Calculation Of Matrix Elements Research Articles

Generalized parton distributions from lattice QCD with asymmetric momentum transfer: Unpolarized quarks

Traditionally, lattice QCD computations of generalized parton distributions (GPDs) have been carried out in a symmetric frame, where the transferred momentum is symmetrically distributed between the incoming and outgoing hadrons. However, such frames are inconvenient since they require a separate calculation for each value of the momentum transfer, increasing significantly the computational cost. In this work, by focusing on the quasi-distribution approach, we lay the foundation for faster and more effective lattice QCD calculations of GPDs exploiting asymmetric frames, with freedom in the transferred momentum distribution. An important ingredient of our approach is the Lorentz covariant parameterization of the matrix elements in terms of Lorentz-invariant amplitudes, which allows one to relate matrix elements in different frames. We also use this amplitude approach to propose a new definition of quasi-GPDs that is frame-independent and, more importantly, may lead to smaller power corrections in the matching relations to the light-cone GPDs. We demonstrate the efficacy of the formalism through numerical calculations using one ensemble of $N_f$=2+1+1 twisted mass fermions with a clover improvement. The value of the light-quark masses lead to a pion mass of about 260 MeV. Concentrating on the proton, and limiting ourselves to a vanishing longitudinal momentum transfer to the target, we extract the invariant amplitudes from matrix element calculations in both the symmetric and asymmetric frame, and obtain results for the twist-2 light-cone GPDs for unpolarized quarks, that is, $H$ and $E$.

Neutrinoless double- β decay: Combining quantum Monte Carlo and the nuclear shell model with the generalized contact formalism

We devise a framework based on the generalized contact formalism that combines the nuclear shell model and quantum Monte Carlo methods and compute the neutrinoless double-beta decay of experimentally relevant nuclei, including $^{76}$Ge, $^{130}$Te, and $^{136}$Xe. In light nuclei, we validate our nuclear matrix element calculations by comparing against accurate variational Monte Carlo results. Due to additional correlations captured by quantum Monte Carlo and introduced within the generalized contact formalism, in heavier systems, we obtain long-range nuclear matrix elements that are about 30% smaller than previous shell-model results. We also evaluate the recently recognized short-range nuclear matrix element estimating its coupling by the charge-independence-breaking term of the Argonne $v_{18}$ potential used in the Monte Carlo calculations. Our results indicate an enhancement of the total nuclear matrix element by around 30%.

Quantum electrodynamics in the null-plane causal perturbation theory. II.

We develop a complete formulation of quantum gauge invariance in light-front dynamics for interacting theories with massless vector gauge fields in the framework of null-plane causal perturbation theory. We apply the general results to quantum electrodynamics, showing that the so-called "gauge terms" present in the photon commutation distribution when quantized under the null-plane gauge condition have no contribution in the calculation of the physical S-operator matrix elements at any order. We use this result to prove the normalizability of the theory, and to calculate the electron's self-energy at second order.

Discovering neutrinoless double-beta decay in the era of precision neutrino cosmology

We evaluate the discovery probability of a combined analysis of proposed neutrinoless double-beta decay experiments in a scenario with normal ordered neutrino masses. The discovery probability strongly depends on the value of the lightest neutrino mass, ranging from zero in case of vanishing masses and up to 80--90% for values just below the current constraints. We study the discovery probability in different scenarios, focusing on the exciting prospect in which cosmological surveys will measure the sum of neutrino masses. Uncertainties in nuclear matrix element calculations partially compensate each other when data from different isotopes are available. Although a discovery is not granted, the theoretical motivations for these searches and the presence of scenarios with high-discovery probability strongly motivates the proposed international, multi-isotope experimental program.

Theoretical research on the relationships between aromatic ligands and spectroscopic properties of Pt(II) complexes

A series of cyclometalated platinum (II) complexes with aromatic ligands, such as pyridyl, pyrimidinyl, and pyrazolate, were investigated with theoretical calculations. To investigate the relationship between ligands with molecular orbital, molecular rigidity, electroluminescent properties, and spectroscopic properties, the electrostatic potential (ESP), density-of-states (DOS), and root mean squared displacement (RMSD) were calculated. On the basis of calculated absorption and phosphorescence data, the analysis of ‘hole’ and ‘electron’ have also been performed. From the RMSD and spin–orbit coupling (SOC) matrix elements calculations, complex 3 shows significant structural distortions on S1 state and it may be applied in thermal activation delayed fluorescence (TADF) materials. The electroluminescent properties calculations show that complex 1 is suitable for hole transport material and complex 4 can be applied to electron transport material.

