5 research outputs found
Phenomenology of 3-Family Grand Unified String Models
In the 3-family grand unified string models constructed so far, there is only
one adjoint (and no higher dimensional representation) Higgs field in the grand
unified gauge group. In this preliminary analysis, we address the proton-decay
problem in the 3-family E_6 and related SO(10) string models. In particular, we
analyze the doublet-triplet splitting (within certain assumptions about
non-perturbative dynamics). It appears that generically some fine-tuning is
necessary to arrange for a pair of Higgs doublets to be light, while having
color Higgs triplets superheavy. We also discuss charge-2/3 quark mass matrix
that generically also seems to require some fine-tuning to have rank 1.Comment: 12 pages, Revtex 3.0. Minor corrections mad
A Review of Three-Family Grand Unified String Models
We review the construction and classification of three-family grand unified
models within the framework of asymmetric orbifolds in perturbative heterotic
superstring. We give a detailed survey of all such models which is organized to
aid analysis of their phenomenological properties. We compute tree-level
superpotentials for these models. These superpotentials are used to analyze the
issues of proton stability (doublet-triplet splitting and R-parity violating
terms) and Yukawa mass matrices. To have agreement with phenomenological data
all these models seem to require certain degree of fine-tuning. We also analyze
the possible patterns of supersymmetry breaking in these models.
We find that the supersymmetry breaking scale comes out either too high to
explain the electroweak hierarchy problem, or below the electroweak scale
unless some degree of fine-tuning is involved. Thus, none of the models at hand
seem to be phenomenologically flawless.Comment: 49 pages, Revtex 3.0; one ps figure included. To appear in the Review
section of Int.J.Mod.Phy
Effective Action of Spontaneously Broken Gauge Theories
The effective action of a Higgs theory should be gauge-invariant. However,
the quantum and/or thermal contributions to the effective potential seem to be
gauge-dependent, posing a problem for its physical interpretation. In this
paper, we identify the source of the problem and argue that in a Higgs theory,
perturbative contributions should be evaluated with the Higgs fields in the
polar basis, not in the Cartesian basis. Formally, this observation can be made
from the derivation of the Higgs theorem, which we provide. We show explicitly
that, properly defined, the effective action for the Abelian Higgs theory is
gauge invariant to all orders in perturbation expansion when evaluated in the
covariant gauge in the polar basis. In particular, the effective potential is
gauge invariant. We also show the equivalence between the calculations in the
covariant gauge in the polar basis and the unitary gauge. These points are
illustrated explicitly with the one-loop calculations of the effective action.
With a field redefinition, we obtain the physical effective potential. The
SU(2) non-Abelian case is also discussed.Comment: Expanded version, 32 pages, figures produced by LaTeX, plain LaTe