Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff

We perform a systematic one-loop renormalization of a general renormalizable Yang-Mills theory coupled to scalars and fermions using a regularization scheme with a smooth momentum cutoff $\Lambda$ (implemented through an exponential damping factor). We construct the necessary finite counterterms restoring the BRST invariance of the effective action by analyzing the relevant Slavnov-Taylor identities. We find the relation between the renormalized parameters in our scheme and in the conventional $\overline{\rm MS}$ scheme which allow us to obtain the explicit two-loop renormalization group equations in our scheme from the known two-loop ones in the $\overline{\rm MS}$ scheme. We calculate in our scheme the divergences of two-loop vacuum graphs in the presence of a constant scalar background field which allow us to rederive the two-loop beta functions for parameters of the scalar potential. We also prove that consistent application of the proposed regularization leads to counterterms which, together with the original action, combine to a bare action expressed in terms of bare parameters. This, together with treating $\Lambda$ as an intrinsic scale of a hypothetical underlying finite theory of all interactions, offers a possibility of an unconventional solution to the hierarchy problem if no intermediate scales between the electroweak scale and the Planck scale exist.Comment: updated references, 90 pages, many figure

Double protection of the Higgs potential

A mechanism of double protection of the Higgs potential, by supersymmetry and by a global symmetry, is investigated in a class of supersymmetric models with the SU(3)xSU(3)xU(1) gauge symmetry. In such models the electroweak symmetry can be broken with no fine-tuning at all.Comment: 10 pages, 2 figures, latex; v2: typos corrected, references added, new paragraph on decoupling D-term

What is the mass of the lightest supersymmetric Higgs boson?

After reviewing briefly the upper bounds on the mass of the lightest Higgs boson in the most general unconstrained minimal supersymmetric extension of the Standard Model, we discuss various arguments which reduce the parameter space of the model and give stronger predictions for $M_{h^0}$. First, the constraints from the presently available experimental data are summarized. Next, the role of of several additional theoretical assumptions is studied, after extrapolating the model to high energy scales. The most important ones are: perturbative validity up to the GUT scale and the electroweak symmetry breaking. A Higgs boson with $M_{h^0}<$100 GeV is predicted in several scenarios. Its absence in that mass range will have important implications for the parameter space of the model.After reviewing briefly the upper bounds on the mass of the lightest Higgs boson in the most general unconstrained minimal supersymmetric extension of the Standard Model, we discuss various arguments which reduce the parameter space of the model and give stronger predictions for $M_{h~0}$. First, the constraints from the presently available experimental data are summarized. Next, the role of of several additional theoretical assumptions is studied, after extrapolating the model to high energy scales. The most important ones are: perturbative validity up to the GUT scale and the electroweak symmetry breaking. A Higgs boson with $M_{h~0}<$100 GeV is predicted in several scenarios. Its absence in that mass range will have important implications for the parameter space of the model.After reviewing briefly the upper bounds on the mass of the lightest Higgs boson in the most general unconstrained minimal supersymmetric extension of the Standard Model, we discuss various arguments which reduce the parameter space of the model and give stronger predictions for $M_{h~0}$. First, the constraints from the presently available experimental data are summarized. Next, the role of of several additional theoretical assumptions is studied, after extrapolating the model to high energy scales. The most important ones are: perturbative validity up to the GUT scale and the electroweak symmetry breaking. A Higgs boson with $M_{h~0}<$100 GeV is predicted in several scenarios. Its absence in that mass range will have important implications for the parameter space of the model.After reviewing briefly the upper bounds on the mass of the lightest Higgs boson in the most general unconstrained minimal supersymmetric extension of the Standard Model, we discuss various arguments which reduce the parameter space of the model and give stronger predictions for $M_{h~0}$. First, the constraints from the presently available experimental data are summarized. Next, the role of of several additional theoretical assumptions is studied, after extrapolating the model to high energy scales. The most important ones are: perturbative validity up to the GUT scale and the electroweak symmetry breaking. A Higgs boson with $M_{h~0}<$100 GeV is predicted in several scenarios. Its absence in that mass range will have important implications for the parameter space of the model.After reviewing briefly the upper bounds on the mass of the lightest Higgs boson in the most general unconstrained minimal supersymmetric extension of the Standard Model, we discuss various arguments which reduce the parameter space of the model and give stronger predictions for $M_{h~0}$. First, the constraints from the presently available experimental data are summarized. Next, the role of of several additional theoretical assumptions is studied, after extrapolating the model to high energy scales. The most important ones are: perturbative validity up to the GUT scale and the electroweak symmetry breaking. A Higgs boson with $M_{h~0}<$100 GeV is predicted in several scenarios. Its absence in that mass range will have important implications for the parameter space of the model.After reviewing briefly the upper bounds on the mass of the lightest Higgs boson in the most general unconstrained minimal supersymmetric extension of the Standard Model, we discuss various arguments which reduce the parameter space of the model and give stronger predictions for Mho. First, the constraints from the presently available experimental data are summarized. Next, the role of several additional theoretical assumptions is studied, after extrapolating the model to high energy scales. The most important ones are: perturbative validity up to the GUT scale and the electroweak symmetry breaking. A Higgs boson with Mho <100 GeV is predicted in several scenarios. Its absence in that mass range will have important implications for the parameter space of the model.After reviewing briefly the upper bounds on the mass of the lightest Higgs boson in the most general unconstrained minimal supersymmetric extension of the Standard Model, we discuss various arguments which reduce the parameter space of the model and give stronger predictions for $M_{h^0}$. First, the constraints from the presently available experimental data are summarized. Next, the role of of several additional theoretical assumptions is studied, after extrapolating the model to high energy scales. The most important ones are: perturbative validity up to the GUT scale and the electroweak symmetry breaking. A Higgs boson with $M_{h^0}<$100 GeV is predicted in several scenarios. Its absence in that mass range will have important implications for the parameter space of the model

