Exact Matrix Elements Research Articles

Resonance-aware NLOPS matching for off-shell toverline{t} + tW production with semileptonic decays

The increasingly high accuracy of top-quark studies at the LHC calls for a theoretical description of toverline{t} production and decay in terms of exact matrix elements for the full 2 → 6 process that includes the off-shell production and the chain decays of toverline{t} and tW intermediate states, together with their quantum interference. Corresponding NLO QCD calculations matched to parton showers are available for the case of dileptonic channels and are implemented in the bb4l Monte Carlo generator, which is based on the resonance-aware POWHEG method. In this paper, we present the first NLOPS predictions of this kind for the case of semileptonic channels. In this context, the interplay of off-shell toverline{t} + tW production with various other QCD and electroweak subprocesses that yield the same semileptonic final state is discussed in detail. On the technical side, we improve the resonance-aware POWHEG procedure by means of new resonance histories based on matrix elements, which enable a realistic separation of toverline{t} and tW contributions. Moreover, we introduce a general approach which makes it possible to avoid certain spurious terms that arise from the perturbative expansion of decay widths in any off-shell higher-order calculation, and which are large enough to jeopardise physical finite-width effects. These methods are implemented in a new version of the bb4l Monte Carlo generator, which is applicable to all dileptonic and semileptonic channels, and can be extended to fully hadronic channels. The presented results include a NLOPS comparison of off-shell against on-shell toverline{t} + tW production and decay, where we highlight various non-trivial aspects related to NLO and parton-shower radiation in leptonic and hadronic top decays.

Numerical Modeling of Lattice Modes of Photonic-Crystal Lasers by Galerkin Method with Exact Matrix Elements

Numerical Modeling of Lattice Modes of Photonic-Crystal Lasers by Galerkin Method with Exact Matrix Elements

Nonequilibrium Dynamics and Weakly Broken Integrability.

Motivated by dynamical experiments on cold atomic gases, we develop a quantum kinetic approach to weakly perturbed integrable models out of equilibrium. Using the exact matrix elements of the underlying integrable model, we establish an analytical approach to real-time dynamics. The method addresses a broad range of timescales, from the intermediate regime of prethermalization to late-time thermalization. Predictions are given for the time evolution of physical quantities, including effective temperatures and thermalization rates. The approach provides conceptual links between perturbed quantum many-body dynamics and classical Kolmogorov-Arnold-Moser theory. In particular, we identify a family of perturbations which do not cause thermalization in the weakly perturbed regime.

Exact matrix elements of the field operator in the thermodynamic limit of the Lieb–Liniger model

We study a matrix element of the field operator in the Lieb–Liniger model using the Bethe ansatz technique coupled with a functional approach to compute Slavnov determinants. We obtain the matrix element exactly in the thermodynamic limit for any coupling constant c, and compare our results to known semiclassics at the limit c → 0

Exact density matrix elements for a driven dissipative system described by a quadratic Hamiltonian

For a prototype quadratic Hamiltonian describing a driven, dissipative system, exact matrix elements of the reduced density matrix are obtained from a generating function in terms of the normal characteristic functions. The approach is based on the Heisenberg equations of motion and operator calculus. The special and limiting cases are discussed.

Quantitative study on helicity inversion in Majorana neutrino decays at the LHC

We report an analytical and numerical investigation into the impact of helicity inversion in LHC processes that do not conserve lepton number ($L$). As a case study, we focus on the production and decay of Majorana neutrinos ($N$) through on- and off-shell $W$ bosons in the phenomenological type I seesaw model. Using the Monte Carlo event generator madgraph5_amc@nlo in conjunction with the heavyn model libraries, we perform exact matrix element (ME) computations without the narrow width approximation. Despite helicity inversion appearing explicitly in MEs, we report the absence of helicity suppression of $L$-violating collider observables for $1\ensuremath{\rightarrow}4$ and $2\ensuremath{\rightarrow}4$ processes that are dominated by resonant $N$ production. We attribute this incongruity to the different scalings of 4-momenta and squared 4-momenta in MEs and squared MEs, with exact cancelations occurring in the latter when $N$ goes on-shell in the small-width limit. In off-shell regimes, total suppression/enhancement of $L$ violation can emerge. Implications for other neutrino mass models are discussed.