Multinode Multi-GPU Two-Electron Integrals: Code Generation Using the Regent Language.

The computation of two-electron repulsion integrals (ERIs) is often the most expensive step of integral-direct self-consistent field methods. Formally it scales as O(N4), where N is the number of Gaussian basis functions used to represent the molecular wave function. In practice, this scaling can be reduced to O(N2) or less by neglecting small integrals with screening methods. The contributions of the ERIs to the Fock matrix are of Coulomb (J) and exchange (K) type and require separate algorithms to compute matrix elements efficiently. We previously implemented highly efficient GPU-accelerated J-matrix and K-matrix algorithms in the electronic structure code TeraChem. Although these implementations supported the use of multiple GPUs on a node, they did not support the use of multiple nodes. This presents a key bottleneck to cutting-edge ab initio simulations of large systems, e.g., excited state dynamics of photoactive proteins. We present our implementation of multinode multi-GPU J- and K-matrix algorithms in TeraChem using the Regent programming language. Regent directly supports distributed computation in a task-based model and can generate code for a variety of architectures, including NVIDIA GPUs. We demonstrate multinode scaling up to 45 GPUs (3 nodes) and benchmark against hand-coded TeraChem integral code. We also outline our metaprogrammed Regent implementation, which enables flexible code generation for integrals of different angular momenta.

Modeling of unidirectional radiation of microdisk resonators with small piercing holes by Galerkin method with accurately computed matrix elements

Using the integral-equation-based in-house guaranteed-convergence numerical code, we study the effect of a circular air hole on the frequency, threshold gain and directionality of emission of the whispering-gallery modes of a two-dimensional model of circular-disk microcavity laser. It is shown that a small hole can enhance the directionality greatly and leave the threshold gain intact, if the disk‘s refractive index is large enough and the hole‘s location is chosen properly. This location should be close to the area, in which the same uniform disk, if illuminated with a plane wave, would display a broadband focusing in the form of a hot spot called a photonic jet.

THE THEORY OF QUASISTATIONARY ENERGY STATES IN A SPHERICAL POTENTIAL WELL

Quasi-stationary electronic states in a spherically symmetric semiconductor potential well are determined in the semiclassical approximation based on the calculation of matrix elements of the transfer matrix. In this case, three regions of the potential well were taken into account, which differ from each other in geometric dimensions. The calculation was carried out by solving the Schrödenger equation in a spherical coordinate system. KEYWORDS: quasistationary electronic states, spherically symmetric semiconductor potential well, semiclassical approximation, matrix elements of the transfer matrix

Multireference Approach to Normal and Resonant Auger Spectra Based on the One-Center Approximation.

A methodology to calculate the decay rates of normal and resonant Auger processes in atoms and molecules based on the One-Center Approximation (OCA), using atomic radial Auger integrals, is implemented within the restricted-active-space self-consistent-field (RASSCF) and the multistate restricted-active-space perturbation theory of second order (MS-RASPT2) frameworks, as part of the OpenMolcas project. To ensure an unbiased description of the correlation and relaxation effects on the initial core excited/ionized states and the final cationic states, their wave functions are optimized independently, whereas the Auger matrix elements are computed with a biorthonormalized set of molecular orbitals within the state-interaction (SI) approach. As a decay of an isolated resonance, the computation of Auger intensities involves matrix elements with one electron in the continuum. However, treating ionization and autoionization problems can be overwhelmingly complicated for nonexperts, because of many peculiarities, in comparison to bound-state electronic structure theory. One of the advantages of our approach is that by projecting the intensities on the atomic center bearing the core hole and using precalculated atomic radial two-electron integrals, the Auger decay rates can be easily obtained directly with OpenMolcas, avoiding the need to interface it with external programs to compute matrix elements with the photoelectron wave function. The implementation is tested on the Ne atom, for which numerous theoretical and experimental results are available for comparison, as well as on a set of prototype closed- and open-shell molecules, namely, CO, N2, HNCO, H2O, NO2, and C4N2H4 (pyrimidine).

