P. Eckert

Counter-example to Michel's conjecture

Abstract We have found a minimum of the Higgs potential for the representation 75 of SU(5) having a non maximal little group with algebra su(2) + u(1), contrary of Michels conjecture. We also find a minimum with non maximal little algebra su(2) + su(2) + u(1) and discrete symmetry, and minima with maximal little algebra su(3) + su(2) + u(1), sp94) + u(1), su(2) + su(2) + u(1) and su(2).

Minima of Higgs potentials corresponding to non-maximal isotropy subgroups

Abstract Results are presented of the minimization of the Higgs potential for the irreducible representation 75 of SU(5). Isotropy groups of minima are determined using a geometrical method developed recently by Abud and Sartori. Minima with the maximal isotropy algebras su(3) + su(2) + u(1), sp(4) + u(1), su(2) + su(2) + u(1) and su(2) were found as well as a minimum with a non-maximal isotropy algebra su(2) + su(2) + u(1) + u(1) and discrete symmetry. A minimum having a non-maximal isotropy group SU(2) ⊗ U(1) ⊗ U(1) was also found, contrary to Michels conjecture. A detailed analysis of the results is presented and the limits of Michels conjecture are pointed out.

Minimization of the SU(5) invariant scalar potential for the 45-dimensional representation

We show that non-minimal SU(5) models involving a 45-plet of scalars with non-vanishing expectation value are consistent with an unbroken SU(3)c × U(1)em as far as minimization of the potential in tree approximation is concerned.

SU(5) WITH A STABLE PROTON A LA JARLSKOG

Abstract We present a specific example of an SU(5) unified model where proton decay via gauge bosons is completly suppressed a la Jarlskog. The one-loop corrections are shown not to change this results.

The mass of the fundamental SU(5) monopole

Abstract We solve numerically the Yang-Mills equations corresponding to the fundamental monopole in SU(5) broken spontaneously by the usual 24-plet of scalars. We also calculate the classical monopole mass as a function of the scalar potential.

The SU(5) monopole and its dependence on the weak scale

Abstract We extend our analysis of the fundamental SU(5) monopole to include the 5-plet of scalars responsible for the weak breaking. We solve numerically the corresponding Yang-Mills equations and calculate the classical monopole mass. The dependence on the weak scale is found to be small but non-vanishing.

Cross sections and mean charges of jets in\(p\bar p\) collisions

Two jet reactions at collider energies within the frame of QCD are studied. Cross sections and mean charges are shown for both cases when one or two jets are observed. Scaling violations are introduced by means of the Altarelli-Parisi equation for a completely asymmetric sea. The effects due to scaling violation, gluon distribution and gluons in the final state are computed.

THE FUNDAMENTAL SU(5) MONOPOLE: CLASSICAL CONFIGURATION AND MASS

Abstract We summarize a numerical analysis of the Yang-Mills equations corresponding to the fundamental monopole in SU(5) broken spontaneously by the usual 24-plet and 5-plet of scalars.

Two Jet events in\(p\bar p\) collisions revisited

AbstractCross sections and mean charges of two jet events at