Perturbative Coupling Research Articles

Bjorken polarised sum rule with IR-finite QCD coupling

We evaluate the Bjorken polarised sum rule (BSR) Γ‾1p−n(Q2) with truncated Operator Product Expansion (OPE) up to the dimension D=4 terms; the leading-twist (D=0) contribution is evaluated with a renormalon motivated resummation, where we use the IR-finite running coupling free of Landau singularities. The free residue parameters at the D=2 and D=4 terms are then extracted by fits to the experimental BSR data. In comparison to the case when perturbative QCD coupling is used in this approach (cf. Refs. [1,2]), many advantages become manifest in the present case: (a) no regularisation in the resummation integral is needed; (b) the Q2-interval in the fit can be significantly extended to lower Q2-values; (c) the extracted residue parameter values are more stable, this being reflected in the significantly reduced experimental uncertainties of these values and the suppressed (almost negligible) central extracted value of the D=4 residue parameter (μ6).

Quantum corrections to tunnelling amplitudes of neutral scalar fields

Though theoretical treatments of quantum tunnelling within single-particle quantum mechanics are well-established, at present, there is no quantum field-theoretic description (QFT) of tunnelling. Due to the single-particle nature of quantum mechanics, many-particle effects arising from quantum field theory are not accounted for. Such many-particle effects, including pair-production, have proved to be essential in resolving the Klein-paradox. This work seeks to determine how quantum corrections affect the tunnelling probability through an external field. We investigate a massive neutral scalar field, which interacts with an external field in accordance with relativistic quantum mechanics. To consider QFT corrections, we include another massive quantised neutral scalar field coupling to the original via a cubic interaction. This study formulates an all-order recursive expression for the loop-corrected scalar propagator, which contains only the class of vertex-corrected Feynman diagrams. This equation applies for general external potentials. Though there is no closed-form analytic solution, we also demonstrate how to approximate the QFT corrections if a perturbative coupling to the quantised field is assumed.

Effect of Pyrrolidinedithiocarbamate Ligand on the Luminescence Properties of Heteroligand Samarium and Europium Complexes: Experimental and Theoretical Study.

The photophysical properties of two isostructural heteroligand lanthanide complexes of general formula Ln(pdtc)3(phen) (pdtc = pyrrolidinedithiocarbamate anion, phen = 1,10-phenanthroline), Ln = Sm3+ (1), Eu3+ (2)) were studied in solid state and dichloromethane (DCM) solution. The two lanthanide complexes were investigated by experimental techniques for structural (single-crystal X-ray diffraction analysis of 1, powder XRD, TG-DTA) and spectroscopic [electron paramagnetic resonance (EPR), infrared (IR), ultraviolet-visible (UV-vis), photoluminescence (PL)] characterization. DFT/TDDFT/ωB97xD and multireference SA-CASSCF/NEVPT2 calculations with perturbative spin-orbit coupling corrections were applied to construct the Jablonski energy diagrams and to discuss the excited state energy transfer mechanism with competing excited state processes and possible sensitized mechanism of metal-centered emission. The first excited state (S1) involved in the excited state energy transfer L(antenna)-to-Ln was predicted to have interligand (pdtc-to-phen) charge transfer character in contrast to the previously predicted ligand-to-metal charge transfer character. The theoretical consideration showed similar relaxation paths and luminescence quenching channels and appropriate Donor*(phen)-Acceptor*(Ln3+) energy gap for 1 and 2. The experimental measurements in the solid state, however, showed efficient luminescence and good ability to convert UV to visible light only for the Sm(pdtc)3(phen) complex. The minor emission of 2 was explained by partial reduction of Eu3+, confirmed by EPR and calculated electron density distribution data.

Tunability in 3-Site Electronic Excitation Transfer Dynamics: Insights into the Role of Perturbative Coupling.