Towards precise collider predictions: the Parton Branching method

The collinear factorization theorem, combined with finite-order calculations in perturbative QCD, provides a powerful framework to obtain predictions for many collider observables. However, for observables which involve multiple energy scales, transverse degrees of freedom cannot be neglected, and finite-order perturbative calculations have to be combined with resummed calculations to all orders in the QCD running coupling in order to obtain reliable theoretical predictions, capable of describing experimental measurements. This is traditionally done either by analytic resummation methods or by parton shower (PS) Monte Carlo (MC) methods. In this talk we present the Parton Branching (PB) MC method to obtain QCD collider predictions based on Transverse Momentum Dependent (TMD) factorization. The PB provides evolution equations for TMD Parton Distribution Functions (PDFs) which, upon fitting TMD PDFs to experimental data, can be used in TMD MC event generators. We present the basic concepts of the method and illustrate its applications to collider measurements focusing on Drell-Yan (DY) lepton-pair production in different kinematic ranges, from fixed-target to LHC energies. We discuss the latest developments of the method concentrating especially on the matching of next-to-leading-order (NLO) TMD evolution with MC-at-NLO calculations of NLO matrix elements.

Detailed analysis of excited-state systematics in a lattice QCD calculation of gA

Excited state contamination remains one of the most challenging sources of systematic uncertainty to control in lattice QCD calculations of nucleon matrix elements and form factors: early time separations are contaminated by excited states and late times suffer from an exponentially bad signal-to-noise problem. High-statistics calculations at large time separations $\gtrsim1$ fm are commonly used to combat these issues. In this work, focusing on $g_A$, we explore the alternative strategy of utilizing a large number of relatively low-statistics calculations at short to medium time separations (0.2--1 fm), combined with a multi-state analysis. On an ensemble with a pion mass of approximately 310 MeV and a lattice spacing of approximately 0.09 fm, we find this provides a more robust and economical method of quantifying and controlling the excited state systematic uncertainty. A quantitative separation of various types of excited states enables the identification of the transition matrix elements as the dominant contamination. The excited state contamination of the Feynman-Hellmann correlation function is found to reduce to the 1% level at approximately 1 fm while for the more standard three-point functions, this does not occur until after 2 fm. Critical to our findings is the use of a global minimization, rather than fixing the spectrum from the two-point functions and using them as input to the three-point analysis. We find that the ground state parameters determined in such a global analysis are stable against variations in the excited state model, the number of excited states, and the truncation of early-time or late-time numerical data.

Quenching of jets tagged with W bosons in high-energy nuclear collisions

We carry out the first detailed calculations of jet production associated with $W$ gauge bosons in Pb+Pb collisions at the Large Hadron Collider (LHC). In our calculations, the production of $W$+jet in p+p collisions as a reference is obtained by Sherpa, which performs next-to-leading-order matrix element calculations matched to the resummation of parton shower simulations, while jet propagation and medium response in the quark-gluon plasma are simulated with the Linear Boltzmann Transport (LBT) model. We provide numerical predictions on seven observables of $W$+jet production with jet quenching in Pb+Pb collisions: the medium modification factor for the tagged jet cross sections $I_{AA}$, the distribution in invariant mass between the two leading jets in $N_{jets}\ge 2$ events $m_{jj}$, the missing $p_T$ or the vector sum of the lepton and jet transverse momentum $|\vec{p}_T^{Miss}|$, the summed scalar $p_T$ of all the jets in an event $S_T$, transverse momentum imbalance $x_{jW}$, average number of jets per $W$ boson $R_{jW}$, and azimuthal angle between the $W$ boson and jets $\Delta \phi_{jW}$. The distinct nuclear modifications of these seven observables in Pb+Pb relative to that in p+p collisions are presented with detailed discussions.

Pfaffian formulation for matrix elements of three-body operators in multiple quasiparticle configurations

We present a Pfaffian formula to calculate matrix elements of three-body operators in symmetry-restoration beyond-mean-field methods, including the case of multiple quasiparticle (qp) configurations. Detailed derivation is provided and the validity of the new formula is checked numerically. The corresponding efficiency is discussed, which turns out to be about five times (one order of magnitude) higher than the conventional method when four (less than four) qp operators are considered.

