfront parton distribution functions (PDFs) and generalized parton distributions (GPDs), the restriction to Euclidean time prevents direct calculation of the desired observable. Recently, progress has been made in relating these quantities to matrix elements of spatially nonlocal, zero-time operators, referred to as quasidistributions. Even for these time-independent matrix elements, potential subtleties have been identified in the role of the Euclidean signature. In this work, we investigate the analytic behavior of spatially non-local correlation functions and demonstrate that the matrix elements obtained from Euclidean lattice QCD are identical to those obtained using the LSZ reduction formula in Minkowski space. After arguing the equivalence on general grounds, we also show that it holds in a perturbative calculation, where special care is needed to identify the lattice prediction. Finally we present a proof of the uniqueness of the matrix elements obtained from Minkowski and Euclidean correlation functions to all order in perturbation theory.

Spectroscopic characterization of N = 9 armchair graphene nanoribbons

We investigate the N = 9 atoms wide armchair‐type graphene nanoribbons (9‐AGNRs) by performing a comprehensive spectroscopic and microscopic characterization of this novel material. In particular, we use X‐ray photoelectron, near edge X‐ray absorption fine structure, scanning tunneling, polarized Raman and angle‐resolved photoemission (ARPES) spectroscopies. The ARPES measurements are aided by calculations of the photoemission matrix elements which yield the position in k space having the strongest photoemission cross section. Comparison with well‐studied narrow N = 7 AGNRs shows that the effective electron mass in 9‐AGNRs is reduced by two times and the valence band maximum is shifted to lower binding energy by ∼0.6 eV. In polarized Raman measurements of the aligned 9‐AGNR, we reveal anisotropic signal depending upon the phonon symmetry. Our results indicate the 9‐AGNRs are a novel 1D semiconductor with a high potential in nanoelectronic applications.

Self-similar analogues of Stark ladders: a path to fractal potentials

We treat the eigenvalue problem posed by self-similar potentials, i.e. homogeneous functions under a particular affine transformation, by means of symmetry techniques. We find that the eigenfunctions of such problems are localized, even when the potential does not rise to infinity in every direction. It is shown that the logarithm of the energy displays levels contained in families that are analogous to Wannier-Stark ladders. The position of each ladder is proved to be determined by the specific details of the potential and not by its transformation properties. This is done by direct computation of matrix elements. The results are compared with numerical solutions of the Schr\"odinger equation.

Lam-Tung relation breaking in Z0 hadroproduction as a probe of parton transverse momentum

The Lam-Tung relation breaking coefficient $A_{\mathrm{LT}} = A_0 - A_2$ in the Drell-Yan dilepton angular distributions in the $Z^0$ boson mass region at the LHC is analyzed in the $k_T$-factorization approach. This observable was recently measured with high precision by ATLAS collaboration. Within the $k_T$-factorization approach we perform an approximate ${\cal O}(\alpha_{\mathrm{em}}\alpha_s^2)$ calculation of the off-shell parton hard matrix elements in which we include the leading tree level contributions of valence quarks and off-shell gluons: the $q_{\mathrm{val}} g^* \to qZ^0$ channel and the $g^*g^* \to q\bar q Z^0$ channel. The resulting $A_{\mathrm{LT}}$ exhibits high sensitivity to the gluon transverse momentum distribution (TMD). Several gluon TMDs are probed derived from the CCFM and BFKL evolution equations, and given by QCD-inspired phenomenological parameterizations. The ATLAS data favor a simple "Weizs\"acker-Williams" (WW) hard gluon TMD with the asymptotic behavior of one-gluon exchange at large gluon transverse momenta and moderate $x$. It is verified that the proposed approach with the WW gluon TMD describes well also the $A_0$ and $A_2$ angular coefficients at the $Z^0$ peak, as well as the Drell-Yan dilepton mass distribution at lower masses. We conclude that inclusion of gluon transverse momentum effects improves description of the angular distributions of Drell-Yan dileptons and that the Drell-Yan scattering provides an excellent probe of the parton TMDs.

Calculation of Gamow-Teller and two-neutrino double- β decay properties for Te130 and Xe136 with a realistic nucleon-nucleon potential

We report on the calculation of Gamow-Teller and double-beta decay properties for nuclei around 132Sn within the framework of the realistic shell model. The effective shell-model Hamiltonian and Gamow-Teller transition operator are derived by way of many-body perturbation theory, without resorting to empirical effective quenching factor for the Gamow-Teller operator. The results are then compared with the available experimental data, in order to establish the reliability of our approach. This is a mandatory step, before we apply the same methodology, in forthcoming studies, to the calculation of the neutrinoless double-beta decay nuclear matrix element for nuclei that are currently considered among the best candidates for the detection of this process.

Multiple gross errors detection, identification and correction in three-phase distribution systems WLS state estimation: A per-phase measurement error approach

This paper presents an analytical methodology for multiple measurement gross error detection, identification and correction for three-phase distribution systems weighted least square (WLS) state estimation. Initially, a three-phase WLS state estimator, considering the inherent distribution systems characteristics, as unbalance operation and different load types, is presented. Extended formulations for Jacobian matrix elements calculation, relating to different load models are proposed. Detection, identification and correction of gross errors are performed considering hypothesis testing in a per-phase component approach. Gross error detection is made through a Chi-square (χ2) Hypothesis Testing (HT) applied to the phase composed measurement error (CME). Composed errors are estimated with measurements’ phase innovation index (II). Gross error identification is made through the Largest Normalized Error Test property. Gross error correction is made considering the phase composed normalized error (CNE). A method to correct pseudo measurements identified as having gross errors is proposed. Validation is made with the IEEE 123 bus test system. Comparative tests with the state of art are presented. Test results are encouraging, indicating potential aspects for real-life applications.

A new sequential AC–DC power flow algorithm for multi‐terminal HVDC systems

This paper presents a new algorithm based on the sequential method for power flow calculation in integrated multi‐terminal, high‐voltage, direct current (HVDC) systems. Unlike similar studies in the literature, a real equivalent circuit model is considered for under‐load tap changer (ULTC) transformers of the DC converters, for the first time. So, new DC equations are obtained. Thus, exact and accurate results can be obtained for practical applications by the proposed algorithm. Adjustment effects of the DC converters' ULTCs tap values are included in the Jacobian matrix instead of the bus admittance matrix in the sequential AC power flow algorithm as well as other ULTCs in AC system. To this aim, new equations for the calculation of power and Jacobian matrix elements are obtained for the AC system. The proposed approach is tested on the modified IEEE 17‐bus AC–DC test system. Numerical results show that the proposed approach is accurate and reliable in convergence. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.