One-loop on-shell renormalization of MSSM vertexes

The on-shell renormalization scheme for electroweak theory is well studied in the standard model (SM), but a consistent on-shell renormalization scheme for the minimal supersymmetric standard model (MSSM) is still unknown. In the MSSM, we study the on-shell scheme for three vertexes: Zl^Il^I, W⁺v^Il^I and , with virtual SUSY particles (chargino, sneutrino, neutralino and slepton) at one-loop order. Instead of the amplitude of a single triangle diagram, the sum of the amplitude of triangle diagrams belonging to one suit can be renormalized in the on-shell scheme. One suit points out that the internal virtual particles are consistent. The zero-momentum scheme is also used for the renormalization. The two schemes can make the renormalized results decoupled, and in the MSSM some of the special characters of the on-shell scheme are shown. This work is propitious in completing the on-shell renormalization scheme in the MSSM.     

Symanzik's improved actions from the viewpoint of the renormalization group

We investigate Symanzik's improvement program in a four-dimensional Euclidean scalar field theory with smooth momentum space cutoff. We use Wilson's renormalization group transformation to define the improved actions as a sequence of initial data for the effective action at the fundamental cutoff. This leads to a sequence of solutions to the renormalization group equation. We define the parameters of the improved actions implicitly by conditions on the effective action at a renormalization scale. The improved actions are close approximations to the continuum effective action. We prove their existence to every order of improvement and to every order of renormalized perturbation theory.Supported in part by a German National Scholarship Foundation fellowship, and by the National Science Foundation under Grant DMS/PHY 86-45122     

Polyakov effective action from functional renormalization group equation

We discuss the Polyakov effective action for a minimally coupled scalar field on a two dimensional curved space by considering a non-local covariant truncation of the effective average action. We derive the flow equation for the form factor in , and we show how the standard result is obtained when we integrate the flow from the ultraviolet to the infrared.     

Revisiting the local potential approximation of the exact renormalization group equation

The conventional absence of field renormalization in the local potential approximation (LPA) — implying a zero value of the critical exponent η   — is shown to be incompatible with the logic of the derivative expansion of the exact renormalization group (RG) equation. We present a LPA with η≠0$\eta \ne 0$ that strictly does not make reference to any momentum dependence. Emphasis is made on the perfect breaking of the reparametrization invariance in that pure LPA (absence of any vestige of invariance) which is compatible with the observation of a progressive smooth restoration of that invariance on implementing the two first orders of the derivative expansion whereas the conventional requirement (η=0$\eta =0$ in the LPA) precluded that observation.     

Self-consistent calculation of real space renormalization group flows and effective potentials

We show how to compute real space renormalization group flows in lattice field theory by a self-consistent method which is designed to preserve the basic stability properties of a Boltzmann factor. Particular attention is paid to controlling the errors which come from truncating the action to a manageable form. In each step, the integration over the fluctuation field (high frequency components of the field) is performed by a saddle point method. The saddle point depends on the block spin. Higher powers of derivatives of the field are neglected in the actions, but no polynomial approximation in the field is made. The flow preserves a simple parameterization of the action. In the first part the method is described and numerical results are presented. In the second part we discuss an improvement of the method where the saddle point approximation is preceded by self-consistent normal ordering, i.e. solution of a gap equation. In the third part we describe a general procedure to obtain higher order corrections with the help of Schwinger-Dyson equations.In this paper we treat scalar field theories as an example. The basic limitations of the method are also discussed. They come from a possible breakdown of stability which may occur when a composite block spin or block variables for domain walls would be needed.     

An infrared renormalization group limit cycle in QCD

We use effective field theories to show that small increases in the up and down quark masses would move QCD very close to the critical renormalization group trajectory for an infrared limit cycle in the three-nucleon system. We conjecture that QCD can be tuned to the critical trajectory by adjusting the quark masses independently. At the critical values of the quark masses, the binding energies of the deuteron and its spin-singlet partner would be tuned to zero and the triton would have infinitely many excited states with an accumulation point at the 3-nucleon threshold. The ratio of the binding energies of successive states would approach a universal constant that is close to 515.     

Causality and the renormalization group

We suppose that for the invariant coupling constant (ICC) the spectral representation of the Källen-Lehmann type is valid. By combining this conjecture with the general solution of the functional renormalization group (RG) equation it is possible to analyze the type of singularity in the coupling constant at g=0. For logarithmic models it is of the form exp (-1/g).     

An introduction to the fundamentals of the renormalization group in critical phenomena

The fundamental concepts underlying the application of the renormalization group and related techniques to critical phenomena are reviewed at an elementary level. Topics discussed include: the definition of the renormalization group as a functional integral over high momentum components of the spin field, the behaviour of the renormalization group near the fixed point and the derivation of scaling, Wilson's approximate recursion relation, trivial and non-trivial fixed points of isotropic spin systems near d = 4, Feynman graph expansions for critical exponents, ? = 4 ? d and 1/n-expansions, the derivation of exact recursion relations and co-ordinate space transformations for d = 2 Ising systems     

The SM as the quantum low-energy effective theory of the MSSM

In the framework of the minimal supersymmetric standard model we compute the one-loop effective action for the electroweak bosons obtained after integrating out the different sleptons, squarks, neutralinos and charginos, and present the result in terms of the physical sparticle masses. In addition we study the asymptotic behavior of the two-, three- and four-point Green's functions with external electroweak bosons in the limit where the physical sparticle masses are very large in comparison with the electroweak scale. We find that in this limit all the effects produced by the supersymmetric particles can either be absorbed in the standard model parameters and gauge bosons wave functions, or else they are suppressed by inverse powers of the supersymmetric particle masses. This work, therefore, completes the proof of decoupling of the heavy supersymmetric particles from the standard ones in the electroweak bosons effective action and in the sense of the Appelquist–Carazzone theorem; we started this proof in a previous work. From the point of view of effective field theories this work can be seen as a (partial) proof that the SM can indeed be obtained from the MSSM as the quantum low-energy effective theory of the latter when the SUSY spectra are much heavier than the electroweak scale. Received: 27 March 1999 / Revised version: 7 September 1999 / Published online: 27 January 2000     

Finite-size scaling and the renormalization group

Renormalization group calculations ind = 4 andd = 4 – are performed for a system of finite size. A form of mean-field theory is used which yields a rounded transition for a finite system, and this allows a sensible expansion in fluctuations. A combination of Ewald and Poisson sum techniques is used to produce explicit numerical results for the specific heat ind = 4 which, with the setting of two nonuniversal metrical factors and the fourth-order coupling constant may be compared with simulations. The numerical visibility of logarithmic corrections is investigated. The universal scaling function for the specific heat to relativeO() is also evaluated numerically.