Nonrelativistic Formalism Research Articles

Radiative dynamics of laser-driven Li@C n embedded in quantum plasma

This work considers a guest Lithium atom (Li@C n ) in an endohedral fullerene, embedded in a quantum plasma modeled by the more general exponential cosine screened Coulomb (MGECSC) potential, under the influence of a spherical confinement and laser radiation field. The system is examined in nonrelativistic form and the related wave equation is solved using the tridiagonal matrix method (TMM), thus obtaining the discrete-continuum spectrum and related wave functions. The numerical values of the relevant parameters in this process are physically accessible values. The effects of the plasma, laser field and endohedral cavity on the photoionization cross section (PCS) are analysed in detail. The shielding effect of the plasma medium and the pulsating effect of the laser field modify the effective potential energy of the system, affecting the localizations of the 2s and continuum states, causing various overlapping cases. Considering different values of the endohedral encompassement parameters, which means that different types of fullerenes are taken into account, overlapping cases occur for different spectra and wave functions. Scrutinising these overlappings, the confinement and Cooper resonances of the PCSs are analysed. This analysis provides many details for the radiative dynamics of an artificial system Li@C n . The relevant ranges and critical values of plasma, laser field, and endohedral encapsulation parameters in the formation process of these resonances and PCSs are explained, as well as the cross-section curves, resonance positions, effective photoelectron energy range, and general PCS behavior, which can be important for potential experiments in addition to other theoretical investigations.

Quantum Scalar Field Theory Based on an Extended Least Action Principle

Recently it is shown that the non-relativistic quantum formulations can be derived from an extended least action principle Yang (2023). In this paper, we apply the principle to massive scalar fields, and derive the Schrödinger equation of the wave functional for the scalar fields. The principle extends the least action principle in classical field theory by factoring in two assumptions. First, the Planck constant defines the minimal amount of action a field needs to exhibit in order to be observable. Second, there are constant random field fluctuations. A novel method is introduced to define the information metrics to measure additional observable information due to the field fluctuations, which is then converted to the additional action through the first assumption. Applying the variation principle to minimize the total actions allows us to elegantly derive the transition probability of field fluctuations, the uncertainty relation, and the Schrödinger equation of the wave functional. Furthermore, by defining the information metrics for field fluctuations using general definitions of relative entropy, we obtain a generalized Schrödinger equation of the wave functional that depends on the order of relative entropy. Our results demonstrate that the extended least action principle can be applied to derive both non-relativistic quantum mechanics and relativistic quantum scalar field theory. We expect it can be further used to obtain quantum theory for non-scalar fields.

Structure and reaction studies of $$Z=120$$ isotopes using non-relativistic and relativistic mean-field formalisms

Structure and reaction studies of $$Z=120$$ isotopes using non-relativistic and relativistic mean-field formalisms

Vector Quarkonia at the LHC with Jethad: A High-Energy Viewpoint

In this review, we discuss and extend the study of the inclusive production of vector quarkonia, J/ψ and Υ, emitted with large transverse momenta and rapidities at the LHC. We adopt the novel ZCW19+ determination of fragmentation functions to depict the quarkonium production mechanism at the next-to-leading level of perturbative QCD. This approach is based on the nonrelativistic QCD formalism well adapted to describe the formation of a quarkonium state from the collinear fragmentation of a gluon or a constituent heavy quark at the lowest energy scale. We rely upon the NLL/NLO+ hybrid high-energy and collinear factorization for differential cross-sections, where the collinear formalism is enhanced by the BFKL resummation of next-to-leading energy logarithms arising in the t-channel. We employ the method to analyze the behavior of the rapidity distributions for double-inclusive vector quarkonium and inclusive vector quarkonium plus jet emissions. We discover that the natural stability of the high-energy series, previously seen in observables sensitive to the emission of hadrons with heavy flavor detected in the rapidity acceptance of LHC barrel calorimeters, becomes even more manifest when these particles are tagged in forward regions covered by endcaps. Our findings present the important message that vector quarkonia at the LHC via hybrid factorization offer a unique chance to perform precision studies of high-energy QCD, as well as an intriguing opportunity to shed light on the quarkonium production puzzle.

