scholarly journals Renormalization Group Theory of Effective Field Theory Models in Low Dimensions

2017 ◽  
Author(s):  
Takashi Yanagisawa
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Group Theory ◽  
Effective Field Theory ◽  
Effective Field ◽  
Renormalization Group Theory ◽  
Low Dimensions

scholarly journals Renormalization Group evolution from on-shell SMEFT

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Minyuan Jiang ◽  
Teng Ma ◽  
Jing Shu
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
High Dimensional ◽  
Anomalous Dimensions ◽  
The Standard Model ◽  
Group Evolution

Abstract We describe the on-shell method to derive the Renormalization Group (RG) evolution of Wilson coefficients of high dimensional operators at one loop, which is a necessary part in the on-shell construction of the Standard Model Effective Field Theory (SMEFT), and exceptionally efficient based on the amplitude basis in hand. The UV divergence is obtained by firstly calculating the coefficients of scalar bubble integrals by unitary cuts, then subtracting the IR divergence in the massless bubbles, which can be easily read from the collinear factors we obtained for the Standard Model fields. Examples of deriving the anomalous dimensions at dimension six are presented in a pedagogical manner. We also give the results of contributions from the dimension-8 H4D4 operators to the running of V+V−H2 operators, as well as the running of B+B−H2D2n from H4D2n+4 for general n.

scholarly journals Effective Field Theory for Shallow P-Wave States

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
E. Epelbaum ◽  
J. Gegelia ◽  
H. P. Huesmann ◽  
Ulf-G. Meißner ◽  
Xiu-Lei Ren
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Finite Number ◽  
Effective Field Theory ◽  
Wave Scattering ◽  
Group Analysis ◽  
Effective Field ◽  
P Wave ◽  
Renormalization Group Analysis ◽  
Wave States

AbstractWe discuss the formulation of a non-relativistic effective field theory for two-body P-wave scattering in the presence of shallow states and critically address various approaches to renormalization proposed in the literature. It is demonstrated that the consistent renormalization involving only a finite number of parameters in the well-established formalism with auxiliary dimer fields corresponds to the inclusion of an infinite number of counterterms in the formulation with contact interactions only. We also discuss the implications from the Wilsonian renormalization group analysis of P-wave scattering.

RENORMALIZATION TOOLS FOR THE NN INTERACTION

2010 ◽  
Vol 19 (08n10) ◽  
pp. 1679-1683 ◽  
Author(s):  
S. SZPIGEL ◽  
V. S. TIMÓTEO ◽  
F. O. DURÃES
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Effective Field Theory ◽  
Kernel Method ◽  
Nucleon Nucleon ◽  
Effective Field ◽  
Leading Order ◽  
Chiral Effective Field Theory ◽  
Similarity Renormalization Group

In this work we apply the similarity renormalization group (SRG) approach to evolve an effective nucleon–nucleon (NN) potential in leading-order (LO) chiral effective field theory (ChEFT). We present the results obtained for a NN potential in the 1S0 channel derived within the framework of the subtracted kernel method (SKM).

scholarly journals A SIMPLE STRATEGY FOR RENORMALIZATION: QED AT ONE-LOOP LEVEL

2010 ◽  
Vol 25 (22) ◽  
pp. 4255-4290
Author(s):  
JI-FENG YANG ◽  
ZHAO-TING PAN
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Effective Field Theory ◽  
Effective Field ◽  
The Self ◽  
Self Energy ◽  
Loop Level ◽  
Simple Strategy ◽  
Renormalization Group Equations ◽  
Physical Boundary

We demonstrate our simple strategy for renormalization with QED at one-loop level, basing on an elaboration of the effective field theory philosophy. No artificial regularization or deformation of the original theory is introduced here and hence no manipulation of infinities, ambiguities arise instead of infinities. Ward identities first come to reduce the number of ambiguities, the residual ones could in principle be removed by imposing physical boundary conditions. Renormalization group equations arise as "decoupling theorems" in the underlying theory perspective. In addition, a technical theorem concerning routing of external momenta is also presented and illustrated with the self-energy and vertex function as examples.

THE NEW MEAN FIELD RENORMALIZATION GROUP FROM EFFECTIVE FIELD THEORY

1995 ◽  
Vol 09 (24) ◽  
pp. 1617-1621 ◽  
Author(s):  
F. O. COELHO ◽  
J. A. PLASCAK
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Effective Field Theory ◽  
Order Parameter ◽  
Mean Field ◽  
Previous Treatment ◽  
Field Approximation ◽  
Effective Field ◽  
Mean Field Approximation ◽  
Field Renormalization

The new mean field renormalization group is used to study the Ising model through the calculation of the order parameter by means of the effective field theory based on Callen–Suzuki identity. By considering one- and two-spin clusters, better results are obtained when compared to the previous treatment using the usual mean field approximation.

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