scholarly journals An Algebra Model for the Higher-Order Sum Rules

2018 ◽  
Vol 48 (3) ◽  
pp. 453-471
Author(s):  
Jun Yan
Keyword(s):  
Sum Rules ◽  
Higher Order ◽  
Algebra Model

THE MASS OF A QUARK–SQUARK BOUND STATE FROM QCD SUM RULES

1999 ◽  
Vol 14 (30) ◽  
pp. 4763-4780
Author(s):  
M. MEYER-HERMANN ◽  
A. SCHÄFER
Keyword(s):  
Sum Rules ◽  
Mass Range ◽  
Bound State ◽  
Higher Order ◽  
Qcd Sum Rules ◽  
Mass Effects ◽  
Squark Mass

We give an estimate of the expected mass range for a possible two-quark two-squark bound state, using QCD sum rules. The sum rules are modified, taking mass effects into account, so that a treatment of heavy squarks becomes justified. The influence of the higher-order mass corrections and the possibility of a bound state mass below the squark mass are discussed.

scholarly journals On the Coulomb and higher-order sum rules in the relativistic Fermi gas

1997 ◽  
Vol 615 (3) ◽  
pp. 353-372 ◽  
Author(s):  
P. Amore ◽  
R. Cenni ◽  
T.W. Donnelly ◽  
A. Molinari
Keyword(s):  
Sum Rules ◽  
Fermi Gas ◽  
Higher Order ◽  
Relativistic Fermi

scholarly journals Small-momentum expansion of heavy-quark correlators in the large-β0 limit and αs extractions

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Diogo Boito ◽  
Vicent Mateu ◽  
Marcus V. Rodrigues
Keyword(s):  
Heavy Quark ◽  
Strong Coupling ◽  
Sum Rules ◽  
Axial Vector ◽  
Vector Current ◽  
Higher Order ◽  
Lattice Data ◽  
Small Momentum ◽  
Pseudo Scalar

Abstract We calculate the small-momentum expansion of vector, axial-vector, scalar, and pseudo-scalar heavy-quark current correlators in the large-β0 limit of QCD, extending the analysis of Grozin and Sturm beyond the vector current. Our results are used to study the higher-order behaviour of dimensionless ratios of vector and pseudo-scalar moments used for the precise extraction of the strong coupling, αs, from relativistic quarkonium sum rules and lattice data, respectively. We show that these ratios benefit from a partial cancellation of the leading renormalon singularities. Our results can guide the design of combinations of moments with improved perturbative behaviour.

scholarly journals ESTIMATES OF THE HIGHER ORDER QCD CORRECTIONS TO R(s), Rτ AND DEEP INELASTIC SCATTERING SUM RULES

1995 ◽  
Vol 10 (03) ◽  
pp. 235-250 ◽  
Author(s):  
ANDREI L. KATAEV ◽  
VALERY V. STARSHENKO
Keyword(s):  
Inelastic Scattering ◽  
Deep Inelastic Scattering ◽  
Sum Rules ◽  
Higher Order ◽  
Analytical Continuation ◽  
Sum Rule ◽  
Euclidean Region ◽  
Effective Charges ◽  
Physical Quantities ◽  
Perturbative Corrections

We present the attempt to study the problem of the estimates of higher order perturbative corrections to physical quantities in the Euclidean region. Our considerations are based on the application of the scheme-invariant methods, namely the principle of minimal sensitivity and the effective charges approach. We emphasize that in order to obtain the concrete results for the physical quantities in the Minkowskian region the results of application of this formalism should be supplemented by the explicit calculations of the effects of the analytical continuation. We present the estimates of the order [Formula: see text] QCD corrections to the Euclidean quantities: the e+e−-annihilation D-function and the deep inelastic scattering sum rules, namely the nonpolarized and polarized Bjorken sum rules and to the Gross–Llewellyn Smith sum rule. The results for the D-function are further applied to estimate the [Formula: see text] QCD corrections to the Minkowskian quantities R(s) = σ tot (e+e− → hadrons )/σ(e+e− → µ+µ−) and [Formula: see text]. The problem of the fixation of the uncertainties due to the [Formula: see text] corrections to the considered quantities is also discussed.

scholarly journals Renormalization scheme dependence and renormalization group summation

2018 ◽  
Vol 96 (2) ◽  
pp. 233-240 ◽  
Author(s):  
F.A. Chishtie ◽  
D.G.C. McKeon
Keyword(s):  
Free Energy ◽  
Renormalization Group ◽  
Effective Action ◽  
Sum Rules ◽  
Scale Parameter ◽  
Higher Order ◽  
Renormalization Scheme ◽  
Radiative Corrections ◽  
Renormalization Scale ◽  
Running Coupling

We consider logarithmic contributions to the free energy, instanton effective action, and Laplace sum rules in QCD that are a consequence of radiative corrections. Upon summing these contributions by using the renormalization group, all dependence on the renormalization scale parameter μ cancels. The renormalization scheme dependence in these processes is examined, and a renormalization scheme is found in which the effect of higher-order radiative corrections is absorbed by the behaviour of the running coupling.

Higher-order sum rules for rotatory strengths

1977 ◽  
Vol 33 (2) ◽  
pp. 483-494 ◽  
Author(s):  
Aage E. Hansen
Keyword(s):  
Sum Rules ◽  
Higher Order

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

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