Electronic excitation transfer dynamics in photosynthetic systems, including the Fenna-Matthews-Olson complex, are often modeled using the interaction picture of three two-level systems, also known as the 3-site system. Among the two possible configurations, uphill and downhill, a recent publication reported an intriguing correlation between population dynamics and the intersite coupling. Specifically, the uphill configuration has been shown to have a pronounced dependence on perturbations in the intersite coupling, whereas the downhill configuration displays negligible dependence. In this study, we consider a generic 3-site configuration and model site interactions through the Markovian master equation. Through this approach, we derive succinct analytical expressions for the population dynamics between the sites, shedding light on the differences in behavior between the two configurations. Using these analytical expressions, we demonstrate the range of tunability in population dynamics achievable with minimal changes in intersite coupling, and we validate these findings through simulation results. These insights into the population dynamics of a 3-site system are expected to play a crucial role in facilitating the design of efficient energy-transfer pathways in molecular systems.

Comparison of Variational and Perturbative Spin-Orbit Coupling within Two-Component CASSCF.

The modeling of spin-orbit coupling (SOC) remains a challenge in computational chemistry due to the high computational cost. With the rising popularity of spin-driven processes and f-block metals in chemistry and materials science, it is incumbent on the community to develop accurate multiconfigurational SOC methods that scale to large systems and understand the limits of different treatments of SOC. Herein, we introduce an implementation of perturbative SOC in scalar-relativistic two-component CASSCF (srX2C-CASSCF-SO). Perspectives on the limitations and accuracy of srX2C-CASSCF-SO are presented via benchmark calculations.

Power corrections to energy flow correlations from large spin perturbation

Dynamics of high energy scattering in Quantum Chromodynamics (QCD) are primarily probed through detector energy flow correlations. One important example is the Energy-Energy Correlator (EEC), whose back-to-back limit probes correlations of QCD on the lightcone and can be described by a transverse-momentum dependent factorization formula in the leading power approximation. In this work, we develop a systematic method to go beyond this approximation. We identify the origin of logarithmically enhanced contributions in the back-to-back limit as the exchange of operators with low twists and large spins in the local operator product expansion. Using techniques from the conformal bootstrap, the large logarithms beyond leading power can be resummed to all orders in the perturbative coupling. As an illustration of this method, we perform an all-order resummation of the leading and next-to-leading logarithms beyond the leading power in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 Super Yang-Mills theory.

The four-dimensional Yang–Mills partition function in the vicinity of the vacuum

The partition function of four-dimensional Euclidean, non-supersymmetric textrm{SU}(2) Yang–Mills theory is calculated in the perturbative and weak coupling regime, i.e., in a small open ball about the flat connection and when the gauge coupling constant acquires a small but finite value. The computation is based on various known inequalities, valid only in four dimensions, providing two-sided estimates for the exponentiated Yang–Mills action in terms of the L^2-norm of the derivative of the gauge potential only; these estimates then give rise to Gaußian-like infinite- dimensional formal integrals involving the Laplacian and hence can be computed via zeta-function and heat kernel techniques. It then turns out that these formal integrals give a sharp value for the partition function in the aforementioned perturbative and weak coupling regime of the theory. In the resulting expression for the partition function, the original classical value of the coupling constant is shifted to a smaller one which can be interpreted as the manifestation, in this approach, of a non-trivial beta -function and asymptotic freedom in pure non-Abelian gauge theories.

New Bound State Solutions of 3-Dimensional Modified Eckart Potential Plus a New Modified Deformed Hylleraas Potential in RNCQM and NRNCQM Symmetries

