Perturbation Formalism Research Articles

Time dependent variation perturbation calculation of two-photon transition probability and hyperfine shift in hydrogen atom under plasma environment

A new theoretical approach has been adopted to calculate the non-relativistic parity conserved two-photon transition probability (TPTP) from ground to excited S and D states along with the hyperfine splitting (HFS) of ground and excited S states of H atom within principal quantum number n≤4 under classical and quantum plasma environment represented by screened potential model. The methodology involves direct calculation of TPTP via an intermediate virtual state obtained from time dependent variation perturbation formalism. The standard formula with sum over states representing the TPTP has been replaced by its variational equivalent obtained from currently established procedure for two-photon excitation via fourth order time dependent variation perturbation theory. Unlike previous methodologies the current formalism yields a compact representation of the physical nature of the intermediate virtual state having well defined profile. The HFS has been evaluated under first order perturbation theory. The plasma embedded ground state energy is obtained from standard diagonalization procedure. Finite Slater type basis sets have been used for the ground and all the excited states. The variational coefficients for the excited states are determined from optimization of an appropriate time averaged variational functional. Results for free H atom agree well with existing estimates for all the states. The results for the plasma embedded states follow smooth and interesting pattern.

García-García etal. Reply.

In a recent comment to the paper Chaotic Integrable transition in the SYK model, it was claimed that, in a certain region of parameters, the Lyapunov exponent of the N Majoranas Sachdev-Ye-Kitaev model with a quadratic perturbation, is always positive. This implies that the model is quantum chaotic. In this reply, we show that the employed perturbative formalism breaks down precisely in the range of parameters investigated in the comment due to a lack of separation of time scales. Moreover, based on recent analytical results, we show that for any large and fixed N, the model has indeed a chaotic-integrable transition that invalidate the results of the comment.

Photoelectron spectra of early 3d-transition metal dioxide molecular anions from GW calculations.

Photoelectron spectra of early 3d-transition metal dioxide anions, ScO2 -, TiO2 -, VO2 -, CrO2 -, and MnO2 -, are calculated using semilocal and hybrid density functional theory (DFT) and many-body perturbation theory within the GW approximation using one-shot perturbative and eigenvalue self-consistent formalisms. Different levels of theory are compared with each other and with available photoelectron spectra. We show that one-shot GW with a PBE0 starting point (G0W0@PBE0) consistently provides very good agreement for all experimentally measured binding energies (within 0.1 eV-0.2 eV or less). We attribute this to the success of PBE0 in mitigating self-interaction error and providing good quasiparticle wave functions, which renders a first-order perturbative GW correction effective. One-shot GW calculations with a Perdew-Burke-Ernzerhof (PBE) starting point do poorly in predicting electron removal energies by underbinding orbitals with typical errors near 1.5 eV. A higher exact exchange amount of 50% in the DFT starting point of one-shot GW does not provide very good agreement with experiment by overbinding orbitals with typical errors near 0.5 eV. While not as accurate as G0W0@PBE0, the G-only eigenvalue self-consistent GW scheme with W fixed to the PBE level provides a reasonably predictive level of theory (typical errors near 0.3 eV) to describe photoelectron spectra of these 3d-transition metal dioxide anions. Adding eigenvalue self-consistency also in W, on the other hand, worsens the agreement with experiment overall. Our findings on the performance of various GW methods are discussed in the context of our previous studies on other transition metal oxide molecular systems.

Electron as Kerr's super-rotating black hole

The known weakness of Gravity in particle physics is a delusion caused by underestimation of the role of spin. Spin of elementary particles is extremely high and exceeds mass on 20-22 orders (in unit’s c = G = m = k = 1). The caused by spinning gravity framedragging distorts space much stronger than mass, that shifts the usual effective scale of gravitational interaction from Planck to Compton distances. We show that compatibility between gravity and quantum theory can be achieved without modifications of the Einstein equations, by using a model of super-bag a no perturbative particle like solution to supersymmetric system of the Landau-Ginzburg (Higgs) field equations. Super-bag generates a free from gravity Compton zone for quantum theory. Shape of the bag is defined unambiguously by spinning Kerr-Newman solution. For parameters of an electron (charge e, spin J, and mass m) super-bag forms a thin superconducting disk of Compton radius coupled with circular string along its perimeter. The supersymmetric LG (Higgs) model is naturally upgraded to Wess-Zumino super-QED model, forming a bridge to perturbative formalism of conventional QED.

