24 research outputs found
Vacuum stability and perturbativity of SU(3) scalars
We calculate the vacuum stability conditions and renormalisation group equations for the extensions of standard model with a higher colour multiplet scalar up to the representation 1 5 0 that leaves the strong interaction asymptotically free. In order to find the vacuum stability conditions, we calculate the orbit spaces for the self-couplings of the higher multiplets, which for the representations 1 5 and 1 5 0 of SU(3)(c) are highly complicated. However, if the scalar potential is linear in orbit space variables, it is sufficient to know the convex hull of the orbit space. Knowledge of the orbit spaces also facilitates the minimisation of the potentials. In contrast to the self-couplings of other multiplets, we find that the scalar quartic couplings of the representations 3 and 8 walk rather than run, remaining nearly constant and perturbative over a vast energy range. We describe the conditions for walking couplings using a schematic model. With these technical results at hand we revise earlier results of generation of new scales with large SU(3) c scalar multiplets. Our results are easily extendable to models of new physics with additional SU(3) or SU(N) gauge symmetries.Peer reviewe
Resummation of small-x double logarithms in QCD: semi-inclusive electron-positron annihilation
We have derived the coefficients of the highest three 1/x-enhanced small-x
logarithms of all timelike splitting functions and the coefficient functions
for the transverse fragmentation function in one-particle inclusive e^+e^-
annihilation at (in principle) all orders in massless perturbative QCD. For the
longitudinal fragmentation function we present the respective two highest
contributions. These results have been obtained from KLN-related decompositions
of the unfactorized fragmentation functions in dimensional regularization and
their structure imposed by the mass-factorization theorem. The resummation is
found to completely remove the huge small-x spikes present in the fixed-order
results for all quantities above, allowing for stable results down to very
small values of the momentum fraction and scaling variable x. Our calculations
can be extended to (at least) the corresponding as^n ln^(2n-l) x contributions
to the above quantities and their counterparts in deep-inelastic scattering.Comment: 27 pages, LaTeX, 6 eps-figure
The one loop MSbar static potential in the Gribov-Zwanziger Lagrangian
We compute the static potential in the Gribov-Zwanziger Lagrangian as a
function of the Gribov mass, gamma, in the MSbar scheme in the Landau gauge at
one loop. The usual gauge independent one loop perturbative static potential is
recovered in the limit as gamma -> 0. By contrast the Gribov-Zwanziger static
potential contains the term gamma^2/(p^2)^2. However, the linearly rising
potential in coordinate space as a function of the radial variable r does not
emerge due to a compensating behaviour as r -> infty. Though in the short
distance limit a dipole behaviour is present. We also demonstrate enhancement
in the propagator of the bosonic localizing Zwanziger ghost field when the one
loop Gribov gap equation is satisfied. The explicit form of the one loop gap
equation for the Gribov mass parameter is also computed in the MOM scheme and
the zero momentum value of the renormalization group invariant effective
coupling constant is shown to be the same value as that in the MSbar scheme.Comment: 54 latex pages, 6 figures, flaw in original Feynman rules corrected
with updated two loop gap equation; new details added on derivation of
propagators and their one loop corrections as well as bosonic ghost
enhancemen