The renormalization-group improved effective potential in the Wess–Zumino model

2004 ◽  
Vol 82 (9) ◽  
pp. 737-742 ◽  
Author(s):  
D.G.C. McKeon
Keyword(s):  
Renormalization Group ◽  
Effective Potential ◽  
Method Of Characteristics ◽  
Background Field ◽  
Scale Dependence ◽  
Supersymmetric Model ◽  
Loop Correction ◽  
The One ◽  
Zumino Model ◽  
Leading Logarithm

The one-loop correction to the effective potential in the massless Wess–Zumino supersymmetric model is computed using operator regularization. The renormalization group is used to determine the scale dependence of the parameters characterizing the model (the coupling and background field strength) and to sum leading logarithm contributions to the effective potential to all orders of perturbation theory, using the method of characteristics. PACS No.: 11.30.Pb

scholarly journals The renormalization group and the effective potential in the Wess–Zumino model

2019 ◽  
Vol 97 (6) ◽  
pp. 596-598
Author(s):  
D.G.C. McKeon
Keyword(s):  
Renormalization Group ◽  
Effective Potential ◽  
Background Field ◽  
Mass Scale ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
General Requirement ◽  
Supersymmetric Gauge ◽  
Implicit Dependence ◽  
Zumino Model

We consider the effective potential V in the massless Wess–Zumino model. By using the renormalization group equation, we show that the explicit and implicit dependence of V on the renormalization mass scale μ cancels. If V has an extremum at some non-vanishing value of the background field, then it follows that V is “flat”, independent of the background field. This is consistent with the general requirement that V be convex. The consequences for supersymmetric gauge theories are briefly considered.

scholarly journals The renormalization group and the effective action

2011 ◽  
Vol 89 (3) ◽  
pp. 277-280 ◽  
Author(s):  
D. G.C. McKeon
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Gauge Field ◽  
Effective Potential ◽  
Effective Action ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
The One ◽  
External Gauge

The renormalization group is used to sum the leading-log (LL) contributions to the effective action for a large constant external gauge field in terms of the one-loop renormalization group (RG) function β, the next-to-leading-log (NLL) contributions in terms of the two-loop RG function, etc. The log-independent pieces are not determined by the RG equation, but can be fixed by considering the anomaly in the trace of the energy-momentum tensor. Similar considerations can be applied to the effective potential V for a scalar field [Formula: see text]; here the log-independent pieces are fixed by the condition [Formula: see text].

CONVERGENCE OF DERIVATIVE AND INVERSE EFFECTIVE MASS EXPANSIONS FOR THE ONE LOOP EFFECTIVE ACTION

1987 ◽  
Vol 02 (05) ◽  
pp. 353-358 ◽  
Author(s):  
ROBERT J. PERRY ◽  
MING LI
Keyword(s):  
Effective Mass ◽  
Effective Action ◽  
Asymptotic Series ◽  
Background Field ◽  
Higher Order ◽  
Numerical Results ◽  
Derivative Expansion ◽  
Loop Correction ◽  
The One ◽  
Higher Order Corrections

Numerical results for the one loop correction to (ϕ4)2 are compared to results obtained from a derivative expansion and an expansion in inverse powers of the effective mass. We vary the scalar background field to illustrate when and why these expansions succeed, and how they break down. It is shown that both expansions behave like asymptotic series, with the approximation improving until higher order corrections grow in magnitude.

scholarly journals Relationship between Fujikawa’s Method and the Background Field Method for the Scale Anomaly

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Chris L. Lin ◽  
Carlos R. Ordóñez
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Effective Potential ◽  
Effective Action ◽  
Background Field ◽  
Field Method ◽  
Scale Dependence ◽  
Classical Action ◽  
Loop Expansion ◽  
Background Field Method

We show the equivalence between Fujikawa’s method for calculating the scale anomaly and the diagrammatic approach to calculating the effective potential via the background field method, for anO(N)symmetric scalar field theory. Fujikawa’s method leads to a sum of terms, each one superficially in one-to-one correspondence with a vacuum diagram of the 1-loop expansion. From the viewpoint of the classical action, the anomaly results in a breakdown of the Ward identities due to scale-dependence of the couplings, whereas, in terms of the effective action, the anomaly is the result of the breakdown of Noether’s theorem due to explicit symmetry breaking terms of the effective potential.