Fast optimization of parametrized quantum optical circuits

Parametrized quantum optical circuits are a class of quantum circuits in which the carriers of quantum information are photons and the gates are optical transformations. Classically optimizing these circuits is challenging due to the infinite dimensionality of the photon number vector space that is associated to each optical mode. Truncating the space dimension is unavoidable, and it can lead to incorrect results if the gates populate photon number states beyond the cutoff. To tackle this issue, we present an algorithm that is orders of magnitude faster than the current state of the art, to recursively compute the exact matrix elements of Gaussian operators and their gradient with respect to a parametrization. These operators, when augmented with a non-Gaussian transformation such as the Kerr gate, achieve universal quantum computation. Our approach brings two advantages: first, by computing the matrix elements of Gaussian operators directly, we don't need to construct them by combining several other operators; second, we can use any variant of the gradient descent algorithm by plugging our gradients into an automatic differentiation framework such as TensorFlow or PyTorch. Our results will find applications in quantum optical hardware research, quantum machine learning, optical data processing, device discovery and device design.

Numerical scheme for evaluating the collision integrals for triple interactions in relativistic plasma

Binary interactions in relativistic plasma, such as Coulomb and Compton scattering as well as pair creation and annihilation are well known and studied in detail. Triple interactions, namely, relativistic bremsstrahlung, double Compton scattering, radiative pair production, and triple pair production and their inverse processes, are usually considered as emission processes in astrophysical problems, as well as in laboratory plasmas. Their role in plasma kinetics is fundamental [A. G. Aksenov et al., Phys. Rev. Lett. 99, 125003 (2007)]. We present a new conservative scheme for computation of the Uehling–Uhlenbeck collision integral for all triple interactions in relativistic plasma based on direct integration of exact QED matrix elements. Reaction rates for thermal distributions are compared, where possible, with the corresponding analytic expressions, showing good agreement. Our results are relevant for quantitative description of relativistic plasmas out of equilibrium, both under astrophysical and laboratory conditions.

Exact matrix elements for general two-body central-force interactions, expressed as sums of products

ABSTRACTIn a manner similar to but distinct from concurrent tensor efforts in electronic structure, it is shown that the Laplace transform can serve as a generator for a sum-of-products (SOP) form that allows one to write essentially any function of distance between two particles (i.e. any central force potential) as an exact two-body matrix. In particular, exact expressions for the Coulomb, Yukawa and long-range Ewald two-body operators are evaluated in a band-limited (Sinc function) basis. The resultant exact, full-basis, SOP representations for these interaction potentials – acting in conjunction with an external harmonic confining field – are validated via comparison with energy eigenstate solutions obtained via an independent calculation based on separation of variables. The new two-body matrix representations may have substantial impact in any of the many disciplines in which pair-wise central force interactions are relevant – especially, electronic structure and dynamics.

Thermalization of electron–positron plasma with quantum degeneracy

The non-equilibrium electron–positron–photon plasma thermalization process is studied using relativistic Boltzmann solver, taking into account quantum corrections both in non-relativistic and relativistic cases. Collision integrals are computed from exact QED matrix elements for all binary and triple interactions in the plasma. It is shown that in non-relativistic case (temperatures kBT≤0.3mec2) binary interaction rates dominate over triple ones, resulting in establishment of the kinetic equilibrium prior to final relaxation towards the thermal equilibrium, in agreement with the previous studies. On the contrary, in relativistic case (final temperatures kBT≥0.3mec2) triple interaction rates are fast enough to prevent the establishment of kinetic equilibrium. It is shown that thermalization process strongly depends on quantum degeneracy in initial state, but does not depend on plasma composition.

Tight-binding calculations of optical matrix elements for conductivity using nonorthogonal atomic orbitals: Anomalous Hall conductivity in bcc Fe

We present a general formula for the tight-binding representation of momentum matrix elements needed for calculating the conductivity based on the Kubo-Greenwood formula using atomic orbitals, which are in general not orthogonal to other orbitals at different sites. In particular, the position matrix element is demonstrated to be important for delivering the exact momentum matrix element. This general formula, applicable to both orthonormal and non-orthonormal bases, solely needs the information of the position matrix elements and the ingredients that have already contained in the tight-binding representation. We then study the anomalous Hall conductivity in the standard example, ferromagnetic bcc Fe, by a first-principles tight-binding Hamiltonian. By assuming the commutation relation $\hat{\vec{p}} = (i m_e/\hbar) [\hat{H},\hat{\vec{r}}]$, the obtained frequency-dependent Hall conductivity is found to be in good agreement with existing theoretical and experimental results. Better agreement with experiments can be reached by introducing a reasonable bandwidth renormalization, evidencing the strong correlation among 3$d$ orbitals in bcc Fe. Since a tight-binding Hamiltonian can be straightforwardly obtained after finishing a first-principles calculation using atomic basis functions that are generated before the self-consistent calculation, the derived formula is particularly useful for those first-principles calculations.

