Stop decays in SUSY-QCD

The partial widths are determined for stop decays to top quarks and gluinos, and gluino decays to stop particles and top quarks (depending on the masses of the particles involved). The widths are calculated including one-loop SUSY-QCD corrections. The radiative corrections for these strong-interaction decays are compared with the SUSY-QCD corrections for electroweak stop decays to quarks and neutralinos/charginos and top-quark decays to stops and neutralinos.     

Properties of the top quark

The top quark was discovered at the CDF and D0 experiments in 1995. As the partner of the bottom quark its properties within the Standard Model are fully defined. Only the mass is a free parameter. The measurement of the top quark mass and the verification of the expected properties have been an important topic of experimental top quark physics since. In this review the recent results on top quark properties obtained by the Tevatron experiments CDF and D0 are summarised. At the advent of the LHC special emphasis is given to the basic measurement methods and the dominating systematic uncertainties.     

Stop coannihilation in the CMSSM and SubGUT models

Stop coannihilation may bring the relic density of heavy supersymmetric dark matter particles into the range allowed by cosmology. The efficiency of this process is enhanced by stop-antistop annihilations into the longitudinal (Goldstone) modes of the W and Z bosons, as well as by Sommerfeld enhancement of stop annihilations and the effects of bound states. Since the couplings of the stops to the Goldstone modes are proportional to the trilinear soft supersymmetry-breaking A-terms, these annihilations are enhanced when the A-terms are large. However, the Higgs mass may be reduced below the measured value if the A-terms are too large. Unfortunately, the interpretation of this constraint on the stop coannihilation strip is clouded by differences between the available Higgs mass calculators. For our study, we use as our default calculator FeynHiggs 2.13.0, the most recent publicly available version of this code. Exploring the CMSSM parameter space, we find that along the stop coannihilation strip the masses of the stops are severely split by the large A-terms. This suppresses the Higgs mass drastically for \(\mu \) and \(A_0 > 0\), whilst the extent of the stop coannihilation strip is limited for \(A_0 < 0\) and either sign of \(\mu \). However, in sub-GUT models, reduced renormalization-group running mitigates the effect of the large A-terms, allowing larger LSP masses to be consistent with the Higgs mass calculation. We give examples where the dark matter particle mass may reach \(\gtrsim 8\) TeV.     

Geometric quantization of the heavy top

The geometric quantization of the heavy top is described and its relation with the geometric quantization of the cotangent bundle of the orthogonal group is pointed out.     

Angular momentum and the electromagnetic top

The electric charge–magnetic dipole interaction is considered. If Γ_em is the electromagnetic and Γ_mech the mechanical angular momentum, the conservation law for the total angular momentum Γ_tot holds: Γ_tot=Γ_em+Γ_mech= const., but when the dipole moment varies with time, Γ_mech is not conserved. We show that the non-conserved Γ_mech of such a macroscopic isolated system might be experimentally observable. With advanced technology, the strength of the interaction hints to the possibility of novel applications for gyroscopes, such as the electromagnetic top.     

Axial contributions at the top threshold

We calculate the contributions of the axial current to top quark pair production in annihilation at threshold. The QCD dynamics is taken into account by solving the Lippmann-Schwinger equation for the P wave production using the QCD potential up to two loops. We demonstrate that the dependence of the total and differential cross section on the polarization of the and beams allows for an independent extraction of the axial current induced cross section. Received: 11 March 1999 / Published online: 20 May 1999     

A generalization of the Kovalevskaya top

Integrals of motion of the Kovalevskaya gyrostat on Lie algebras O(4), e(3), o(3, 1) are constructed both in classical and quantum mechanics. The additional term to the classical Kovalevskaya integral on e(3) is shown to be proportional to the integral of the Goryachev-Chaplygin gryostat.     

On the quantization of the Kowalevskaya top

The equations of motion of a heavy top can be integrated for three different combinations of the parameters of the system. Historically, the discovery of these three integrable cases is attributed to Euler, Lagrange and Kowalevskaya, respectively. While the quantization of the first two cases can be performed in a straightforward way, the quantum integrability of the Kowalevskaya top is far from trivial. We show here how one can recover quantum integrability for this case as well.     

The Goryachev-Chaplygin top and the Toda lattice

The Goryachev-Chaplygin top is a rigid body rotating about a fixed point with principal moments of inertiaA, B, C satisfyingA=B=4C and with center of mass lying in the equatorial plane. The problem is algebraically completely integrable as a linear flow on a hyperelliptic Jacobian, only upon putting the principal angular momentum in the horizontal plane.This system admits asymptotic solutions with fractional powers int and depending on 4 degrees of freedom. As a consequence, the affine invariant surfaces of the Chaplygin top are double covers of the hyperelliptic Jacobian above, ramified along two translates of the theta divisor, touching in one point. This system is an instance of a (master) system of differential equations in 7 unknowns having 5 quadratic constants of motion; a careful analysis of this system reveals an intimate (rational) relationship with the 3-body periodic Toda lattice.The support of National Science Foundation grant No. DMS-8403136 is gratefully acknowledged. I thank Victor Guillemin for mentioning this problem