scholarly journals Effective free-fermionic form factors and the XY spin chain

2021 ◽  
Vol 10 (3) ◽  
Author(s):  
Oleksandr Gamayun ◽  
Nikolai Iorgov ◽  
Yu. Zhuravlev
Keyword(s):  
Form Factors ◽  
Elementary Functions ◽  
Fredholm Determinants ◽  
Tau Functions ◽  
Effective Form ◽  
Arbitrary Phase ◽  
Quantum Chain ◽  
Static Correlation ◽  
The One ◽  
Exact Summation

We introduce effective form factors for one-dimensional lattice fermions with arbitrary phase shifts. We study tau functions defined as series of these form factors. On the one hand we perform the exact summation and present tau functions as Fredholm determinants in the thermodynamic limit. On the other hand simple expressions of form factors allow us to present the corresponding series as integrals of elementary functions. Using this approach we re-derive the asymptotics of static correlation functions of the XY quantum chain at finite temperature.

scholarly journals THE TOROID DIPOLE MOMENT OF THE NEUTRINO

1998 ◽  
Vol 13 (30) ◽  
pp. 5257-5277 ◽  
Author(s):  
VLADIMIR M. DUBOVIK ◽  
VALENTIN E. KUZNETSOV
Keyword(s):  
Dipole Moment ◽  
Mass Shell ◽  
Dipole Moments ◽  
Form Factors ◽  
Dispersion Method ◽  
Anapole Moment ◽  
Electromagnetic Interactions ◽  
Loop Approximation ◽  
The Standard Model ◽  
The One

We discuss the third electromagnetic characteristic of the neutrino, i.e. the toroid dipole moment (TDM), in the framework of the Standard Model. The TDM's distinctions from and similarities to an anapole moment are mentioned. The calculations of toroid dipole moments of νe,μ,τ neutrinos have been done by the dispersion method in the one-loop approximation of the SM for the Majorana case and generalized to the Dirac one. We found them to be different from zero in the case of massive as well as massless neutrinos. The behavior of the νe,μ,τ toroid form factors is also presented in the [Formula: see text] range. All external particles are on the mass shell and there are no problems with the physical interpretation of the final result. Some manifestations of the electromagnetic interactions of neutrinos, induced by their toroid moments, are also remarked on.

scholarly journals Eta Prime Gluonic Contribution to the Nucleon Self-Energy in an Effective Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
A. Upadhyay ◽  
J. P. Singh
Keyword(s):  
Charge Density ◽  
Topological Charge ◽  
Form Factors ◽  
Heavy Baryon ◽  
Effective Theory ◽  
Nucleon Mass ◽  
Total Contribution ◽  
Self Energy ◽  
Qcd Vacuum ◽  
The One

We estimate a possibleη′gluonic contribution to the self-energy of a nucleon in an effective theory. The couplings of the topological charge density to nucleons give rise to OZI violatingη′-nucleon interactions. The one-loop self-energy of nucleon arising due to these interactions is studied using a heavy baryon chiral perturbation theory. The divergences have been removed using appropriate form factors. The nontrivial structure of the QCD vacuum has also been taken into account. The numerical results are sensitive to the choice of the regulator to a nonnegligible extent. We get the total contribution to the nucleon mass coming from its interaction with the topological charge densityδmtot≅-(2.5–7.5)% of the nucleon mass.

scholarly journals Hadron Form Factors at BESIII

2018 ◽  
Vol 46 ◽  
pp. 1860027
Author(s):  
Zhaoxia Meng
Keyword(s):  
Cross Section ◽  
Center Of Mass ◽  
Polar Angle ◽  
Form Factors ◽  
Angle Distribution ◽  
Initial State ◽  
Fundamental Information ◽  
Born Cross Section ◽  
Effective Form ◽  
State Radiation

Form factors of hadron provide fundamental information about its structure and dynamics. They constitute a rigorous test of non-perturbative QCD as well as of phenomenological models. Based on data samples collected with BESIII detector at BEPCII collider, born cross section of [Formula: see text] and proton effective form factors are measured at 12 center-of-mass energies between 2.2324 and 3.671 GeV. The ratio [Formula: see text]s are extracted by fitting polar angle distribution of proton for data samples with large statistics. For data between 3.773 and 4.6 GeV, we use initial state radiation (ISR) method to study [Formula: see text] by tagged or un-tagged ISR photon, where the pair cross section, effective form factors and [Formula: see text]s are obtained from proton pair threshold to about 3 GeV. For [Formula: see text] and [Formula: see text], the pair cross section and [Formula: see text] form factors are measured near threshold. With data scanned in 2015 from 2-3.08 GeV, charged Kaon pair cross section and form factors are measured at 21 center-of-mass energies.

scholarly journals New explicit analytical solutions of equations for heat and mass transfer in a cooling tower energy system