A Variational Approach to Resistive General Relativistic Two-Temperature Plasmas

We develop an action principle to construct the field equations for dissipative/resistive general relativistic two-temperature plasmas, including a neutrally charged component. The total action is a combination of four pieces: an action for a multifluid/plasma system with dissipation/resistivity and entrainment; the Maxwell action for the electromagnetic field; the Coulomb action with a minimal coupling of the four-potential to the charged fluxes; and the Einstein–Hilbert action for gravity (with the metric being minimally coupled to the other action pieces). We use a pull-back formalism from spacetime to abstract matter spaces to build unconstrained variations for the neutral, positively, and negatively charged fluid species and for three associated entropy flows. The full suite of field equations is recast in the so-called “3+1” form (suitable for numerical simulations), where spacetime is broken up into a foliation of spacelike hypersurfaces and a prescribed “flow-of-time”. A previously constructed phenomenological model for the resistivity is updated to include the modified heat flow and the presence of a neutrally charged species. We impose baryon number and charge conservation as well as the Second Law of Thermodynamics in order to constrain the number of free parameters in the resistivity. Finally, we take the Newtonian limit of the “3+1” form of the field equations, which can be compared to existing non-relativistic formulations. Applications include main sequence stars, neutron star interiors, accretion disks, and the early universe.

Spectroscopy of Heavy–Heavy Flavour Mesons and Annihilation Widths of Quarkonia

Within the framework of nonrelativistic quark-antiquark Cornell potential model formalism, we study the annihilation of heavy quarkonia. We determine their annihilation widths resulting into digluon, dilepton, $3\gamma$, $3g$ and $\gamma gg$ and compare our findings with the available theoretical results and experimental data. We also provide the charge radii and absolute square of radial Schr\"odinger wave function at zero quark-antiquark separation for heavy quarkonia and $B_c$ mesons.

Nucleon-nucleon scattering up to next-to-next-to-leading order in manifestly Lorentz-invariant chiral effective field theory: Peripheral phases

We study the nucleon-nucleon interaction up to next-to-next-to-leading order using time-ordered perturbation theory in the framework of manifestly Lorentz-invariant chiral effective field theory. We present the two-pion exchange contribution at one-loop level, which is consistent with the corresponding non-relativistic expressions in the large-nucleon-mass limit. Using the Born series truncated at one-loop order, we calculate the phase shifts and mixing angles of the partial waves with the angular momentum $l\geq 2$. Comparing with the results of non-relativistic formulation, we find an improved description of the phase shifts for some $D$ waves such as the $^3D_3$ one. For the other partial waves, both approaches show the globally similar results.

Nonrelativistic axion electrodynamics in p+is superconductors

In previous works, axion electrodynamics in three-dimensional $p+is$ superconductors is discussed by borrowing the results from superconducting Dirac systems. However, in this work, based on a systematic path integral approach, we show that the axion electrodynamics in $p+is$ superconductors exhibits a nonrelativistic form, which is different from the superconducting Dirac and Weyl systems. More precisely, the induced electric field does not enter into the axion action, and gauge invariance is ensured by the combination of the electric potential and the Nambu-Goldstone phase mode. Furthermore, unlike the axion angle in the Dirac case which is equal to the difference between the superconducting phases on the two Fermi surfaces of different helicities, the axion angle in the present case contains an additional sinusoidal term. As applications of the derived nonrelativistic axion electrodynamics, physical effects related to vortex lines and Witten effect are discussed. Our work reveals the differences for axion electrodynamics between the relativistic and nonrelativistic systems.