Shell-model calculation of Mo100 double- β decay

For the first time, the calculation of the nuclear matrix element of the double-$\beta$ decay of $^{100}$Mo, with and without the emission of two neutrinos, is performed in the framework of the nuclear shell model. This task is accomplished starting from a realistic nucleon-nucleon potential, then the effective shell-model Hamiltonian and decay operators are derived within the many-body perturbation theory. The exotic features which characterize the structure of Mo isotopes -- such as shape coexistence and triaxiality softness -- push the shell-model computational problem beyond its present limits, making it necessary to truncate the model space. This has been done with the goal to preserve as much as possible the role of the rejected degrees of freedom in an effective approach that has been introduced and tested in previous studies. This procedure is grounded on the analysis of the effective single-particle energies of a large-scale shell-model Hamiltonian, that leads to a truncation of the number of the orbitals belonging to the model space. Then, the original Hamiltonian generates a new one by way of a unitary transformation onto the reduced model space, to retain effectively the role of the excluded single-particle orbitals. The predictivity of our calculation of the nuclear matrix element for the neutrinoless double-$\beta$ decay of $^{100}$Mo is supported by the comparison with experiment of the calculated spectra, electromagnetic transition strengths, Gamow-Teller transition strengths and the two-neutrino double-beta nuclear matrix elements.

High-precision Q-value measurement and nuclear matrix element calculations for the double-beta decay of ^{98}Mo

The ^{98}Mo double-beta decay Q-value has been measured, and the corresponding nuclear matrix elements of neutrinoless double-beta (0nu beta beta ) decay and the standard two-neutrino double-beta (2nu beta beta ) decay have been provided by nuclear theory. The double-beta decay Q-value has been determined as Q_{beta beta }=113.668(68) keV using the JYFLTRAP Penning trap mass spectrometer. It is in agreement with the literature value, Q_{beta beta }=109(6) keV, but almost 90 times more precise. Based on the measured Q-value, precise phase-space factors for 2nu beta beta decay and 0nu beta beta decay, needed in the half-life predictions, have been calculated. Furthermore, the involved nuclear matrix elements have been computed in the proton–neutron quasiparticle random-phase approximation (pnQRPA) and the microscopic interacting boson model (IBM-2) frameworks. Finally, predictions for the 2nu beta beta decay are given, suggesting a much longer half-life than for the currently observed cases.

Pair production of magnetic monopoles and stable high-electric-charge objects in proton–proton and heavy-ion collisions

We describe pair-production models of spin-0 and spin-½ magnetic monopoles and high-electric-charge objects (HECOs) in proton–proton (pp) and heavy-ion collisions, considering both the Drell–Yan (DY) and the photon-fusion processes. In particular, we extend the DY production model of spin-½ HECOs to include Z 0-boson exchange for pp collisions. Furthermore, we explore spin-½ and, for the first time, spin-0 production in ultraperipheral heavy-ion collisions. With matrix element calculations and equivalent photon fluxes implemented in MadGraph5_aMC@NLO, we present leading-order production cross sections of these mechanisms in TeV pp collisions and TeV ultraperipheral lead–lead collisions at the LHC. While the mass range accessible in ultraperipheral lead–lead collisions is much lower than that in pp collisions, we find that the theoretical production cross sections are significantly enhanced in the former for masses below 82 GeV.

Peculiarities of matrix-element calculations with few Coulomb functions for particles' scattering processes

We present ultra high resolution data on single ionization of helium under impact of 1-MeV protons in comparison with theoretical calculations. Good agreement between theory and experiment [1] is obtained. Three initial trial helium wave functions are employed: a weakly correlated Roothaan-Hartree-Fock function, a simple Silverman-Platas-Matsen function ofthe configuration interaction family, and a strongly correlated function [2,3]. Multidimensional singular integrals which defining differential cross sections are calculated using special transform for each above trial function. Results of some calculations arepresented in Figure 1.