2019 ◽  
Vol 11 (12) ◽  
pp. 168781401989614
Author(s):  
Qianjian Guo ◽  
Xiaoni Qi ◽  
Peng Sun ◽  
Pengjiang Guo
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Analytical Solutions ◽  
Cooling Tower ◽  
Mass Transfer Process ◽  
Energy System ◽  
Transfer Model ◽  
Elementary Functions ◽  
Solutions Of Equations ◽  
The One

The aim of this article is to develop an accurate and fast analytical method for heat and mass transfer model in a cooling tower energy system. Some algebraic explicit analytical solutions of the one-dimensional differential equation sets describing the coupled heat and mass transfer process in a cooling tower are derived. The explicit solutions have not yet been published before. The explicit equations of heat and mass transfer are expressed in elementary functions. By solving these differential equations in a cooling tower, the temperature distribution of liquid and gas, the moisture content in the air can be obtained in each section over the vertical height of the tower. A comparison of analytical and experimental results was given in this article, and good agreements were shown for the typical cases studied. The analytical solutions can serve as a benchmark to check the results of numerical calculation.

scholarly journals Averaging of Earth-Crossing Orbits

1999 ◽  
Vol 172 ◽  
pp. 433-434
Author(s):  
G.F. Gronchi ◽  
A. Milani
Keyword(s):  
Equations Of Motion ◽  
Generalized Solution ◽  
Elementary Functions ◽  
Averaged Equations ◽  
Major Planet ◽  
The One ◽  
Polar Singularity ◽  
Straight Lines ◽  
Method Of Extraction ◽  
Inverse Distance

The orbits of planet-crossing asteroids (and comets) can undergo close approaches and collisions with some major planet. This introduces a singularity in the N-body Hamiltonian, and the averaging of the equations of motion, traditionally used to compute secular perturbations, is undefined. We have shown (Gronchi and Milani, 1998) that it is possible to define in a rigorous way some generalised averaged equations of motion, in such a way that the generalised solutions are unique and piecewise smooth, with corners on the node crossing lines.The model is the averaged equations of motion first introduced by Kozai (1962): the perturbing planets are assumed to move in circular, coplanar orbits, and the equations of motion are averaged over the anomalies of the asteroid and of the planets. In the non-crossing case the averaging is integrable; in the planet-crossing case there is a polar singularity of order two in the equations of motion, and averaging is not possible. To define a generalized solution, we decrease the order of the polar singularity by the method of extraction of the singularities by Kantorovich. The singularity of the perturbing function is approximated by a modified inverse distance, the one between the straight lines tangent to the two orbits at the nodal points. In this approximation the averaged perturbing function has an analytical expression, allowing explicit computation with elliptic integrals and elementary functions.

Inverse Solutions for One-Dimensional Seismic Waves in Elastic, Inhomogeneous Media

1977 ◽  
Vol 44 (3) ◽  
pp. 469-474 ◽  
Author(s):  
H. L. Schreyer
Keyword(s):  
Wave Equation ◽  
Seismic Waves ◽  
Homogeneous Material ◽  
Elementary Functions ◽  
One Dimensional ◽  
Seismic Shear ◽  
Inhomogeneous Wave Equation ◽  
Inverse Solutions ◽  
The One ◽  
Different Characteristics

An inverse procedure is developed for obtaining exact solutions to the one-dimensional inhomogeneous wave equation. Transformations of the independent spatial variable and the dependent variable are introduced so that the wave equation assumes the form associated with a homogeneous material. The resulting transformation relations are nonlinear but of such a nature that they can be easily integrated if the reciprocal of the wave speed distribution can be expressed in terms of elementary functions. One functional form that yields realistic values for material properties of soil layers is investigated in detail. Amplification factors for a sinusoidal seismic shear wave in inhomogeneous and homogeneous layers are derived and illustrations of significantly different characteristics for the two types of layers are shown.

Λ-Σ COUPLING EFFECT ON NONMESONIC DECAY OF HYPERNUCLEI

1988 ◽  
Vol 03 (07) ◽  
pp. 1581-1592 ◽  
Author(s):  
H. BANDŌ ◽  
Y. SHONO ◽  
H. TAKAKI
Keyword(s):  
Coupling Effect ◽  
Form Factors ◽  
Pion Exchange ◽  
Closure Approximation ◽  
The One

In addition to the one-pion-exchange ΛN→NN process with a weak ΛNπ and a strong NNπ vertex, the ΛN→ΣN→NN process is considered, where the ΛN-ΣN coupling is induced mainly by π exchange. For the weak ΛNπ and ΣNπ vertices, the empirical values are used along with the SU3 symmetry and the ΔI=1/2 rule. The closure approximation is employed for the intermediate ΣN state. The form factors and the initial and final correlations are taken into account. Calculations are done for the [Formula: see text] hypernucleus.

scholarly journals Dispersion relations for hadronic light-by-light scattering and the muon g – 2

