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.

scholarly journals RENORMALIZATION SCHEMES AND RENORMALONS

1996 ◽  
Vol 11 (10) ◽  
pp. 835-851 ◽  
Author(s):  
N.V. KRASNIKOV ◽  
A.A. PIVOVAROV
Keyword(s):  
Renormalization Group ◽  
Higher Order ◽  
Coupling Constant ◽  
Landau Pole ◽  
Running Coupling ◽  
Running Coupling Constant ◽  
Higher Order Corrections

Various ways on how higher order corrections can reveal themselves if integrated over the ir region are discussed. We show that in different renormalization group (RG) schemes and for some observables one has no factorial divergences. We argue that for treating things in the ir region it is preferable to start with a RG scheme without the ir Landau pole in the running coupling constant. The uncertainties for the τ lepton width resulting from accounting for higher order corrections are also discussed.

Higher-order prediction terms and fixing the renormalization scale using the BLM approach

2014 ◽  
Vol 29 (31) ◽  
pp. 1450178 ◽  
Author(s):  
Abolfazl Mirjalili ◽  
Mohammad Reza Khellat
Keyword(s):  
Higher Order ◽  
Order Correction ◽  
Renormalization Scale ◽  
Perturbative Series ◽  
Running Coupling ◽  
Correction Terms

There is an ambiguity in the perturbative series of QCD observables on how to choose the renormalization and even more the factorization scale. There are many approaches to overcome this obstacle and to fix the scales. Among them, there is the Brodsky–Lepage–Mackenzie (BLM) approach which is based on an intriguing principle. Based on the BLM approach, we intend to absorb the nf-terms in the pQCD series that rightly determines the running behavior of the running coupling into the running coupling. We make an extensive use of the BLM approach to investigate the details of predicting higher order correction terms of some QCD observables. By this way we test different methods to improve the prediction process. It is also found out that an overall normalization could change BLM predictions effectively.

scholarly journals Evidence for a 5d F-theorem

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Martin Fluder ◽  
Christoph F. Uhlemann
Keyword(s):  
Free Energy ◽  
Renormalization Group ◽  
General Expression ◽  
Geometric Parameters ◽  
Regularity Conditions ◽  
Large Sample ◽  
Large Numbers ◽  
Renormalization Group Flows

Abstract Renormalization group flows are studied between 5d SCFTs engineered by (p, q) 5-brane webs with large numbers of external 5-branes. A general expression for the free energy on S5 in terms of single-valued trilogarithm functions is derived from their supergravity duals, which are characterized by the 5-brane charges and additional geometric parameters. The additional geometric parameters are fixed by regularity conditions, and we show that the solutions to the regularity conditions extremize a trial free energy. These results are used to survey a large sample of $$ \mathcal{O} $$ O (105) renormalization group flows between different 5d SCFTs, including Higgs branch flows and flows that preserve the SU(2) R- symmetry. In all cases the free energy changes monotonically towards the infrared, in line with a 5d F -theorem.

RENORMALIZATION GROUP EQUATION AND EFFECTIVE ACTION IN STRING THEORY

1989 ◽  
Vol 04 (10) ◽  
pp. 941-951 ◽  
Author(s):  
J. GAITE
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Effective Action ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Generating Functional ◽  
S Matrix

The connection between the renormalization group for the σ-model effective action for the Polyakov string and the S-matrix generating functional for dual amplitudes is studied. A more general approach to the renormalization group equation for string theory is proposed.

Higher Order Conditional Probabilities and Thermodynamics of Binary Molten Alloys

1997 ◽  
Vol 11 (02n03) ◽  
pp. 93-106 ◽  
Author(s):  
O. Akinlade
Keyword(s):  
Free Energy ◽  
Experimental Evidence ◽  
Cluster Model ◽  
Excess Free Energy ◽  
Higher Order ◽  
Thermodynamic Quantities ◽  
Equiatomic Composition ◽  
Conditional Probabilities ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

The recently introduced four atom cluster model is used to obtain higher order conditional probabilities that describe the atomic correlations in some molten binary alloys. Although the excess free energy of mixing for all the systems studied are almost symmetrical about the equiatomic composition, most other thermodynamic quantities are not and thus, the study enables us to explain the subtle differences in their physical characteristics required to describe the mechanism of the observed strong heterocoordination in Au–Zn or homocoordination in Cu–Ni within the same framework. More importantly, we obtain all calculated quantities for the whole concentration range thus complimenting experimental evidence.

scholarly journals Renormalization group methods and the 2PI effective action

2015 ◽  
Vol 91 (2) ◽  
Author(s):  
M. E. Carrington ◽  
Wei-Jie Fu ◽  
D. Pickering ◽  
J. W. Pulver
Keyword(s):  
Renormalization Group ◽  
Effective Action ◽  
Group Methods ◽  
Renormalization Group Methods

scholarly journals Renormalization group invariance and optimal QCD renormalization scale-setting: a key issues review

2015 ◽  
Vol 78 (12) ◽  
pp. 126201 ◽  
Author(s):  
Xing-Gang Wu ◽  
Yang Ma ◽  
Sheng-Quan Wang ◽  
Hai-Bing Fu ◽  
Hong-Hao Ma ◽  
...  
Keyword(s):  
Renormalization Group ◽  
Renormalization Scale ◽  
Group Invariance ◽  
Key Issues
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