The Derivative Expansion of the Effective Action and the Renormalization Group Equation

Physical review D: Particles and fields 07/2007; DOI:10.1103/PHYSREVD.76.105006
Source: arXiv

ABSTRACT The perturbative evaluation of the effective action can be expanded in powers of derivatives of the external field. We apply the renormalization group equation to the term in the effective action that is second order in the derivatives of the external field and all orders in a constant external field, considering both massless scalar $\phi_4^4$ model and massless scalar electrodynamics. A so-called ``on shell'' renormalization scheme permits one to express this ``kinetic term'' for the scalar field entirely in terms of the renormalization group functions appropriate for this scheme. These renormalization group functions can be related to those associated with minimal subtraction.

0 0
  • Source
    [show abstract] [hide abstract]
    ABSTRACT: The effective potential for radiatively broken electroweak symmetry in the single Higgs doublet Standard Model is explored to four sequentially subleading logarithm-summation levels (5-loops) in the dominant Higgs self-interaction couplant $\lambda$. We augment these results with all contributing leading logarithms in the remaining large but sub-dominant Standard Model couplants (t-quark, QCD and $SU(2)\otimes U(1)$ gauge couplants) as well as next to leading logarithm contributions from the largest of these, the t-quark and QCD couplants. Order-by-order stability is demonstrated for earlier leading logarithm predictions of an order 220 GeV Higgs boson mass in conjunction with fivefold enhancement of the value for $\lambda$ over that anticipated from conventional spontaneous symmetry breaking.
    Physical review D: Particles and fields 11/2004; 72(3).
  • Source
    [show abstract] [hide abstract]
    ABSTRACT: In the absence of a tree-level scalar-field mass, renormalization-group (RG) methods permit the explicit summation of leading-logarithm contributions to all orders of the perturbative series for the effective-potential functions utilized in radiative symmetry breaking. For scalar-field electrodynamics, such a summation of leading logarithm contributions leads to upper bounds on the magnitudes of both gauge and scalar-field coupling constants, and suggests the possibility of an additional phase of spontaneous symmetry breaking characterized by a scalar-field mass comparable to that of the theory's gauge boson. For radiatively-broken electroweak symmetry, the all-orders summation of leading logarithm terms involving the dominant three couplings (quartic scalar-field, t-quark Yukawa, and QCD) contributing to standard-model radiative corrections leads to an RG-improved potential characterized by a 216 GeV Higgs boson mass. Upon incorporation of electroweak gauge couplants we find that the predicted Higgs mass increases to 224 GeV. The potential is also characterized by a quartic scalar-field coupling over five times larger than that anticipated for an equivalent Higgs mass obtained via conventional spontaneous symmetry breaking, leading to a concomitant enhancement of processes (such as W+W−→ZZ) sensitive to this coupling. Moreover, if the QCD coupling constant is taken to be sufficiently strong, the tree potential's local minimum at φ=0 is shown to be restored for the summation of leading logarithm corrections. Thus if QCD exhibits a two-phase structure similar to that of N=1 supersymmetric Yang–Mills theory, the weaker asymptotically-free phase of QCD may be selected by the large logarithm behaviour of the RG-improved effective potential for radiatively broken electroweak symmetry.
    Nuclear Physics B 09/2003; · 4.33 Impact Factor

Full-text (2 Sources)

Available from
May 31, 2013