scholarly journals Study of the renormalization-group evolution ofN=1supersymmetric gauge theories using Padé approximants

2016 ◽  
Vol 93 (6) ◽  
Author(s):  
Gongjun Choi ◽  
Robert Shrock
Keyword(s):  
Renormalization Group ◽  
Gauge Theories ◽  
Padé Approximants ◽  
Pade Approximants ◽  
Group Evolution

scholarly journals Probing the Infrared Structure of Gauge Theories: A Padé-Approximant Approach

2001 ◽  
Vol 16 (supp01c) ◽  
pp. 913-915 ◽  
Author(s):  
F. A. Chishtie ◽  
V. Elias ◽  
V. A. Miransky ◽  
T. G. Steele
Keyword(s):  
Fixed Point ◽  
Gauge Theory ◽  
Gauge Theories ◽  
Padé Approximants ◽  
Padé Approximant ◽  
Pade Approximants ◽  
Pade Approximant ◽  
Specific Choice ◽  
Large N ◽  
Β Function

Padé-approximant treatments of the known terms of the QCD β-function are seen to develop possible infrared fixed point structure only if the number of fermion flavours is sufficiently large. This flavour threshold is seen to be between six and nine flavours, depending upon both the specific choice of approximant as well as on the presently-unknown five-loop β-function contribution. Below this flavour threshold, Padé approximants based upon the QCD β-function manifest the same infrared attractor structure as that which characterizes the exact NSVZ β-function of supersymmetric gluodynamics. Such infrared attractor structure is also seen to characterize Padé-approximant treatments of vector SU(N) gauge theory in the large N limit, suggesting common infrared dynamics for the strong and weak phases of this theory.

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.

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