Low-frequency approximation for high-order harmonic generation by a bicircular laser field

We present low-frequency approximation (LFA) for high-order harmonic generation (HHG) process. LFA represents the lowest-order term of an expansion of the final-state interaction matrix element in powers of the laser-field frequency $\ensuremath{\omega}$. In this approximation the plane-wave recombination matrix element which appears in the strong-field approximation is replaced by the exact laser-free recombination matrix element calculated for the laser-field dressed electron momenta. First, we have shown that the HHG spectra obtained using the LFA agree with those obtained solving the time-dependent Schr\odinger equation. Next, we have applied this LFA to calculate the HHG rate for inert gases exposed to a bicircular field. The bicircular field, which consists of two coplanar counter-rotating fields having different frequencies (usually $\ensuremath{\omega}$ and $2\ensuremath{\omega}$), is presently an important subject of scientific research since it enables efficient generation of circularly polarized high-order harmonics (coherent soft x rays). Analyzing the photorecombination matrix element we have found that the HHG rate can efficiently be calculated using the angular momentum basis with the states oriented in the direction of the bicircular field components. Our numerical results show that the HHG rate for atoms having $p$ ground state, for higher high-order harmonic energies, is larger for circularly polarized harmonics having the helicity $\ensuremath{-}1$. For lower energies the harmonics having helicity $+1$ prevails. The transition between these two harmonic energy regions can appear near the Cooper minimum, which, in the case of Ar atoms, makes the selection of high-order harmonics having the same helicity much easier. This is important for applications (for example, for generation of attosecond pulse trains of circularly polarized harmonics).

Supernova-Explosion Mechanism Involving Neutrinos

A major part of the energy released upon the gravitational collapse of massive-star cores is carried away by neutrinos. Neutrinos play a crucial role in collapsing supernovae (SNe). At the present time, mathematical models of core-collapse SNe are based on multidimensional gas dynamics and thermonuclear reactions, whereas the neutrino transport is frequently treated in simplified way. An accurate analysis of neutrinos in a spherically symmetric gravitational collapse is performed on the basis of Boltzmann kinetic equations including all weak-interaction reactions with exact quantum-mechanical matrix elements. The role of multidimensional effects is studied bymeans of multidimensional gas dynamics allowing for the neutrino transport via diffusion treated by employing flux limiters. The possibility of largescale convection, which is of interest both from the point of view of explaining a type II supernova (SN) and from the point of view of implementing an experiment aimed at detecting possible energetic (≳10 MeV) neutrinos from an SN, is discussed. Thermonuclear burning leads to the explosion of a type I SN. A hot central region and the subsequent large-scale convection may also play an important role in the SN mechanism. If neutrinos and convection play a key role for a type II SN, then, in order to explain gamma radiation from product radioactive elements, convection is of importance in the case of SNe belonging to both types. In addition, convection may be important for bright type I SNe. Original methods are presented for multidimensional gas dynamics involving thermonuclear burning and for multitemperature gas dynamics involving radiative transfer.

Nonequilibrium photon production in partonic transport simulations

We discuss the implementation of leading-order photon production in nonequilibrium partonic transport simulations. In this framework photons are produced by microscopic scatterings, where we include the exact matrix elements of Compton scattering, quark-antiquark annihilation, and bremsstrahlung processes. We show how the hard-thermal loop inspired screening of propagators has to be modified such that the microscopic production rate agrees well with the analytically known resummed leading-order rate. We model the complete quark-gluon plasma phase of heavy-ion collisions by using the partonic transport approach called the Boltzmann approach to multiparton scatterings (BAMPS), which solves the ultrarelativistic Boltzmann equation with Monte Carlo methods. We show photon spectra and elliptic flow of photons from BAMPS and discuss nonequilibrium effects. Due to the slow quark chemical equilibration in BAMPS, the yield is lower than the results from other groups; in turn we see a strong effect from scatterings of energetic jet-like partons with the medium. This nonequilibrium photon production can dominate the thermal emission, such that the spectra are harder and the photonic elliptic flow of the quark-gluon plasma becomes negative.

