We calculate the two-loop QCD correction to the scalar quark contributions to the electroweak gaugeboson self-energies at zero momentum transfer in the supersymmetric extension of the standard model (SM) and derive the associated O ͑a s ͒ correction to the r parameter. The two-loop corrections modify the one-loop contribution by up to 30%; the gluino decouples for large masses. Contrary to the SM case where the QCD corrections are negative and screen the one-loop value, the corresponding corrections in the supersymmetric case are in general positive, increasing the sensitivity in the search for scalar quarks through their virtual effects in high-precision electroweak observables. [S0031-9007(97)03176-1] PACS numbers: 12.15. Lk, 12.38.Bx, 12.60.Jv Supersymmetric (SUSY) theories [1] are the best motivated extensions of the standard model (SM) of the electroweak and strong interactions. They provide an elegant way to break the electroweak symmetry and to stabilize the huge hierarchy between the grand unified theory and the Fermi scales, and allow for a consistent unification of the gauge coupling constants as well as a natural solution of the dark matter problem; for recent reviews, see Ref.[2].Supersymmetry predicts the existence of scalar partners to each SM fermion, and spin-1͞2 partners to the gauge and Higgs bosons. So far, the direct search of SUSY particles at colliders has not been successful, and under some assumptions one can only set lower bounds of O ͑100͒ GeV on their masses [3]. The search can be extended to slightly larger values at LEP2 and the upgraded Tevatron; higher energy hadron or e 1 e 2 colliders will be required to sweep the entire range of the SUSY particle masses up to the TeV scale.An alternative way to probe SUSY is to search for the virtual effects of the additional particles. Indeed, now that the top-quark mass-the measured value of which being in remarkable agreement with the predicted oneis known [3], one can use the high-precision electroweak data to search for the quantum effects of the SUSY particles: sfermions, charginos/neutralinos, and gluinos.In the minimal supersymmetric standard model (MSSM) it is well known that, besides the rare decay b ! sg [4], there are two possibilities for the virtual effects of SUSY particles to be large enough to be detected in present high-precision experiments. The first possibility is that charginos and scalar top quarks are light enough to affect the decay width of the Z boson into b quarks [5]; however, for masses beyond the LEP2 or Tevatron reach, these effects become too small to be observable [6].The second possibility is the contribution of the scalar top and bottom quark loops to the electroweak gaugeboson self-energies [7]: if there is a large splitting between the masses of these particles, the contribution will grow with the mass of the heaviest scalar quark and can be sizable. This is similar to the SM case, where the top/bottom weak isodoublet generates a quantum correction that grows as m 2 t . This contribution enters the electro...

In supersymmetric theories, the main decay modes of scalar quarks are decays into quarks plus charginos or neutralinos, if the gluinos are heavy enough. We calculate the O(α s ) QCD corrections to these decay modes in the minimal supersymmetric extension of the Standard Model. In the case of scalar top and bottom quarks, where mixing effects can be important, these corrections can reach values of the order of a few ten percent. They can be either positive or negative and increase logarithmically with the gluino mass. For the scalar partners of light quarks, the corrections do not exceed in general the level of ten percent for gluino masses less than 1 TeV.

In the supersymmetric extension of the Standard Model we derive the two-loop QCD corrections to the scalar quark contributions to the electroweak precision observables entering via the ρ parameter. A very compact expression is derived for the gluon-exchange contribution. The complete analytic result for the gluino-exchange contribution is very lengthy; we give expressions for several limiting cases that were derived from the general result. The two-loop corrections, generally of the order of 10 to 30% of the one-loop contributions, can be very significant. Contrary to the Standard Model case, where the QCD corrections are negative and screen the one-loop value, the corresponding corrections in the supersymmetric case are in general positive, therefore increasing the sensitivity in the search for scalar quarks through their virtual effects in high-precision electroweak observables.

In supersymmetric theories, the decays of the neutral CP-even and CP-odd as well as the charged Higgs bosons into scalar quarks, in particular into top and bottom squarks, can be dominant if they are kinematically allowed. We calculate the QCD corrections to these decay modes in the minimal supersymmetric extension of the standard model, including all quark mass terms and squark mixing. These corrections turn out to be rather large, altering the decay widths by an amount which can be larger than 50%. The corrections can be either positive or negative, and depend strongly on the mass of the gluino. We also discuss the QCD corrections to the decays of heavy scalar quarks into light scalar quarks and Higgs bosons. ͓S0556-2821͑98͒02809-4͔

We compute the one-loop supersymmetric QCD quantum effects on the width Γ(t → W + b) of the canonical main decay of the top quark within the framework of the MSSM. The corrections can be of either sign depending on whether the stop squark mass is above or below the top quark decay threshold into stop and gluino Γ(t →tg). For mt above that threshold, the corrections are negative and can be of the same order (and go in the same direction) as the ordinary QCD corrections, even for stop and gluino masses of O(100) GeV . Since the electroweak supersymmetric quantum effects turn out to be also of the same sign and could be of the same order of magnitude, the total MSSM correction to the top quark width could potentially result in a rather large O(10 − 25)% reduction of Γ(t → W + b) far beyond the conventional QCD expectations.