Form factors for the processes Bc+→D0ℓ+νℓ and Bc+→Ds+ℓ+ℓ−(νν¯) from lattice QCD

We present results of the first lattice QCD calculations of the weak matrix elements for the decays $B_c^+ \to D^0 \ell^+ \nu_{\ell}$, $B_c^+ \to D_s^+ \ell^+ \ell^-$ and $B_c^+ \to D_s^+ \nu \overline{\nu}$. Form factors across the entire physical $q^2$ range are then extracted and extrapolated to the continuum limit with physical quark masses. Results are derived from correlation functions computed on MILC Collaboration gauge configurations with three different lattice spacings and including 2+1+1 flavours of sea quarks in the Highly Improved Staggered Quark (HISQ) formalism. HISQ is also used for all of the valence quarks. The uncertainty on the decay widths from our form factors is similar in size to that from the present value for $V_{ub}$. We obtain the ratio $\Gamma (B_{c}^{+} \rightarrow D^0 \mu^{+} \nu_{\mu}) /\left|\eta_{\mathrm{EW}} V_{u b}\right|^{2}=4.43(63) \times 10^{12} \mathrm{~s}^{-1}$. Combining our form factors with those found previously by HPQCD for $B_{c}^{+} \rightarrow J / \psi \mu^{+} \nu_{\mu}$, we find $\left|V_{cb}/V_{ub} \right|^2 \Gamma( B_c^+ \to D^0 \mu^+ \nu_\mu )/\Gamma(B_{c}^{+} \rightarrow J / \psi \mu^{+} \nu_{\mu}) = 0.257(36)_{B_c \to D}(18)_{B_c \to J/\psi}$. We calculate the differential decay widths of $B_c^+ \to D_s^+ \ell^+ \ell^-$ across the full $q^2$ range, and give integrated results in $q^2$ bins that avoid possible effects from charmonium and $u \overline{u}$ resonances. For example, we find that the ratio of differential branching fractions integrated over the range $q^2 = 1 \; \mathrm{GeV}^2 - 6 \; \mathrm{GeV}^2$ for $B_c^+ \to D_s^+ \mu^+ \mu^-$ and $B_{c}^{+} \rightarrow J / \psi \mu^{+} \nu_{\mu}$ is $5.23{\tiny }(73)_{B_c \to D_s}(54)_{B_c \to J/\psi} \times 10^{-6}$. We also give results for the branching fraction of $B_c^+ \to D_s^+ \nu \overline{\nu}$. Prospects for reducing our errors in the future are discussed.

Measurement of double-parton scattering in inclusive production of four jets with low transverse momentum in proton-proton collisions at sqrt{s} = 13 TeV

A measurement of inclusive four-jet production in proton-proton collisions at a center-of-mass energy of 13 TeV is presented. The transverse momenta of jets within |η| < 4.7 are required to exceed 35, 30, 25, and 20 GeV for the first-, second-, third-, and fourth-leading jet, respectively. Differential cross sections are measured as functions of the jet transverse momentum, jet pseudorapidity, and several other observables that describe the angular correlations between the jets. The measured distributions show sensitivity to different aspects of the underlying event, parton shower modeling, and matrix element calculations. In particular, the interplay between angular correlations caused by parton shower and double-parton scattering contributions is shown to be important. The double-parton scattering contribution is extracted by means of a template fit to the data, using distributions for single-parton scattering obtained from Monte Carlo event generators and a double-parton scattering distribution constructed from inclusive single-jet events in data. The effective double-parton scattering cross section is calculated and discussed in view of previous measurements and of its dependence on the models used to describe the single- parton scattering background.

Sensitivity of Future \(e^+e^-\) Colliders to Processes of Dark Matter Production with Light Mediator Exchange

One of the primary goals of the proposed future collider experiments is to search for dark matter (DM) particles using different experimental approaches. High energy $e^+e^-$ colliders offer unique possibility for the most general search based on the mono-photon signature. As any $e^+e^-$ collision process may include hard initial-state photon radiation, analysis of the energy spectrum and angular distributions of observed photons can be used to search for hard processes with an invisible final state. Dedicated procedure of merging the matrix element calculations with the lepton ISR structure function was developed to model the Standard Model background processes contributing to mono-photon signature with WHIZARD. In this work, we consider production of DM particles at the International Linear Collider (ILC) and Compact Linear Collider (CLIC) experiments via a mediator exchange. Detector effects are taken into account within the DELPHES fast simulation framework. Limits on the light DM production in a simplified model are set as a function of the mediator mass and width based on the expected two-dimensional distributions of the reconstructed mono-photon events. The experimental sensitivity is extracted in terms of the DM production cross section. Limits on the mediator couplings are then presented for a wide range of mediator masses and widths. For light mediators, for masses up to the centre-of-mass energy of the collider, coupling limits derived from the mono-photon analysis are more stringent than those expected from direct resonance searches in decay channels to SM particles.