Production and polarization of S -wave quarkonia in potential nonrelativistic QCD

Based on the potential nonrelativistic QCD formalism, we compute the nonrelativistic QCD long-distance matrix elements (LDMEs) for inclusive production of $S$-wave heavy quarkonia. This greatly reduces the number of nonperturbative unknowns and brings in a substantial enhancement in the predictive power of the nonrelativistic QCD factorization formalism. We obtain improved determinations of the LDMEs and find cross sections and polarizations of $J/\ensuremath{\psi}$, $\ensuremath{\psi}(2S)$, and excited $\mathrm{\ensuremath{\Upsilon}}$ states that agree well with LHC data. Our results may have important implications in pinning down the heavy quarkonium production mechanism.

Macroscopic Reality from Quantum Complexity

Beginning with the Everett–DeWitt many-worlds interpretation of quantum mechanics, there have been a series of proposals for how the state vector of a quantum system might split at any instant into orthogonal branches, each of which exhibits approximately classical behavior. Here we propose a decomposition of a state vector into branches by finding the minimum of a measure of the mean squared quantum complexity of the branches in the branch decomposition. In a non-relativistic formulation of this proposal, branching occurs repeatedly over time, with each branch splitting successively into further sub-branches among which the branch followed by the real world is chosen randomly according to the Born rule. In a Lorentz covariant version, the real world is a single random draw from the set of branches at asymptotically late time, restored to finite time by sequentially retracing the set of branching events implied by the late time choice. The complexity measure depends on a parameter b with units of volume which sets the boundary between quantum and classical behavior. The value of b is, in principle, accessible to experiment.

Bottomonium production and polarization in the NRQCD with k_T-factorization. III: Upsilon (1S) and chi _b(1P) mesons

The Upsilon (1S) meson production and polarization at high energies is studied in the framework of the k_T-factorization approach. Our consideration is based on the non-relativistic QCD formalism for a bound states formation and off-shell production amplitudes for hard partonic subprocesses. The direct production mechanism, feed-down contributions from radiative chi _b(mP) decays and contributions from Upsilon (3S) and Upsilon (2S) decays are taken into account. The transverse momentum dependent (TMD) gluon densities in a proton were derived from the Ciafaloni–Catani–Fiorani–Marchesini evolution equation and the Kimber-Martin–Ryskin prescription. Treating the non-perturbative color octet transitions in terms of multipole radiation theory, we extract the corresponding non-perturbative matrix elements for Upsilon (1S) and chi _b(1P) mesons from a combined fit to transverse momenta distributions measured at various LHC experiments. Then we apply the extracted values to investigate the polarization parameters lambda _theta , lambda _phi and lambda _{theta phi }, which determine the Upsilon (1S) spin density matrix. Our predictions have a reasonably good agreement with the currently available Tevatron and LHC data within the theoretical and experimental uncertainties.

Thermal impacts on the properties of nuclear matter and young neutron star

We present a methodical study of the thermal and nuclear properties for the hot nuclear matter using relativistic-mean field theory. We examine the effects of temperature on the binding energy, pressure, thermal index, symmetry energy, and its derivative for the symmetric nuclear matter using temperature-dependent relativistic mean-field formalism for the well-known G2⁎ and recently developed IOPB-I parameter sets. The critical temperature for the liquid-gas phase transition in an asymmetric nuclear matter system has also been calculated and collated with the experimentally available data. We investigate the approach of the thermal index as a function of nucleon density in the wake of relativistic and non-relativistic formalism. The computation of neutrino emissivity through the direct Urca process for the supernovae remnants has also been performed, which manifests some exciting results about the thermal stabilization and evolution of the newly born proto-neutron star. The central temperature and the maximum mass of the proto-neutron star have also been calculated for different entropy values.

