arXiv subjects
Publications and source records attributed to Aaron K. Grant.
We compute loop corrections to the effective action of a field theory on a five-dimensional $S_1/Z_2$ orbifold. We find that the quantum loop effects of interactions in the bulk produce infinite contributions that require renormalization by four-dimensional couplings on the orbifold fixed planes. Thus bulk couplings give rise to renormalization group running of brane couplings.
We note that orbifold boundary conditions that produce chiral fermion zero modes in compactified higher dimensional theories may distort scalar field vacuum expectation values, giving rise to nontrivial dependence on the extra dimensions. We illustrate this in a simple five dimensional model which has chiral fermion zero-modes stuck to fat branes. The model could provide a simple and explicit realization of the separation of quarks and leptons in the fifth dimension. We discuss the KK expansion in some detail. We find that there are in general non-zero-mode states stuck to the brane, like the chiral zero modes. We see explicitly the transition from states dominated by the internal structure of the fat brane to those dominated by the compactification.
We construct models in which electroweak symmetry is spontaneously broken by supersymmetric strong dynamics at the TeV scale. The order parameter is a composite of scalars, and the longitudinal components of the W and Z are strongly-coupled bound states of scalars. The usual phenomenological problems of dynamical electroweak symmetry breaking are absent: the sign of the S parameter unconstrained in strongly interacting SUSY theories, and fermion masses are generated without flavor-changing neutral currents or large corrections to the rho parameter. The lightest neutral Higgs scalar can be heavier than M_Z without radiative corrections from standard-model fields. All the mass scales in the model can be naturally related in low-scale models of supersymmetry breaking. The mu problem can also be solved naturally, and the model can incorporate perturbative unification of standard-model gauge couplings with intermediate thresholds.
We discuss an alternative to the topcolor seesaw mechanism. In our scheme, all the light quarks carry topcolor, and there are many composite SU(2) doublets. This makes it possible to get the observed top quark mass and observed $SU(2) \times U(1)$ breaking in a way that is quite different from the classic seesaw mechanism. We discuss a model of this kind that arises naturally in the context of dynamically broken topcolor. There are many composite scalars in a theory of this kind. This has important effects on the Pagels-Stokar relation and the Higgs mass. We find $m_{\rm Higgs} < 330$ GeV, lighter than in typical topcolor models. We also show that the electroweak singlet quarks in such a model can be lighter than the corresponding quarks in a seesaw model.
The top quark seesaw mechanism offers a method for constructing a composite Higgs field without the usual difficulties that accompany traditional technicolor or topcolor theories. The focus of this article is to study the phenomenology of the new physics required by this mechanism. After establishing a set of criteria for a plausible top quark seesaw theory, we develop two models, the first of which has a heavy weak singlet fermion with hypercharge 4/3 while the second has, in addition, a heavy weak singlet hypercharge -2/3 fermion. At low energies, these theories contain one or two Higgs doublets respectively. We then derive the low energy effective Higgs potential in detail for the two-doublet theory as well as study the likely experimental signatures for both theories. A strong constraint on the one-doublet model is the measured value of the rho parameter which permits the new heavy fermion to have a mass of about 5-7 TeV, when the Higgs has a mass greater than 300 GeV. In the two-doublet model, mixing of the new heavy Y=-2/3 fermion and the b quark affects the prediction for R_b. In order to agree with the current limits on R_b, the mass of this fermion should be at least 12 TeV. The mass of the heavy Y=4/3 fermion in the two-doublet model is not as sharply constrained by experiments and can be as light as 2.5 TeV.
We analyze a model of dynamically broken topcolor in the limit in which the number of colors is large. We show that the second order nature of the phase transition, necessary for the success of topcolor models, passes the nontrivial check of consistency with the large N limit. We also identify and discuss a class of theories that generalizes the topcolor phenomenon to a theory with a richer structure of fermions and global symmetries.
In theories with TeV scale quantum gravity there is a logical possibility where the electroweak Higgs can be a fourth generation slepton. Despite maximal supersymmetry breaking such a scenario turns out to be tightly constrained, and might be testable already at present collider experiments. Also, a light Higgs is no longer a prediction of supersymmetry.