Perturbative computation of thermal characteristics of the Stoner phase transition

We apply the thermal (imaginary time) perturbative expansion to the relevant effective field theory to compute characteristics of the phase transition to the ordered state which can occur at low temperatures in the gas of (nonrelativistic) spin 1/2 fermions interacting through a short-range spin independent repulsive binary interaction potential. We show how to obtain a systematic expansion of the system's free energy depending on the densities $n_+$ and $n_-$ of spin-up and spin-down fermions. In this paper we truncate this expansion at the second order and determine, by numerically minimizing the free energy, the equilibrium proportions of $n_+$ and $n_-$ (that is, the system's polarization) as functions of the temperature, the system's overall density $n = n_+ + n_-$ and the strength of the interaction

Complete On-Shell Renormalization Scheme for the Minimal Supersymmetric Higgs Sector

Systematic on-shell renormalization programme is carried out for the Higgs and gauge boson sectors of the Minimal Supersymmetric Standard Model. Complete 1-loop results for the 2- and 3-point Green's functions are explicitly given. The Higgs boson masses and the cross sections for the neutral scalar production in the $e^+e^-$ colliders are calculated.Comment: 64 pages, 10 figures (not included, availaible on request in PostScript format), LaTeX, preprint no MPI-Ph/92-117 and DFPD 93/TH/1

Fixed points in the evolution of neutrino mixings

We derive the renormalization group equations for the neutrino masses and mixing angles in explicit form and discuss the possible classes of their solutions. We identify fixed points in the equations for mixing angles, which can be reached during the evolution for several mass patterns and give present experimental information. Further experimental test of this relation is of crucial interest. Moreover, we discuss the stability of quantum corrections to neutrino mass squared differences. Several interesting mass patterns show stability in the presence of fixed point solutions for the angles

CP violation in B0_d --> tau+ tau- decays

Establishing CP violation in B0 (bar{B0}) --> l+ l- decays requires a measurement of polarization of the final lepton pair, or a precise determination of the B0 --> l+ l- and bar{B0} --> l+ l- rates. We first argue that if the amplitudes of these decays are dominated by the scalar and pseudoscalar Higgs penguin diagrams, as happens e.g. in supersymmetry with large tan(beta), the CP asymmetries depend practically on only one CP violating phase. This phase can be large, of the order of the CKM phase, leading to large CP asymmetries in the tau+ tau- decay channel of B0_d (bar{B0}_d) mesons, potentially measurable in BELLE or BABAR experiments. Secondly, we show that the existing TAUOLA tau-lepton decay library supplemented by its universal interface can efficiently be used to search for B0 (bar{B0}) --> tau+ tau- decays, and to investigate how the CP asymmetry is reflected in realistic experimental observables.Comment: 1+20 pages, 5 figures, LaTe

Precision tests of the MSSM

We present the results of a first global fit to the electroweak observables in the MSSM. The best fit selects either very low or very large values of ~$\tan\beta$ ~and, correspondingly, chargino (higgsino--like) and stop or the ~$CP-$odd Higgs boson are within the reach of LEP 2. Moreover, the best fit gives ~ $\alpha_s(M_Z)=0.118^{+0.005}_{-0.010}$, ~which is lower than the one obtained from the SM fits. The overall fit is excellent ~ ($\chi^2=7.2$ ~for 15 d.o.f. as compared to ~$\chi^2=11$ ~in the SM). Those results follow from the fact that in the MSSM one can increase the value of ~ $R_b\equiv\Gamma_{Z^0\to\bar bb}/\Gamma_{Z^0\to hadrons}$ ~ {\it without} modyfying the SM predictions for other observables.Comment: 10 pages, LaTEX, 7 figures (not included) may be obtained from [email protected] upon request. Modified version of the plenary talk given by S. Pokorski at the ``Beyond the Standard Model IV'', Lake Tahoe, CA, December 199