Three-quark static potential in perturbation theory

2010 ◽  
Vol 81 (5) ◽  
Author(s):  
Nora Brambilla ◽  
Jacopo Ghiglieri ◽  
Antonio Vairo
Keyword(s):  
Perturbation Theory ◽  
Static Potential

scholarly journals Determination of α(Mz) from an hyperasymptotic approximation to the energy of a static quark-antiquark pair

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Cesar Ayala ◽  
Xabier Lobregat ◽  
Antonio Pineda
Keyword(s):  
Perturbation Theory ◽  
Energy Range ◽  
Short Distance ◽  
Weak Coupling ◽  
Strong Consistency ◽  
Lattice Data ◽  
Static Potential ◽  
Static Energy ◽  
Static Quark

Abstract We give the hyperasymptotic expansion of the energy of a static quark-antiquark pair with a precision that includes the effects of the subleading renormalon. The terminants associated to the first and second renormalon are incorporated in the analysis when necessary. In particular, we determine the normalization of the leading renormalon of the force and, consequently, of the subleading renormalon of the static potential. We obtain $$ {Z}_3^F $$ Z 3 F (nf = 3) = $$ 2{Z}_3^V $$ 2 Z 3 V (nf = 3) = 0.37(17). The precision we reach in strict perturbation theory is next-to-next-to-next-to-leading logarithmic resummed order both for the static potential and for the force. We find that the resummation of large logarithms and the inclusion of the leading terminants associated to the renormalons are compulsory to get accurate determinations of $$ {\Lambda}_{\overline{\mathrm{MS}}} $$ Λ MS ¯ when fitting to short-distance lattice data of the static energy. We obtain $$ {\Lambda}_{\overline{\mathrm{MS}}}^{\left({n}_f=3\right)} $$ Λ MS ¯ n f = 3 = 338(12) MeV and α(Mz) = 0.1181(9). We have also MS found strong consistency checks that the ultrasoft correction to the static energy can be computed at weak coupling in the energy range we have studied.

Expansion in angular momenta in bound-state perturbation theory

1956 ◽  
Vol 233 (1195) ◽  
pp. 527-536 ◽  
Keyword(s):  
Perturbation Theory ◽  
Relativistic Electron ◽  
Bound State ◽  
Static Potential ◽  
Heavy Atoms ◽  
Angular Momenta

An expansion of the propagator S F (F) (x 2 , x 1 ) of a relativistic electron in a central static potential is given. The terms of this expansion correspond to the angular momenta of the electron propagated by this function. Applications to problems concerning heavy atoms are indicated.

scholarly journals Masses of heavy–light mesons with two-loop static potential in a variational approach

2019 ◽  
Vol 34 (14) ◽  
pp. 1950106
Author(s):  
Jugal Lahkar ◽  
Rashidul Hoque ◽  
D. K. Choudhury
Keyword(s):  
Perturbation Theory ◽  
Variational Method ◽  
Stationary State ◽  
Variational Approach ◽  
Wave Functions ◽  
Approximation Methods ◽  
Static Potential ◽  
Cornell Potential ◽  
Light Mesons ◽  
The Masses

In this work, we investigate the masses of a few heavy–light mesons with variational method, taking into account the two-loop effects in the static Cornell potential. Specifically, we consider two wave functions, Gaussian and Coulomb. Our analysis suggests that phenomenologically such approach is more successful in the heavy flavored meson sector than the stationary state perturbation theory and other approximation methods.

The coherent scattering of γ -rays by K electrons in heavy atoms - I. Method

1954 ◽  
Vol 227 (1168) ◽  
pp. 51-58 ◽  
Keyword(s):  
Perturbation Theory ◽  
Coherent Scattering ◽  
Static Field ◽  
Matrix Elements ◽  
Static Potential ◽  
Heavy Atoms ◽  
Intermediate States ◽  
Γ Rays ◽  
Bound Electrons ◽  
Made In

A method for evaluating transition amplitudes for bound electrons in second order in the effects of the radiation field is outlined. An example of the type of problem concerned is the coherent scattering of γ -rays by the K electrons in heavy atoms. The static field in which the electron moves is taken into account exactly; no expansion is made in its effects. In the usual perturbation theory this is equivalent to summing matrix elements over intermediate states which are solutions of the wave equation including the static potential. In the method presented here, however, the sum over radial eigenstates for a particular angular momentum of intermediate state is replaced by quadratures of the products of known functions with the solution of a pair of coupled inhomogeneous differential equations.

A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

The Contribution of Phonon-Scattered Electrons to High-Resolution Electron Micrographs of Crystals

1990 ◽  
Vol 48 (1) ◽  
pp. 62-63
Author(s):  
H. Kohl
Keyword(s):  
High Resolution ◽  
Spherical Aberration ◽  
High Resolution Electron Microscopy ◽  
Static Potential ◽  
Qualitative Comparison ◽  
The Past ◽  
Resolution Electron ◽  
High Resolution Images ◽  
High Resolution Electron Micrographs ◽  
Extract Information

High-Resolution Electron Microscopy is able to determine structures of crystals and interfaces with a spatial resolution of somewhat less than 2 Å. As the image is strongly dependent on instrumental parameters, notably the defocus and the spherical aberration, the interpretation of micrographs necessitates a comparison with calculated images. Whereas one has often been content with a qualitative comparison of theory with experiment in the past, one is currently striving for quantitative procedures to extract information from the images [1,2]. For the calculations one starts by assuming a static potential, thus neglecting inelastic scattering processes.We shall confine the discussion to periodic specimens. All electrons, which have only been elastically scattered, are confined to very few directions, the Bragg spots. In-elastically scattered electrons, however, can be found in any direction. Therefore the influence of inelastic processes on the elastically (= Bragg) scattered electrons can be described as an attenuation [3]. For the calculation of high-resolution images this procedure would be correct only if we had an imaging energy filter capable of removing all phonon-scattered electrons. This is not realizable in practice. We are therefore forced to include the contribution of the phonon-scattered electrons.

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