RG IMPROVEMENT OF THE EFFECTIVE POTENTIAL AT FINITE TEMPERATURE

1996 ◽  
Vol 11 (28) ◽  
pp. 2259-2269 ◽  
Author(s):  
HISAO NAKKAGAWA ◽  
HIROSHI YOKOTA
Keyword(s):  
Renormalization Group ◽  
Effective Potential ◽  
Finite Temperature ◽  
Renormalization Group Equation ◽  
Effective Procedure ◽  
Coefficient Function ◽  
Group Equation ◽  
Leading Order ◽  
Effective Potentials ◽  
The One

We present a simple and effective procedure to improve the finite temperature effective potential so as to satisfy the renormalization group equation (RGE). With the L-loop knowledge of the effective potential and of the RGE coefficient function, this procedure carries out a systematic resummation of large-T as well as large-log terms up to the Lth-to-leading order, giving an improved effective potential which satisfies the RGE and is exact up to the Lth-to-leading T and log terms. Applications to the one- and two-loop effective potentials are explicitly performed.

scholarly journals On the one-loop calculations with Reggeized quarks

2017 ◽  
Vol 32 (40) ◽  
pp. 1750207 ◽  
Author(s):  
Maxim Nefedov ◽  
Vladimir Saleev
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Effective Field Theory ◽  
Effective Action ◽  
Gauge Invariance ◽  
Effective Field ◽  
Loop Correction ◽  
Gauge Invariant ◽  
The One ◽  
Regge Limit

The technique of one-loop calculations for the processes involving Reggeized quarks is described in the framework of gauge invariant effective field theory for the Multi-Regge limit of QCD, which has been introduced by Lipatov and Vyazovsky. The rapidity divergences, associated with the terms enhanced by log(s), appear in the loop corrections in this formalism. The covariant procedure of regularization of rapidity divergences, preserving the gauge invariance of effective action is described. As an example application, the one-loop correction to the propagator of Reggeized quark and [Formula: see text]-scattering vertex are computed. Obtained results are used to construct the Regge limit of one-loop [Formula: see text] amplitude. The cancellation of rapidity divergences and consistency of the EFT prediction with the full QCD result is demonstrated. The rapidity renormalization group within the EFT is discussed.

scholarly journals Renormalization group improvement of the effective potential: an EFT approach

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Aneesh V. Manohar ◽  
Emily Nardoni
Keyword(s):  
Renormalization Group ◽  
Effective Potential ◽  
Goldstone Boson ◽  
Large Mass ◽  
Infrared Divergence ◽  
Effective Field ◽  
Mass Hierarchy ◽  
Yukawa Model ◽  
Divergence Problem ◽  
The One

Abstract We apply effective field theory (EFT) methods to compute the renormalization group improved effective potential for theories with a large mass hierarchy. Our method allows one to compute the effective potential in a systematic expansion in powers of the mass ratio, as well as to sum large logarithms of mass ratios using renormalization group evolution. The effective potential is the sum of one-particle irreducible diagrams (1PI) but information about which diagrams are 1PI is lost after matching to the EFT, since heavy lines get shrunk to a point. We therefore introduce a tadpole condition in place of the 1PI condition, and use the renormalization group improved value of the tadpole in computing the effective potential. We explain why the effective potential computed using an EFT is not the same as the effective potential of the EFT. We illustrate our method using the O(N) model, a theory of two scalars in the unbroken and broken phases, and the Higgs-Yukawa model. Our leading-log result, obtained by integrating the one-loop β-functions, correctly reproduces the log-squared term in explicit two-loop calculations. Our method does not have a Goldstone boson infrared divergence problem.

scholarly journals THE RENORMALIZATION GROUP IMPROVED EFFECTIVE POTENTIAL IN MASSLESS MODELS

2005 ◽  
Vol 20 (29) ◽  
pp. 2215-2226 ◽  
Author(s):  
F. T. BRANDT ◽  
F. A. CHISHTIE ◽  
D. G. C. MCKEON
Keyword(s):  
Renormalization Group ◽  
Effective Potential ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Background Field ◽  
Massless Scalar ◽  
Expectation Value

The effective potential V is considered in massless [Formula: see text] theory. The expansion of V in powers of the coupling λ and of the logarithm of the background field ϕ is reorganized in two ways; first as a series in λ alone, then as a series in ln ϕ alone. By applying the renormalization group (RG) equation to V, these expansions can be summed. Using the condition V′(v)=0 (where v is the vacuum expectation value of ϕ) in conjunction with the expansion of V in powers of ln ϕ fixes V provided v≠0. In this case, the dependence of V on ϕ drops out and V is not analytic in λ. Massless scalar electrodynamics is considered using the same approach.

scholarly journals ON THE ONE-LOOP CORRECTION OF φ4 THEORY IN HIGHER DIMENSIONS

2007 ◽  
Vol 22 (29) ◽  
pp. 5369-5377 ◽  
Author(s):  
RIZWAN UL HAQ ANSARI ◽  
P. K. SURESH
Keyword(s):  
Phase Transitions ◽  
Critical Temperature ◽  
Scalar Field ◽  
Effective Potential ◽  
Higher Dimensions ◽  
Temperature Dependent ◽  
Loop Correction ◽  
Five Dimensions ◽  
Fundamental Scale ◽  
The One

We consider in this paper φ4 theory in higher dimensions. Using functional diagrammatic approach, we compute the one-loop correction to effective potential of the scalar field in five dimensions. It is shown that φ4 theory can be regularized in five dimensions. Temperature dependent one-loop correction and critical temperature βc are computed and βc depends on the fundamental scale [Formula: see text] of the theory. A brief discussion of symmetry restoration is also presented. The nature of phase transitions is examined and is of second order.

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