Abstract: In this study, the solution of the deformed Klein-Gordon and deformed Schrödinger equations (DKGE and DSE for short) for the modified Eckart potential plus a new modified deformed Hylleraas potential (MEPNMDHP, for short) with the improved approximation to deal with the centrifugal term is investigated using Bopp’s shift and standard perturbation theory methods in the symmetries of relativistic noncommutative quantum mechanics RNCQM and nonrelativistic noncommutative quantum mechanics NRNCQM. To the best of our knowledge, this problem is examined in literature in usual RQM and NRQM. The new potential suggested describes some selected diatomic molecules such as the homogeneous diatomic molecules (N2 and H2) and heterogeneous diatomic molecules (HCl, HBr, SO, NO, and HI). The new values that we get appeared sensitive to the quantum numbers (j,s,m) in addition to the usual states’ numbers (n,l), the potential depths of the potential (V_0,V_1,V_2), the range of the potential α and noncommutativity parameters (Θ,σ,χ). We have highlighted three physical phenomena that automatically generate a result of the topological properties of non-commutativity. The first physical phenomenon is the perturbative spin-orbit coupling, the second is the magnetic induction, and the third is the rotational proper phenomenon. In both relativistic and nonrelativistic problems, we show that the corrections on the spectrum energy are smaller than the main energy in the ordinary cases of quantum field theory and quantum mechanics. In the new symmetries of NCQM, it is not possible to get the exact analytical solutions for l=0 and l≠0, so the approximate solutions are available. We have observed that the DKGE under the MEPNMDHP has a physical behavior similar to the Duffin-Kemmer equation that can describe the dynamic state of a particle with spin-1 in the symmetries of RNCQM. Four special cases; i.e., l wave is investigated in the context of DKGE and Schrödinger theories. The new relativistic and nonrelativistic energy for some potentials, such as only modified Eckart potential and only new modified Hylleraas potential, have also been obtained by varying some potential parameters. Keywords: Klein-Gordon equation, Schrödinger equation, Eckart potentials, Modified Hylleraas potential, Diatomic molecules, Noncommutative geometry, Star products, Bopp's shift method. PACs: 03.65. Ge; 03.65. Pm; 03.65.−w, 32.30 – r, 02.30. Gp.

Baryon number violation from confining new physics

The detection of neutron-antineutron oscillation will be a discovery of fundamental importance in particle physics and cosmology. In models discussed widely in literature, the process is generated through heavy new physics with weak, perturbative coupling at the scale of the experiment. Acknowledging the fact that nature has been quite evasive regarding the strength and scale of new physics, we discuss a new mechanism, generated by confining new physics, at $\ensuremath{\sim}2\text{ }\text{ }\mathrm{GeV}$, resulting in low-energy baryon number violating effects. The mechanism predicts baryon number violating processes like neutron disappearance, neutron-neutron annihilation and neutron-antineutron oscillation generated through the condensation of the linear moose.

State Interaction Linear Response Time-Dependent Density Functional Theory with Perturbative Spin-Orbit Coupling: Benchmark and Perspectives.

Spin-orbit coupling (SOC) is an important driving force in photochemistry. In this work, we develop a perturbative spin-orbit coupling method within the linear response time-dependent density function theory framework (TDDFT-SO). A full state interaction scheme, including singlet-triplet and triplet-triplet coupling, is introduced to describe not only the coupling between the ground and excited states, but also between excited states with all couplings between spin microstates. In addition, expressions to compute spectral oscillator strengths are presented. Scalar relativity is included variationally using the second-order Douglas-Kroll-Hess Hamiltonian, and the TDDFT-SO method is validated against variational SOC relativistic methods for atomic, diatomic, and transition metal complexes to determine the range of applicability and potential limitations. To demonstrate the robustness of TDDFT-SO for large-scale chemical systems, the UV-Vis spectrum of Au25(SR)18 - is computed and compared to experiment. Perspectives on the limitation, accuracy, and capability of perturbative TDDFT-SO are presented via analyses of benchmark calculations. Additionally, an open-source Python software package (PyTDDFT-SO) is developed and released to interface with the Gaussian 16 quantum chemistry software package to perform this calculation.