BFV quantization of the nonprojectable ( 2+1 )-dimensional Hořava theory

We show that the Batalin-Fradkin-Vilkovisky (BFV) quantization scheme can be implemented in the nonprojectable ($2+1$)-Ho\ifmmode \check{r}\else \v{r}\fi{}ava theory. This opens the possibility of imposing more general gauge conditions in the quantization of this theory. The BFV quantization is based on the canonical formalism, which is suitable to incorporate the measure associated to the second-class constraints that the theory has. Special features of the Hamiltonian density and the matrix of second-class constraints allow that the system be involutive in terms of Dirac brackets, which is a nontrivial requisite for implementing the BFV formalism. We present the Becchi-Rouet-Stora-Tyutin symmetry transformations in the canonical variables. The theory is of rank one in the classification introduced by Fradkin and Fradkina. The originally called relativistic gauge-fixing conditions of the BFV formalism can be implemented in the nonprojectable Ho\ifmmode \check{r}\else \v{r}\fi{}ava theory, extended to nonrelativistic forms. We show that the nonlocal gauge condition introduced in the projectable theory can be included among these gauges.

Extracting the number of short-range correlated nucleon pairs from inclusive electron scattering data

The extraction of the relative abundances of short-range correlated (SRC) nucleon pairs from inclusive electron scattering is studied using the generalized contact formalism (GCF) with several nuclear interaction models. GCF calculations can reproduce the observed scaling of the cross-section ratios for nuclei relative to deuterium at high-$x_B$ and large-$Q^2$, $a_2=(\sigma_A/A)/(\sigma_d/2)$. In the non-relativistic instant-form formulation, the calculation is very sensitive to the model parameters and only reproduces the data using parameters that are inconsistent with ab-initio many-body calculations. Using a light-cone GCF formulation significantly decreases this sensitivity and improves the agreement with ab-initio calculations. The ratio of similar mass isotopes, such as $^{40}$Ca and $^{48}$Ca, should be sensitive to the nuclear asymmetry dependence of SRCs, but is found to also be sensitive to low-energy nuclear structure. Thus the empirical association of SRC pair abundances with the measured $a_2$ values is only accurate to about $20\%$. Improving this will require cross-section calculations that reproduce the data while properly accounting for both nuclear structure and relativistic effects.

Chi _{c1} and chi _{c2} polarization as a probe of color octet channel

We analyze joint LHC data on the production of chi _{c1} and chi _{c2} mesons together with the polarization data obtained very recently by the CMS Collaboration at sqrt{s} = 8 TeV. Our consideration is based on the k_T-factorization approach and nonrelativistic QCD formalism for the formation of bound states. The observed polar anisotropy of chi _{c1} and chi _{c2} decays can be described as a combined effect of the color-singlet and color-octet contributions. We extract the corresponding long-distance matrix elements from the fits. Our fits point to unequal color singlet wave functions for chi _{c1} and chi _{c2} states.

Nonlocal Interferences Induced by the Phase of the Wavefunction for a Particle in a Cavity with Moving Boundaries

We investigate the dynamics of a particle in a confined periodic system—a time-dependent oscillator confined by infinitely high and moving walls—and focus on the evolution of the phase of the wavefunction. It is shown that, for some specific initial states in this potential, the phase of the wavefunction throughout the cavity depends on the walls motion. We further elaborate a thought experiment based on interferences devised to detect this form of single-particle nonlocality from a relative phase. We point out that, within the non-relativistic formalism based on the Schrödinger equation (SE), detecting this form of nonlocality can give rise to signaling. We believe this effect is an artifact, but the standard relativistic corrections to the SE do not appear to fix it. Specific illustrations are given, with analytical results in the adiabatic approximation, and numerical computations to show that contributions from high-energy states (corresponding to superluminal velocities) are negligible.