We review the current status of precision electroweak measurements and the constraints they impose on new physics. We perform a model independent analysis using the STU-formalism of Ref. 1, and then discuss how the Z-pole data from LEP and SLD can be used to constrain models that are not covered within that framework.
We update our analysis of precision electroweak measurements using the latest data announced at Moriond, March 1998. Possible oblique corrections from new physics are parametrized using the STU formalism of Ref.[1], and non-oblique corrections to the Zbb vertex are parametrized using the xi_b zeta_b formalism of Ref.[2]. The implications of the analysis on minimal SU(5) grand unification is discussed.
The impact of a light, long lived gluino on jet production cross sections in $\bar p p$ collisions is estimated. The effect is found to be relatively modest, particularly when gluinos are incorporated into the parton densities of the proton. Although a light gluino does enhance the production of jets at high $E_T$, the effect is insufficient, by itself, to explain the high $E_T$ excess observed by CDF.
The spacings between bound-state levels of the Schrödinger equation with the same principal quantum number $N$ but orbital angular momenta $\ell$ differing by unity are found to be nearly equal for a wide range of power potentials $V = λr^ν$, with $E_{N \ell} \approx F(ν, N) - G(ν,N) \ell$. Semiclassical approximations are in accord with this behavior. The result is applied to estimates of masses for quarkonium levels which have not yet been observed, including the 2P $c \bar c$ states and the 1D $b \bar b$ states.
We discuss the difficulties that arise when one tries to calculate $δρ$ using dispersion relations.
Constraints on the two Higgs doublet model are presented, assuming a top mass of 174 $\pm$ 17 GeV. We concentrate primarily on the ``type II'' model, where up--type quarks receive their mass from one Higgs doublet, and down--type quarks receive their mass from the second doublet. High energy constraints derived from the $W$ mass, the full width of the $Z$ and the $b \bar b$ partial width of the $Z$ are combined with low energy constraints from $Γ(b\to s γ)$, $Γ(b \to c τ\barν_τ)$ and $B^0$-$\bar B^0$ mixing to determine the experimentally favored configurations of the model. This combination of observables rules out small charged Higgs masses and small values of $\tanβ$, and provides some information about the neutral Higgs masses and the mixing angle $α$. In particular, constraints derived from the $ρ$ parameter rule out configurations where the charged Higgs is much heavier or much lighter than the neutral Higgses. We discuss a scenario where $Γ(Z\to b \bar b)$ is enhanced relative to the standard model result, which unfortunately is on the verge of being ruled out by the combination of $Γ(b\to s γ)$ and $ρ$ parameter constraints. Implications for various extensions of the standard model are briefly discussed.
We present a model--independent analysis of the $Z b \bar b$ vertex, with the aim of constraining contributions of new physics to the left- and right--handed couplings of the $b$. We find that the left--handed coupling of the $b$ is quite narrowly constrained by present data, but that the right--handed coupling is still largely unconstrained.
We use the Operator Product Expansion (OPE) of quark vacuum polarization functions to show that the dispersion relation of Kniehl and Sirlin will yield the correct result to all orders in $α_s$ when applied to the QCD correction to the leptonic decay width of the Higgs boson.
We use the operator product expansion (OPE) to show that non-perturbative QCD corrections to $Δρ$ can be calculated using unsubtracted dispersion relations for either the transverse or the longitudinal vacuum polarization functions. Recent calculations of the non-perturbative contribution to $Δρ$ based on a non-relativistic calculation of corrections to the $\ttbar$ threshold are inconsistent with this result.
The connection between supersymmetric quantum mechanics and the Korteweg- de Vries (KdV) equation is discussed, with particular emphasis on the KdV conservation laws. It is shown that supersymmetric quantum mechanics aids in the derivation of the conservation laws, and gives some insight into the Miura transformation that converts the KdV equation into the modified KdV equation. The construction of the $τ$-function by means of supersymmetric quantum mechanics is discussed.
The spectra and decay rates of $c \bar c$ and $b \bar b$ levels are well described, for the most part, by a power-law potential of the form $V(r)=λ(r^α-1)/α+{\rm const.}$, where $α\simeq 0$. The results of an up-to-date fit to the data on spin-averaged levels are presented. Results on electric dipole transitions in systems bound by power law potentials are also presented, with applications to the bottomonium system.