2018 ◽  
Vol 166 ◽  
pp. 00014 ◽  
Author(s):  
Massimiliano Procura ◽  
Gilberto Colangelo ◽  
Martin Hoferichter ◽  
Peter Stoffer
Keyword(s):  
Partial Wave ◽  
Form Factors ◽  
Pion Pole ◽  
Vector Form ◽  
Partial Wave Expansion ◽  
Left Hand ◽  
Pion Polarizability ◽  
Pion Loop ◽  
Crossing Symmetry ◽  
The One

The largest uncertainties in the Standard Model calculation of the anomalous magnetic moment of the muon (g – 2)μ come from hadronic effects, and in a few years the subleading hadronic light-by-light (HLbL) contribution might dominate the theory error. We present a dispersive description of the HLbL tensor, which is based on unitarity, analyticity, crossing symmetry, and gauge invariance. This opens up the possibility of a data-driven determination of the HLbL contribution to (g – 2)μ with the aim of reducing model dependence and achieving a reliable error estimate. Our dispersive approach defines unambiguously the pion-pole and the pion-box contribution to the HLbL tensor. Using Mandelstam double-spectral representation, we have proven that the pion-box contribution coincides exactly with the one-loop scalar-QED amplitude, multiplied by the appropriate pion vector form factors. Using dispersive fits to high-statistics data for the pion vector form factor, we obtain [see formula in PDF]. A first model-independent calculation of effects of ππ intermediate states that go beyond the scalar-QED pion loop is also presented. We combine our dispersive description of the HLbL tensor with a partial-wave expansion and demonstrate that the known scalar-QED result is recovered after partial-wave resummation. After constructing suitable input for the γ*γ* → ππ helicity partial waves based on a pion-pole left-hand cut (LHC), we find that for the dominant charged-pion contribution this representation is consistent with the two-loop chiral prediction and the COMPASS measurement for the pion polarizability. This allows us to reliably estimate S-wave rescattering effects to the full pion box and leads to [see formula in PDF].

scholarly journals Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions

2020 ◽  
Vol 9 (3) ◽  
Author(s):  
Etienne Granet ◽  
Maurizio Fagotti ◽  
Fabian Essler
Keyword(s):  
Form Factor ◽  
Form Factors ◽  
Transverse Field ◽  
Natural Generalization ◽  
Point Function ◽  
Quench Dynamics ◽  
Density Expansions ◽  
The One ◽  
Transverse Field Ising Model ◽  
Partial Fractions

We consider the problems of calculating the dynamical order parameter two-point function at finite temperatures and the one-point function after a quantum quench in the transverse field Ising chain. Both of these can be expressed in terms of form factor sums in the basis of physical excitations of the model. We develop a general framework for carrying out these sums based on a decomposition of form factors into partial fractions, which leads to a factorization of the multiple sums and permits them to be evaluated asymptotically. This naturally leads to systematic low density expansions. At late times these expansions can be summed to all orders by means of a determinant representation. Our method has a natural generalization to semi-local operators in interacting integrable models.

THE QUARK MODEL, DEUTERON FORM FACTORS AND NUCLEAR MAGNETIC MOMENTS

1993 ◽  
Vol 02 (01) ◽  
pp. 39-185 ◽  
Author(s):  
AMAND FAESSLER ◽  
A. BUCHMANN ◽  
Y. YAMAUCHI
Keyword(s):  
Deuteron Wave Function ◽  
Magnetic Moments ◽  
Form Factors ◽  
Pauli Principle ◽  
Group Method ◽  
Gluon Exchange ◽  
Nuclear Magnetic Moments ◽  
Nuclear Operators ◽  
Quark Level ◽  
The One

The study of the deuteron electromagnetic form factors based on the quark cluster model is reviewed. The deuteron wave function is derived from a microscopic quark Hamiltonian with the help of the Resonating Group Method. One-pion and one-gluon exchange potentials are included in addition to a quadratic confinement potential. The photon is coupled directly to the quarks. Aside from the one-body impulse current, pion and gluon exchange currents are included on the quark level. Due to the Pauli principle on the quark level, new electromagnetic currents arise which are not present on the nucleon level. These currents, called quark exchange currents, describe processes in which a photon couples to a quark or a pair of quarks interacting via gluon or pion exchange and which are accompanied by a simultaneous quark interchange between the two threequark clusters (nucleons). They are small for low momentum transfers but appreciably influence the electromagnetic structure of the deuteron beyond a momentum transfer of q=5 fm−1. The discussion is extended to the magnetic moments of 15N, 17O and 39K by introducing the quark exchange currents as effective operators on the nucleon level. The quark exchange currents written in terms of nonlocal and spin-isospin dependent nuclear operators are effective only at short distances. They are evaluated with shell-model (harmonic oscillator) wave functions including the (short-range) Brueckner correlations. The Bethe-Goldstone equation is solved with our effective NN potential, which is derived from a microscopic quark Hamiltonian. The quark exchange currents shift the isovector magnetic moment of 39K by −20% from its Schmidt value.

Sign in / Sign up

Export Citation Format

Share Document