Perturbative approach to tunneling and quantum interferences in spin clusters

Collective tunneling is a ubiquitous phenomenon in finite-size spin clusters that shows up in systems as diverse as molecular magnets or spin clusters adsorbed at surfaces. The problem we explore is to understand how small flipping terms can cooperate to flip a large spin to the opposite direction or a cluster of interacting elementary Ising spins into the time-reversed state. These high order processes will involve at least two channels, a single spin-flip channel due to a transverse field and a two-spin flip channel due to exchange or due to single-ion anisotropies. In the present paper, we show that high-order perturbation theory can be formulated and evaluated with the help of simple recurrence relations, leading to a compact theory of tunnelling in macroscopic spins, in one-dimensional clusters, as well as in small higher-dimensional clusters. This is demonstrated explicitly in the case of the Ising model with a transverse field and transverse exchange, and in the case of macroscopic spins with uniaxial anisotropy. Our approach provides a transparent theory of level crossings, where the tunneling between time reversed configurations vanishes as a function of the external field. The crossings result from destructive quantum interferences between competing flipping channels. Our theory consistently predicts N crossings in chains of N Ising spins, 2S crossings in single spins of magnitude S, and yields explicit analytical formulae for the level crossings of open chains and macroscopic spins. Disorder can be easily implemented in this perturbative formalism. Leading disorder effects can be treated analytically for spin rings. At the smallest transverse field crossing, the suppression of tunneling is most robust with respect to disorder. We briefly discuss the implications of our findings for the use of realistic spin clusters on surfaces to store information.

Teukolsky formalism for nonlinear Kerr perturbations

We develop a formalism to treat higher order (nonlinear) metric perturbations of the Kerr spacetime in a Teukolsky framework. We first show that solutions to the linearized Einstein equation with nonvanishing stress tensor can be decomposed into a pure gauge part plus a zero mode (infinitesimal perturbation of the mass and spin) plus a perturbation arising from a certain scalar (‘Debye–Hertz’) potential, plus a so-called ‘corrector tensor’. The scalar potential is a solution to the spin −2 Teukolsky equation with a source. This source, as well as the tetrad components of the corrector tensor, are obtained by solving certain decoupled ordinary differential equations involving the stress tensor. As we show, solving these ordinary differential equations reduces simply to integrations in the coordinate r in outgoing Kerr–Newman coordinates, so in this sense, the problem is reduced to the Teukolsky equation with source, which can be treated by a separation of variables ansatz. Since higher order perturbations are subject to a linearized Einstein equation with a stress tensor obtained from the lower order perturbations, our method also applies iteratively to the higher order metric perturbations, and could thus be used to analyze the nonlinear coupling of perturbations in the near-extremal Kerr spacetime, where weakly turbulent behavior has been conjectured to occur. Our method could also be applied to the study of perturbations generated by a pointlike body traveling on a timelike geodesic in Kerr, which is relevant to the extreme mass ratio inspiral problem.

Determination of Ds+ meson fragmentation functions through two different approaches

The hadronization mechanism is described by the fragmentation functions (FFs) which are universal and process-independent quantities. They can be generally determined theoretically or phenomenologically. In the phenomenological approach which is based on the data analysis, we present the FFs of ${D}_{s}^{+}$ both at leading-order (LO) and next-to-leading order (NLO) and, for the first time, at next-to-next-to-leading order in the minimal subtraction factorization scheme with five massless quarks. These functions are determined by fitting all available experimental data of inclusive single ${D}_{s}^{+}$-meson production in electron-positron annihilation, from the OPAL Collaboration at CERN LEP1. We shall also estimate the uncertainties in these FFs as well as in the corresponding observables. In the theoretical approach, we apply the perturbative FFs formalism based on the Suzuki's model and present our analytical results at LO and NLO perturbative QCD framework. For the first time, a comparison between both approaches will be presented in this work. We also apply our new FFs to generate theoretical predictions for the energy distribution of ${D}_{s}^{+}$ mesons produced through the decay of unpolarized top quarks, to be measured at the CERN LHC.