An NLO+PS generator for $${\varvec{t \bar{t}}}$$ t t ¯ and $${\varvec{W t}}$$ W t production and decay including non-resonant and interference effects

We present a Monte Carlo generator that implements significant theoretical improvements in the simulation of top-quark pair production and decay at the LHC. Spin correlations and off-shell effects in top-decay chains are described in terms of exact matrix elements for $p p \to \ell^+\nu_{\scriptscriptstyle\ell}\, l^-\bar{\nu}_{\scriptscriptstyle l} b \bar{b}$ at NLO QCD, where the leptons $\ell$ and $l$ belong to different families, and $b$ quarks are massive. Thus, the contributions from $t\bar{t}$ and $Wt$ single-top production as well as their quantum interference are fully included. Matrix elements are matched to the Pythia8 parton shower using a recently proposed method that allows for a consistent treatment of resonances in the POWHEG framework. These theoretical improvements are especially important for the interpretation of precision measurements of the top-quark mass, for single-top analyses in the $Wt$ channel, and for $t\bar{t}$ and $Wt$ backgrounds in the presence of jet vetoes or cuts that enhance off-shell effects. The new generator is based on a process-independent interface of the OpenLoops amplitude generator with the POWHEGBOX framework.

Symmetry‐based Study of MoS2 and WS2 Nanotubes

AbstractThe symmetry‐based study of MS2 (M=Mo, W) single‐wall nanotubes (SWNTs) is reviewed. First, the structure and symmetry of MS2 NTs is determined. Then, conserved quantum numbers and general forms of potentials are derived. The valence force‐field method implemented into the POLSym code is used to calculate phonon dispersions. Phonons characterized by a zero angular‐momentum quantum number are studied in detail. The functional dependence of the frequency of rigid layer modes on NT diameter and chirality are found, and Raman‐ and infrared‐active modes are singled out. Electronic band structure calculations are performed by the symmetry‐based density functional tight‐binding (DFTB) method. Changes in the band‐gap type and size with NT chirality and diameter are evaluated. Optical absorption spectra of individual NTs are calculated using DFTB wave functions for exact transition matrix element calculations. Diffraction patterns of MS2 are predicted and NT characterization by different diffraction methods is discussed.

Multivalley envelope function equations and effective potentials for phosphorus impurity in silicon

We propose a system of real-space envelope function equations without fitting parameters for modeling the electronic spectrum and wave functions of a phosphorus donor atom embedded in silicon. The approach relies on the Burt-Foreman envelope function representation and leads to coupled effective-mass Schroedinger equations containing smooth effective potentials. These potentials result from the spatial filtering imposed on the exact potential energy matrix elements in the envelope function representation. The corresponding filter function is determined from the definition of the envelope function. The resulting effective potentials and the system of envelope functions jointly reproduce the valley-orbit coupling effect in the doped silicon. Including the valley-orbit coupling not only of the 1s, but also for 2s atomic orbitals, as well as static dielectric screening is found crucial to accurately reproduce experimental data. The measured binding energies are recovered with a maximum relative error of 1.53 %. The computed wave functions are in a good agreement with experimental measurements of the electron density provided by scanning tunneling microscopy.

Exact photoionization and radiative recombination cross section in a Coulomb potential

In this work, we analytically evaluate the exact matrix element for a non-relativistic Continuum-Bound radiative transition in a Coulomb potential. We apply this result to the photoionization (and radiative recombination) process, and calculate the total cross sections giving an analytical expression for the transition from the ground state. To our best knowledge the exact solution to this problem has never been addressed even though the analytical calculation is quite simple, and the final result is not more complicated than any of its approximations. We compare our result with the well-known plane wave and Coulombian dipolar approximations, in a wide range of energies.

Single-parton scattering versus double-parton scattering in the production of twocc¯pairs and charmed meson correlations at the LHC

We compare results of exact calculations of single parton scattering (SPS) and double parton scattering (DPS) for production of $c \bar c c \bar c$ and for $D$ meson correlations. The SPS calculations are performed in collinear approximation with exact matrix element for $g g \to c \bar c c \bar c$ and $q \bar q \to c \bar c c \bar c$ subprocesses. It is shown that the contribution of gluon-gluon subprocess is about factor 50 larger than that for quark-antiquark annihilation. The new results are compared with results of previous calculation with the approximate matrix element for $g g \to c \bar c c \bar c$ in the high-energy approximation. The cross section for the present exact calculation is bigger only at small invariant masses and small rapidity difference between two $c$ quarks (or two $\bar c$ antiquarks). We compare correlations in rapidities of two $c$ (or two $\bar c$) for DPS and SPS contributions. Finally we compare our predictions for $D$ mesons with recent results of the LHCb collaboration for invariant mass, rapidity distance between mesons and dimeson invariant mass. The predicted shapes are similar to the measured ones, however, some strength seems to be lacking. Our new calulations clearly confirm the dominance of DPS in the production of events with double charm.

The Sp(3, R) Sympletic Model: a comparison of exact and approximate matrix elements

The Sp(3, R) Sympletic Model: a comparison of exact and approximate matrix elements