Power corrections to electroweak boson production from threshold resummation

We study the power corrections for electroweak boson production that are implied by threshold resummation, which we have extended to massive particles produced at measured transverse momentum, $p_T$, and rapidity. Power corrections in the resulting expressions arise from ambiguities in the low-scale behavior of the perturbative running coupling. Arguing for the relevance of the eikonal approximation, we show that such power corrections begin at order $1/p_T^2$ in full QCD, consistent with fixed-order, massive-gluon analysis. For large-$N$ Mellin moments, the leading behavior is $N^2/p_T^2$, which exponentiates along with the logarithms of threshold resummation.

Gauge coupling unification in simplified grand gauge-Higgs unification

Grand gauge-Higgs unification of five dimensional SU(6) gauge theory on an orbifold $S^1/Z_2$ with localized gauge kinetic terms is discussed. The Standard model (SM) fermions on the boundaries and some massive bulk fermions coupling to the SM fermions on the boundary are introduced. Taking the power-law running contributions from the bulk fields into account, perturbative gauge coupling unification is shown to be realized at around $10^{14}$ GeV, which is a few order smaller than the unification scale of four dimensional grand unified theories.

Perturbative Quantum Simulation.

Approximation based on perturbation theory is the foundation for most of the quantitative predictions of quantum mechanics, whether in quantum many-body physics, chemistry, quantum field theory, or other domains. Quantum computing provides an alternative to the perturbation paradigm, yet state-of-the-art quantum processors with tens of noisy qubits are of limited practical utility. Here, we introduce perturbative quantum simulation, which combines the complementary strengths of the two approaches, enabling the solution of large practical quantum problems using limited noisy intermediate-scale quantum hardware. The use of a quantum processor eliminates the need to identify a solvable unperturbed Hamiltonian, while the introduction of perturbative coupling permits the quantum processor to simulate systems larger than the available number of physical qubits. We present an explicit perturbative expansion that mimics the Dyson series expansion and involves only local unitary operations, and show its optimality over other expansions under certain conditions. We numerically benchmark the method for interacting bosons, fermions, and quantum spins in different topologies, and study different physical phenomena, such as information propagation, charge-spin separation, and magnetism, on systems of up to 48 qubits only using an 8+1 qubit quantum hardware. We demonstrate our scheme on the IBM quantum cloud, verifying its noise robustness and illustrating its potential for benchmarking large quantum processors with smaller ones.

Approximate k-state solutions of the deformed Dirac equation in spatially dependent mass for the improved Eckart potential including the improved Yukawa tensor interaction in ERQM symmetries

In this work, we considered analytical approximate bound state solutions of the mass-dependent deformed Dirac equation with the improved vector Eckart potential including the Yukawa tensor interaction (IEPDMYI for short) in the context of extended relativistic quantum mechanics ERQM symmetries. The new relativistic energy spectra of the DDE for the IEPDMYI with spin symmetry and pseudospin symmetry are obtained. The solutions for arbitrary k-wave are obtained by using the basic concept of Bopp’s shift approach and standard perturbation by applying an approximation to the centrifugal-like term in the calculations. The new values that we get appeared sensitive to the discrete quantum numbers [Formula: see text], the mixed potential depths [Formula: see text], the range of the potential [Formula: see text] and noncommutativity parameters [Formula: see text]. We have highlighted three physical phenomena that automatically generate a result of the topological properties of noncommutativity, the first physical phenomena are the perturbative spin-orbit coupling, the second is the magnetic induction while the third corresponds to the rotational proper phenomena. We show that the corrections on the spectrum energy are smaller than the main energy in the usual cases of quantum field theory. In the ERQM symmetries, it is not possible to get the exact analytical solutions for [Formula: see text], only the approximate solutions are available. We have obtained the energy equation for several well-known potentials by choosing appropriate parameters in the improved Eckart potential model such as the improved Hulthén potential and the improved generalized Morse potential.