Spin-polarized β -stable neutron star matter: The nuclear symmetry energy and GW170817 constraint

Magnetic field of rotating pulsar might be so strong that the equation of state (EOS) of neutron star (NS) matter is significantly affected by the spin polarization of baryons. In the present work, the EOS of the spin-polarized nuclear matter is investigated in the nonrelativistic Hartree-Fock formalism, using a realistic density dependent nucleon-nucleon interaction with its spin and spin-isospin dependence accurately adjusted to the Brueckner-Hartree-Fock results for the spin-polarized nuclear matter. The nuclear symmetry energy and proton fraction are found to increase significantly with the increasing spin polarization of baryons, leading to a larger probability of the direct Urca process in the cooling of magnetar. The EOS of the $\beta$-stable np$e\mu$ matter obtained at different spin polarizations of baryons is used as the input for the Tolman-Oppenheimer-Volkov equations to determine the hydrostatic configuration of NS. Based on the GW170817 constraint on the radius $R_{1.4}$ of NS with $M\approx 1.4_\odot$, our mean-field results show that up to $60~\%$ of baryons in the NS merger might be spin-polarized. This result supports the magnetar origin of the blue kilonova ejecta of GW170817 suggested by Metzger et al., and the spin polarization of baryons needs, therefore, to be properly treated in the many-body calculation of the EOS of NS matter before comparing the calculated NS mass and radius with those constrained by the multi-messenger GW170817 observation.

Bottomonium spectroscopy motivated by general features of pNRQCD

The bottomonium mass spectra are computed in the framework of potential non-relativistic quantum chromodynamics. The potential consists of a static term incorporating the Coulomb plus confinement part along with a correction term added non-perturbatively from pNRQCD, which is classified in powers of the inverse of the heavy quark mass O(1/m). The masses of excited bottomonia are calculated by perturbatively adding spin–hyperfine, spin–orbit and tensor components of one-gluon exchange interactions in powers of O(1/m 2). Calculated masses are found to be consistent with other theoretical studies and experimental data. The Regge trajectories of the calculated mass spectra are also constructed. The values of the wave functions are extracted and employed to calculate the electromagnetic transition widths and γγ, e + e −, light hadron and γγγ decay widths of several states at various leading orders, within the non-relativistic QCD formalism. Some of the experimentally reported states of bottomonium family like ϒ(10 860), ϒ(11 020) and X(10 610) are identified as mixed S–D wave and P wave states.

EFT approach to general relativity: correction to EIH Lagrangian due to electromagnetic charge

We extend the Non-Relativistic formulation of General Relativity (NRGR) given in Goldberger et al. (Phys Rev D 73:104029, 2006) to incorporate the effects of electromagnetic charge of the constituents of the binary. We incorporate the photon field in NRGR by giving the field decomposition and power counting rules. Using these, we develop the Feynman rules to describe photon and graviton interactions with point particle worldline. We then find the corrections to the Einstein-Infeld-Hoffmann Lagrangian (Einstein et al. in Ann Math 39:65-100, 1938) due to the presence of the photon field and electromagnetic charge of the constituents of the binary.

Mass–radius relation and dynamical stability of strongly magnetized white dwarfs in anisotropic configuration using Bowers and Liang model

This paper is concerned with the effect of anisotropic pressure in the mass–radius relation and dynamical stability for strongly magnetized white dwarfs using Bowers and Liang model. Strongly magnetized white dwarfs is hot topic where it is believed that it can be a progenitor for some peculiar type Ia supernovae that was observed recently. In order to get the equation of state we assumed that the internal magnetic field strength of the star is constant and strong enough to oblige the electrons to occupy the first Landau level. We dealt with the problem by using both relativistic and non-relativistic equilibrium equations. In non-relativistic formalism, the mass–radius relation of the star was investigated and it is found that the dynamical stability of the star does not depend on the radius but on the mass of the star. In relativistic formalism, it is found that the radius of the star decreases in comparison with non-relativistic case. Also the maximum mass limit of the star does not exceed the non-relativistic one in isotropic case. Unfortunately, in both cases the predicted internal magnetic field of the star always exceeds the magnetic field strength needed for the stability. This leads to weaken the stability of the star and making the star deviates from the spherical configuration to oblate spheroidal shape. Thus according to this model the magnetic white dwarfs configurations are unstable and unbound.