Universal thermodynamics of a trapped Fermi gas in the superfluid regime: the role of the Pauli principle

Understanding the universal behavior of strongly-interacting systems of particles has been a major goal in multiple fields of physics from atomic physics to cosmology. Using a recently introduced manybody perturbation formalism for fermions which uses group theoretic and graphical techniques to solve the N-body problem, I study the thermodynamic behavior of the unitary regime for a trapped Fermi gas and investigate the role of the Pauli principle in the emergence of collective behavior, specifically superfluidity at ultralow temperatures. The method, which is called symmetry invariant perturbation theory, has no adjustable parameters and currently offers a solution to the manybody Schrodinger equation through first order in inverse dimensionality exactly. The solution at first order defines collective coordinates in terms of five types of N-body normal modes, identified as symmetric stretch, symmetric bend, single particle angular excitation, single particle radial excitation and phonon. A correspondence is established ‘on paper’ that enforces the Pauli principle through the assignment of specific normal mode quantum numbers. Applied at ultracold temperatures, this normal mode assignment yields occupation only in an extremely low frequency N-body phonon mode. A single particle radial excitation mode at a much higher frequency creates a gap that stabilizes the superfluidity at low temperatures. This radial excitation involves excitation of a single particle out of the synced motion of the phonon mode, rather than the breaking of a fermion pair. Coupled with the corresponding values for the energies at unitarity obtained by this manybody calculation, I obtain good agreement with experimental thermodynamic results. In particular, the lambda transition in the specific heat is clearly seen. Based on these findings, I propose a mechanism for the emergence of superfluidity at ultralow temperatures in this unitary regime that is driven by quantum statistics and the enforcement of the Pauli principle through the selection of normal modes. My results for the calculated thermodynamic quantities suggest that the emergence of some collective behaviors in macroscopic systems is due to the Pauli principle producing manybody pairing and the resulting macroscopic occupation of an N-body phonon mode.

Phenomenological studies on the Bd,s0→J/ψf0(500)[f0(980)] decays

Encouraged by the global agreement between theoretical predictions and experimental measurements for $B \to J/\psi V$ decays, we extend that perturbative QCD formalism to $B_{d,s}^0 \to J/\psi f_0(500) [f_0(980)]$ decays at the presently known next-to-leading order in the quark-antiquark description of $f_0(500)$ and $f_0(980)$. With the angle $\phi_f \approx 25^\circ$ of the $f_0(500)-f_0(980)$ mixing in the quark-flavor basis, we find that the branching ratios of the $B_d^0 \to J/\psi f_0(500) (\to \pi^+ \pi^-)$ and $B_{d,s}^0 \to J/\psi f_0(980) (\to \pi^+ \pi^-)$ modes generally agree with the current data or the upper limits within uncertainties, except for the seemingly challenging $B_s^0 \to J/\psi f_0(500) (\to \pi^+\pi^-)$ one. Then, we further explore the relevant observables of the $B_{d,s}^0 \to J/\psi f_0(500) [f_0(980)]$ decays, which could provide further constraints on the mixing angle $\phi_f$ and/or SU(3) flavor symmetry breaking effects. As a byproduct, we predict ${\rm BR}(B_{d}^0 \to J/\psi f_0(980)(\to K^+ K^-))=5.8^{+3.1}_{-2.9} \times 10^{-7}$ and ${\rm BR}(B_{s}^0 \to J/\psi f_0(980)(\to K^+ K^-)) =4.6^{+2.6}_{-2.3} \times 10^{-5}$. All theoretical predictions await the future examinations with high precision.

Viable inflationary models in a ghost-free Gauss\u2013Bonnet theory of gravity

In this work we investigate the inflationary phenomenological implications of a recently developed ghost-free Gauss–Bonnet theory of gravity. The resulting theory can be viewed as a scalar Einstein–Gauss–Bonnet theory of gravity, so by employing the formalism for cosmological perturbations for the latter theory, we calculate the slow-roll indices and the observational indices, and we compare these with the latest observational data. Due to the presence of a freely chosen function in the model, in principle any cosmological evolution can be realized, so we specify the Hubble rate and the freely chosen function and we examine the phenomenology of the model. Specifically we focus on de Sitter, quasi-de Sitter and a cosmological evolution in which the Hubble rate evolves exponentially, with the last two being more realistic choices for describing inflation. As we demonstrate, the ghost-free model can produce inflationary phenomenology compatible with the observational data. We also briefly address the stability of first order scalar and tensor cosmological perturbations, for the exponential Hubble rate, and as we demonstrate, stability is achieved for the same range of values of the free parameters that guarantee the phenomenological viability of the models.

Studies on the decays in the perturbative QCD approach**Research exercises for excellent undergraduate students.