Diatomic molecules and fermionic particles with improved Hellmann-generalized Morse potential through the solutions of the deformed Klein-Gordon, Dirac and Schrödinger equations in extended relativistic quantum mechanics and extended nonrelativistic quantum mechanics symmetries

In this paper, we investigate the new approximate bound state solution of deformed Klein--Gordon, Dirac and Schr\"{o}dinger equations in the symmetries of extended relativistic quantum mechanics ERQM and extended nonrelativistic quantum mechanics ENRQM have been obtained with a newly proposed potential called improved Hellmann-generalized Morse potential (IHGMP, for short). To the best of our knowledge, this problem is examined in literature in the usual RQM and NRQM with Hellmann-generalized Morse potential. The potential is a superposition of Hellmann potential, generalized Morse or Deng-Fan potential, and some other exponential terms. By employing the improved approximation to deal with the centrifugal term, Bopp's shift and standard perturbation theory method. The new approximate analytical energy shift and the corrections of bound state energyeigenvalues in ERQM and ENRQM are obtained for some selected diatomic molecules such as (HCl, LiH, H2, ScH, TiH, VH, CrH, CuLi, TiC, NiC, ScN and ScF). The new values that we get appeared sensitive to the quantum numbers $% \left( j,l,s,m\right) $, the potential depths of the improved Hellmann-generalized Morse potential ($a,b$), the range of the potential $%\alpha $, the dissociation energy $D_{e}$, the equilibrium bond length $%r_{e} $, and noncommutativity parameters$\left( \Theta ,\sigma ,\chi \right)$ . We have highlighted three physical phenomena that automatically generate a result of the topological properties of noncommutativity, the first physical phenomena are the perturbative spin-orbit coupling, the second the magnetic induction while the third corresponds to the rotational proper phenomena. In both relativistic and nonrelativistic problems, we show thatthe corrections on the spectrum energy are smaller than the main energy in the ordinary cases of quantum field theory and quantum mechanics. In the new symmetries of NCQM, it is not possible to get the exact analytical solutions for $l=0$ and $l\neq 0$, the approximate solutions are available. Four special cases, i.e., l wave are investigated in the context of deformed Klien-Gordon and Schr\"{o}dinger theories. The relativistic energy equations and the new nonrelativistic energy for some potentials such as improved Hellmann potential and improved generalized Morse potential have also been obtained by varying some potential parameters. We have clearly shown that the Schr\"{o}dinger and Klein Gordon equations in the new symmetries canphysically describe each of the two Dirac equations and the Duffin--Kemmer equation under the effect of IHGMP.

Diagrammatic strong coupling expansion of a U(1) lattice model in the Fourier basis

The transfer-matrix of the U(1) lattice gauge theory is investigated in the field Fourier space, the basis of which consists of the quantized currents on lattice links. Based on a lattice version of the current conservation, the transfer-matrix elements are shown to be nonzero only between current states that differ in circulating currents inside plaquettes. In the strong coupling limit, a series expansion is developed for the elements of the transfer matrix, to which a diagrammatic representation based on the occurrence of virtual link and loop currents can be associated. With $g$ as the coupling, the weight of each virtual current in the expansion is $1/{g}^{2}$, by which at any given order the relevant diagrams are determined. Either by interpretation or through their role in fixing the relevant terms, the diagrams are reminiscent of the Feynman ones of the perturbative small coupling expansions.

Determination of perturbative QCD coupling from ALEPH tau decay data using pinched Borel\u2013Laplace and Finite Energy Sum Rules

We present a determination of the perturbative QCD (pQCD) coupling using the V+A channel ALEPH tau -decay data. The determination involves the double-pinched Borel–Laplace Sum Rules and Finite Energy Sum Rules. The theoretical basis is the Operator Product Expansion (OPE) of the V+A channel Adler function in which the higher order terms of the leading-twist part originate from a model based on the known structure of the leading renormalons of this quantity. The applied evaluation methods are contour-improved perturbation theory (CIPT), fixed-order perturbation theory (FOPT), and Principal Value of the Borel resummation (PV). All the methods involve truncations in the order of the coupling. In contrast to the truncated CIPT method, the truncated FOPT and PV methods account correctly for the suppression of various renormalon contributions of the Adler function in the mentioned sum rules. The extracted value of the {overline{mathrm{MS}}} coupling is alpha _s(m_{tau }^2) = 0.3116 pm 0.0073 [alpha _s(M_Z^2)=0.1176 pm 0.0010] for the average of the FOPT and PV methods, which we regard as our main result. On the other hand, if we include in the average also the CIPT method, the resulting values are significantly higher, alpha _s(m_{tau }^2) = 0.3194 pm 0.0167 [alpha _s(M_Z^2)=0.1186 pm 0.0021].

