Logarithmic perturbation theory for a spiked oscillator and sum rules

2005 ◽  
Vol 103 (1) ◽  
pp. 19-24 ◽  
Author(s):  
S. K. Bandyopadhyay ◽  
K. Bhattacharyya
Keyword(s):  
Perturbation Theory ◽  
Sum Rules

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.

Breakdown of Asymptotic Sum Rules in Perturbation Theory

1969 ◽  
Vol 22 (18) ◽  
pp. 978-981 ◽  
Author(s):  
Stephen L. Adler ◽  
Wu-Ki Tung
Keyword(s):  
Perturbation Theory ◽  
Sum Rules

scholarly journals Improved calculation of the γ*γ → π process at low Q2 using LCSR’s and renormalization-group summation

2022 ◽  
Vol 258 ◽  
pp. 03003
Author(s):  
Sergey Mikhailov ◽  
Alexandr Pimikov ◽  
N.G. Stefanis
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Transition Form Factor ◽  
Sum Rules ◽  
Power Series Expansion ◽  
Transition Form ◽  
Analytic Perturbation Theory ◽  
Fixed Order ◽  
Best Fit ◽  
Good Agreement

We study two versions of lightcone sum rules to calculate the γ*γ → π0 transition form factor (TFF) within QCD. While the standard version is based on fixed-order perturbation theory by means of a power-series expansion in the strong coupling, the new method incorporates radiative corrections by renormalization-group summation and generates an expansion within a generalized fractional analytic perturbation theory involving only analytic couplings. Using this scheme, we determine the relative nonperturbative parameters and the first two Gegenbauer coefficients of the pion distribution amplitude (DA) to obtain TFF predictions in good agreement with the preliminary BESIII data, while the best-fit pion DA satisfies the most recent lattice constraints on the second moment of the pion DA at the three-loop level.

scholarly journals The strong coupling from $e^+e^-\to$~hadrons

2019 ◽  
Author(s):  
Diogo Boito ◽  
Maarten Golterman ◽  
Alex Keshavarzi ◽  
Kim Maltman ◽  
Daiskuke Nomura ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Strong Coupling ◽  
Sum Rules ◽  
Finite Energy ◽  
Order Perturbation ◽  
Decay Data ◽  
Systematic Effects ◽  
Fixed Order ◽  
Charm Mass ◽  
Good Agreement

We use a new compilation of the hadronic RR-ratio from available data for the process e^+e^-\toe+e−→ hadrons below the charm mass to determine the strong coupling \alpha_sαs, using finite-energy sum rules. Quoting our results at the \tauτ mass to facilitate comparison to the results obtained from similar analyses of hadronic \tauτ-decay data, we find \alpha_s(m_\tau^2)=0.298\pm 0.016\pm 0.006αs(mτ2)=0.298±0.016±0.006 in fixed-order perturbation theory, and \alpha_s(m_\tau^2)=0.304\pm 0.018\pm 0.006αs(mτ2)=0.304±0.018±0.006 in contour-improved perturbation theory, where the first error is statistical, and the second error combines various systematic effects. These values are in good agreement with a recent determination from the OPAL and ALEPH data for hadronic \tauτ decays. We briefly compare the R(s)R(s)-based analysis with the \tauτ-based analysis.

ON PERTURBATIVE CALCULABILITY OF THE COEFFICIENT FUNCTIONS OF CONDENSATES IN THE QCD SUM RULES

1989 ◽  
Vol 04 (08) ◽  
pp. 765-773 ◽  
Author(s):  
L.R. SURGULADZE ◽  
F.V. TKACHOV
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Sum Rules ◽  
Group Analysis ◽  
Coefficient Function ◽  
Qcd Sum Rules ◽  
Renormalization Group Analysis ◽  
Light Mesons ◽  
Pseudo Scalar

We calculate two-loop corrections to the coefficient functions of the condensates 〈G2〉0 and [Formula: see text] in the QCD sum rules for the light mesons in the vector, scalar and pseudoscalar channels, and three-loop corrections to the coefficient function of the condensate 〈G2〉0 in the (pseudo)scalar channel. We find that a renormalization-group analysis casts strong doubts on the feasibility of obtaining correct estimates for the coefficient functions via perturbation theory.

A Class of Sum Rules with Application to Nondegenerate Perturbation Theory

1966 ◽  
Vol 7 (12) ◽  
pp. 2271-2277 ◽  
Author(s):  
P. T. Landsberg ◽  
D. J. Morgan
Keyword(s):  
Perturbation Theory ◽  
Sum Rules

scholarly journals PION TRANSITION FORM FACTOR AT THE TWO-LOOP LEVEL VIS-À-VIS EXPERIMENTAL DATA

2009 ◽  
Vol 24 (35n37) ◽  
pp. 2858-2867 ◽  
Author(s):  
S. V. MIKHAILOV ◽  
N. G. STEFANIS
Keyword(s):  
Experimental Data ◽  
Perturbation Theory ◽  
Form Factor ◽  
Light Cone ◽  
Transition Form Factor ◽  
Sum Rules ◽  
Leading Order ◽  
Transition Form ◽  
Qcd Sum Rules ◽  
Theoretical Results

We use light-cone QCD sum rules to calculate the pion-photon transition form factor, taking into account radiative corrections up to the next-to-next-to-leading order of perturbation theory. We compare the obtained predictions with all available experimental data from the CELLO, CLEO, and the BaBar Collaborations. We point out that the BaBar data are incompatible with the convolution scheme of QCD, on which our predictions are based, and can possibly be explained only with a violation of the factorization theorem. We pull together recent theoretical results and comment on their significance.

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