The decays are investigated for the first time in the perturbative QCD formalism based on the kT factorization theorem, where the light scalar κ is assumed as a two-quark state. Our numerical results and phenomenological analyses on the CP-averaged branching ratios and CP-violating asymmetries show that: (a) the and decays have large decay rates around , which could be examined by the upgraded large hadron collider beauty and/or Belle-II experiments in the near future; (b) a large decay rate of about appears in the pure annihilation channel, which could provide more evidence to help distinguish different QCD-inspired factorization approaches, even understand the annihilation decay mechanism; (c) the pure penguin modes and would provide a promising ground to search for the possible new physics because of their zero direct and mixing-induced CP violations in the standard model. The examinations with good precision from the future experiments will help to further study the perturbative and/or nonperturbative QCD dynamics involved in these considered decay modes.

Pulsar-timing arrays, astrometry, and gravitational waves

We discuss the theory of pulsar-timing and astrometry probes of a stochastic gravitational-wave background with a recently developed "total-angular-momentum" (TAM) formalism for cosmological perturbations. We review the formalism, emphasizing in particular the features relevant for this work and describe the observables we consider (i.e. the pulsar redshift and stellar angular displacement). Using the TAM approach, we calculate the angular power spectra for the observables and from them derive angular auto- and cross-correlation functions. We provide the full set of power spectra and correlation functions not only for the standard transverse-traceless propagating degrees of freedom in general relativity, but also for the four additional non-Einsteinian polarizations that may arise in alternative-gravity theories. We discuss how pulsar-timing and astrometry surveys can complement and serve as cross checks to one another and comment on the importance of testing the chirality of the gravitational-wave background as a tool to understand the nature of its sources. A simple rederivation of the power spectra from the plane-wave formalism is provided in an Appendix.

Inhomogeneous universe from group field theory condensate

One of the fundamental challenges for quantum cosmology is to explain the emergence of our macroscopic Universe from physics at the Planck scale. In the group field theory (GFT) approach to quantum gravity, such a macroscopic universe results from the formation of a “condensate” of fundamentally discrete degrees of freedom. It has been shown that the effective dynamics of such GFT condensates follows the classical Friedmann dynamics at late times, while avoiding the classical singularity by a bounce akin to the one of loop quantum cosmology (LQC). It was also shown how quantum fluctuations in a GFT condensate provide an initial power spectrum of volume fluctuations around exact homogeneity. Here we connect the results for quantum fluctuations in GFT to the usual formalism for cosmological perturbations within quantum field theory in curved spacetime. We consider a bouncing universe filled with a massless scalar field, in which perturbations are generated by vacuum fluctuations in the contracting phase. Matching conditions at the bounce are provided by working within LQC. We then compare the results to the GFT condensate scenario for quantum gravity with massless scalar matter. Here, instead, an initial quantum phase described by a GFT condensate generates initial scalar perturbations through quantum fluctuations. We show general agreement in the predictions of both approaches, suggesting that GFT condensates can provide a physical mechanism for the emergence of a slightly inhomogeneous universe from full quantum gravity.

Compton scattering from hydrogen and helium atoms

We develop an approach to describing Compton scattering of photons in the keV energy range from hydrogen and helium atoms based on a relativistic version of the AA-approximation within the standard perturbative S-matrix formalism. The resulting formulas for the cross section take into account the effects of the electron boundness and correctly reproduce the behavior of the cross section with the growth of photon energy, as it goes to the Thomson cross section, which coincides with the Klein–Nishina–Tamm formula for the cross section in the non-relativistic limit.

Estimates of the Bc wave function from the CDF and LHCb production data

In the framework of perturbative QCD and nonrelativistic bound state formalism, we calculate the production of Bc and B*c mesons at the conditions of the CDF andLHCb experiments. We derive first estimations for the Bc wave function from a comparison with the available data.

Rigorous Free Energy Perturbation Approach to Estimating Relative Binding Affinities between Ligands with Multiple Protonation and Tautomeric States.

Accurate prediction of ligand binding affinities is of key importance in small molecule lead optimization and a central task in computational medicinal chemistry. Over the years, advances in both computer hardware and computational methodologies have established free energy perturbation (FEP) methods as among the most reliable and rigorous approaches to compute protein-ligand binding free energies. However, accurate description of ionization and tautomerism of ligands is still a major challenge in structure-based prediction of binding affinities. Druglike molecules are often weak acid or bases with multiple accessible protonation and tautomeric states that can contribute significantly to the binding process. To address this issue, we introduce in this work the p Ka and tautomeric state correction approach. This approach is based on free energy perturbation formalism and provides a rigorous treatment of the ionization and tautomeric equilibria of ligands in solution and in the protein complexes. A series of Kinesin Spindle Protein (KSP) and Factor Xa inhibitor molecules were used as test cases. Our results demonstrate that the p Ka and tautomeric state correction approach is able to rigorously and accurately incorporate multiple protonation and tautomeric states in the binding affinity calculations.