Heterobilayer moiré magnets: Moiré skyrmions and commensurate-incommensurate transitions

We study untwisted heterobilayers of ferromagnetic and antiferromagnetic van der Waals materials, with in particular a Dzyaloshinskii-Moriya interaction in the ferromagnetic layer. A continuum low energy field theory is utilized to study such systems. We develop a phase diagram as a function of the strength of inter-layer exchange and Dzyaloshinskii-Moriya interactions, combining perturbative and strong coupling analyses with numerical simulations using Landau-Lifshitz-Gilbert equations. Various moir\'e-periodic commensurate phases are found, and the commensurate-incommensurate transition is discussed. Among the commensurate phases, we observe an interesting skyrmion lattice phase wherein each moir\'e unit cell hosts one skyrmion.

Lattice-motivated QCD coupling and hadronic contribution to muon g − 2

We present an updated version of a QCD coupling which fulfills various physically motivated conditions: at high momenta it practically coincides with the perturbative QCD coupling; at intermediate momenta it reproduces correctly the physics of the semihadronic tau decay; and at very low momenta it is suppressed as suggested by large-volume lattice calculations. An earlier presented analysis is updated here in the sense that the Adler function, in the regime |Q 2|≲ 1 GeV2, is evaluated by a renormalon-motivated resummation method. This Adler function is then used here in the evaluation of the quantities related with the semihadronic (strangeless) τ-decay spectral functions, including Borel–Laplace sum rules in the (V + A)-channel. The analysis is then extended to the evaluation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment, , where we include in the Adler function the V-channel higher-twist OPE terms which are regulated in the infrared (IR) by mass parameters which are expected to be ≲1 GeV. The correct value of can be reproduced with the mentioned IR-regulating mass parameters if the value of the condensate is positive (and thus the gluon condensate value is positive). This restriction and the requirement of the acceptable quality of the fits to the various mentioned sum rules then lead us to the restriction .

Phenanthroline chromophore as efficient antenna for Tb3+ green luminescence: A theoretical study

The photophysical processes, from excitation in the UV range, energy migration pathways to luminescence of Tb(phen)2(NO3)3 complex in the Vis region have been studied by theoretical approaches and spectroscopic measurements. The UV–Vis absorption, diffuse reflectance, excitation and luminescence spectra indicated that the ligand 1,10-phenanthroline (phen) was a suitable antenna chromophore for Tb3+ luminescence at excitation of wavelength range 350–352 nm, corresponding to the S1 state of phen. The energy level diagram and character of the singlet and triplet excited states of the ligand-chromophore and Tb(phen)2(NO3)3 in gas phase and polar solution were obtained by the DFT/TDDFT/ωB97xD/B1 method and multireference ab-initio calculations with perturbative spin-orbit coupling corrections. It was also established that the vibro-electronic contribution to the excitation energy is important for correct reproduction and interpretation of the experimental absorption and emission spectra of Tb(phen)2(NO3)3. The rate constants for competitive singlet-triplet intersystem crossing relaxation transitions, as well as radiative and non-radiative deactivation of the ligand-centered excited states were qualitatively estimated and the fastest electronic relaxation mechanism was revealed. The excitation channel S0→S1→T2→T1→5D4 was predicted as the most probable one for effective phen→Tb3+ energy transfer. The sensitization results in a high luminescent quantum yield of 13%, which suggests energy transfer rates, sufficiently higher than the rates of radiative and non-radiative depopulation of the T1 state.