Estimate of the Three-Loop MS bar Contribution to sigma(W_L^+ W_L^- --> Z_L Z_L)

The three-loop contribution to the MS bar single-Higgs-doublet standard-model cross-section $\sigma(W_L^+ W_L^- \to Z_L Z_L)$ at s = (5M_H)^2 is estimated via least-squares matching of the asymptotic Pade-approximant prediction of the next order term, a procedure that has been previously applied to QCD corrections to correlation functions and decay amplitudes. In contrast to these prior applications, the expansion parameter for the W_L^+ W_L^- \to Z_L Z_L process is the non-asymptotically-free quartic scalar-field coupling of the standard model, suggesting that the least-squares matching be performed over the "infrared" mu^2 <= s region of the scale parameter. All three coefficients of logarithms within the three-loop term obtained by such matching are found to be within 6.6% relative error of their true values, as determined via renormalization-group methods. Surprisingly, almost identical results are obtained by performing the least squares matching over the mu^2 >= s region.Comment: 9 pages, LaTeX, 3 figures adde

Asymptotic Pad\'e Approximants and the SQCD β\beta-function

We present a prediction for the four loop $\beta$-function for SQCD based on the method of Asymptotic Pad\'e Approximants.Comment: 8 pages, including 2 figures. Plain TeX. Uses Harvmac and eps

TeV-Scale Horizontal Symmetry and the Slepton Mass Problem of Anomaly Mediation

We propose a new scenario for solving the tachyonic slepton mass problem of anomaly mediated supersymmetry breaking models with a non-Abelian horizontal gauge symmetry broken at the TeV scale. A specific model based on SU(3)_{H} horizontal symmetry is presented wherein the sleptons receive positive mass-squared from the asymptotically free SU(3)_{H} gauge sector. Approximate global symmetries present in the model strongly suppress flavor changing processes induced by the horizontal vector gauge bosons. The model predicts m_{h} < 120 GeV for the lightest Higgs boson mass, tan{beta} nearly equal to 4, and M_V = 1-4 TeV for the SU(3)_{H} gauge boson masses. The lightest SUSY particle is found to be the neutral Wino, which is a candidate for cold dark matter.Comment: 25 pages in LaTeX, 2 eps figure

Automatic Calculation of supersymmetric Renormalization Group Equations and Self Energies

SARAH is a Mathematica package for studying supersymmetric models. It calculates for a given model the masses, tadpole equations and all vertices at tree-level. Those information can be used by \SARAH to write model files for CalcHep/CompHep or FeynArts/FormCalc. In addition, the second version of SARAH can derive the renormalization group equations for the gauge couplings, parameters of the superpotential and soft-breaking parameters at one and two-loop level. Furthermore, it calculates the one-loop self energies and the one-loop corrections to the tadpoles. SARAH can handle all N=1 SUSY models whose gauge sector is a direct product of SU(N) and U(1) gauge groups. The particle content of the model can be an arbitrary number of chiral superfields transforming as any irreducible representation with respect to the gauge groups. To implement a new model, the user has just to define the gauge sector, the particle, the superpotential and the field rotations to mass eigenstates.Comment: 32 pages, some typoes corrected, matches published versio

No-Scale Solution to Little Hierarchy

We show that the little hierarchy problem can be solved in the no-scale supergravity framework. In this model the supersymmetry breaking scale is generated when the electroweak symmetry breaking condition is satisfied and therefore, unlike usual supersymmetric models, the correlation between the electroweak symmetry breaking scale and the average stop mass scale can be justified. This correlation solves the little hierarchy puzzle. Using minimal supergravity boundary conditions, we find that the parameter space predicted by no-scale supergravity is allowed by all possible experimental constraints. The predicted values of supersymmetric particle masses are low enough to be very easily accessible at the LHC. This parameter space will also be probed in the upcoming results from the dark matter direct detection experiments.Comment: 15 pages, 2 figure

Two-loop effective potential in quantum field theory in curved space-time

The method of the calculation of effective potential (in linear curvature approximation and at any loop) in massless gauge theory in curved space- time by the direct solution of RG equation is given.The closed expression for two-loop effective potential is obtained.Two-loop effective potential in scalar self-interacting theory is written explicitly.Some comments about it as well as about two-loop effective potential in standard model are presented.Comment: 8page

Solving the Supersymmetric Flavor Problem with Radiatively Generated Mass Hierarchies

The supersymmetric flavor problem may be solved if the first and second generation scalars are heavy (with multi-TeV masses) and scalars with large Higgs couplings are light (with sub-TeV masses). We show that such an inverted spectrum may be generated radiatively; that is, from initial conditions where all scalar masses are multi-TeV at some high scale, those with large Higgs couplings may be driven asymptotically to the weak scale in the infra-red. The lightness of third generation scalars is therefore a direct consequence of the heaviness of third generation fermions, and fine-tuning is avoided even though the fundamental scale of the soft supersymmetry breaking parameters is multi-TeV. We investigate this possibility in the framework of the usual Yukawa quasi-fixed point solutions. The required high scale boundary conditions are found to be simple and highly predictive. This scenario also alleviates the supersymmetric CP and Polonyi problems.Comment: 18 pages, 3 figures; typos corrected, refs added, conforms to published versio

β\beta-functions in large-NfN_f supersymmetric gauge theories

We present calculations of the leading and $O(1/N_f)$ terms in a large-$N_f$ expansion of the $\beta$-functions and anomalous dimensions for various supersymmetric gauge theories, including supersymmetric QCD. In the case of supersymmetric QCD, we show that our $O(1/N_f)$ approximation displays an infra-red fixed point in the conformal window $3N_c/2 < N_f < 3N_c$.Comment: 22 pages, tex, 7 figures. Uses harvmac and eps

Two-loop corrections to Radiative Electroweak Symmetry Breaking in the MSSM

We study the O(at*as + at^2) two-loop corrections to the minimization conditions of the MSSM effective potential, providing compact analytical formulae for the Higgs tadpoles. We connect these results with the renormalization group running of the MSSM parameters from the grand unification scale down to the weak scale, and discuss the corrections to the Higgs mixing parameter mu and to the running CP-odd Higgs mass mA in various scenarios of gravity-mediated SUSY breaking. We find that the O(at*as) and O(at^2) contributions partially cancel each other in the minimization conditions. In comparison with the full one-loop corrections, the O(at*as + at^2) two-loop corrections significantly weaken the dependence of the parameters mu and mA on the renormalization scale at which the effective potential is minimized. The residual two-loop and higher-order corrections to mu and mA are estimated to be at most 1% in the considered scenarios.Comment: 23 pages, 7 figures. Version to appear in Nucl. Phys.

Can we distinguish SUSY breaking terms between weakly and strongly coupled heterotic string theories ?

We study soft SUSY breaking terms in heterotic M-theory. We show that both weakly and strongly coupled heterotic string models lead to the same relations of soft SUSY breaking terms, $A=-M$ and $m^2 = M^2/3$, up to $O((\alpha T/S)^2)$.Comment: 11 pages, late