K− over K+ multiplicity ratio for kaons produced in DIS with a large fraction of the virtual-photon energy

The K− over K+ multiplicity ratio is measured in deep-inelastic scattering, for the first time for kaons carrying a large fraction z of the virtual-photon energy. The data were obtained by the COMPASS collaboration using a 160 GeV muon beam and an isoscalar 6LiD target. The regime of deep-inelastic scattering is ensured by requiring Q2>1(GeV/c)2 for the photon virtuality and W>5GeV/c2 for the invariant mass of the produced hadronic system. Kaons are identified in the momentum range from 12 GeV/c to 40 GeV/c, thereby restricting the range in Bjorken-x to 0.01<x<0.40. The z-dependence of the multiplicity ratio is studied for z>0.75. For very large values of z, i.e.z>0.8, we observe the kaon multiplicity ratio to fall below the lower limits expected from calculations based on leading and next-to-leading order perturbative quantum chromodynamics. Also, the kaon multiplicity ratio shows a strong dependence on the missing mass of the single-kaon production process. This suggests that within the perturbative quantum chromodynamics formalism an additional correction may be required, which takes into account the phase space available for hadronisation.

Semileptonic decays of Bc meson to P -wave charmonium states

Inspired by a series of unexpected measurements of semileptonic decays mediated via $b\rightarrow c $ charged current interactions, we explore semileptonic $B_c$ decays to the four lightest $P$-wave charmonium states, $\chi_{c0}, \chi_{c1}, \chi_{c2}, h_c$, by the recently developed improved perturbative QCD formalism, in which the charm quark mass effect is included both in the Sudakov factor and the hard kernels. We first directly evaluate the concerned transition form factors with vector and axial-vector currents in the region of small momentum transfer squared, and then recast them to the full kinematical region by adopting the exponential parametrization. The obtained form factors are used to evaluate the semileptonic decay branching ratios, which can reach the order of $10^{-3}$, letting the corresponding measurement appear feasible. For a better analysis, a comparison of our results with the predictions of other models is provided. We also present the ratios between the tau and light lepton branching ratios and the polarization contributions in the relevant processes, which still need experimental tests in the ongoing and forthcoming experiments. Any significant deviations from the Standard Model results may provide some hints of new physics effects.

Layered nested Markov chain Monte Carlo.

A configurational sampling algorithm based on nested layerings of Markov chains (Layered Nested Markov Chain Monte Carlo or L-NMCMC) is presented for simulations of systems characterized by rugged free energy landscapes. The layerings are generated using a set of auxiliary potential energy surfaces. The implementation of the method is demonstrated in the context of a rugged, two-dimensional potential energy surface. The versatility of the algorithm is next demonstrated on a simple, many-body system, namely, a canonical Lennard-Jones fluid in the liquid state. In that example, different layering schemes and auxiliary potentials are used, including variable cutoff distances and excluded-volume tempering. In addition to calculating a variety of properties of the system, it is also shown that L-NMCMC, when combined with a free-energy perturbation formalism, provides a straightforward means to construct approximate free-energy surfaces at no additional computational cost using the sampling distributions of each auxiliary Markov chain. The proposed L-NMCMC scheme is general in that it could be complementary to any number of methods that rely on sampling from a target distribution or methods that exploit a hierarchy of time scales and/or length scales through decomposition of the potential energy.

Quantum field-theoretical description of neutrino and neutral kaon oscillations

It is shown that the neutrino and neutral kaon oscillation processes can be consistently described in quantum field theory using only plane waves of the mass eigenstates of neutrinos and neutral kaons. To this end, the standard perturbative S-matrix formalism is modified so that it can be used for calculating the amplitudes of the processes passing at finite distances and finite time intervals. The distance-dependent and time-dependent parts of the amplitudes of the neutrino and neutral kaon oscillation processes are calculated and the results turn out to be in accordance with those of the standard quantum mechanical description of these processes based on the notion of neutrino flavor states and neutral kaon states with definite strangeness. However, the physical picture of the phenomena changes radically: now, there are no oscillations of flavor or definite strangeness states, but, instead of it, there is interference of amplitudes due to different virtual mass eigenstates.