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Kenichiro Aoki

Publications and source records attributed to Kenichiro Aoki.

47 records · Page 3Linked to original sources
arXiv1996

Non-critical strings at high energy

We consider scattering amplitudes in non-critical string theory of $N$ external states in the limit where the energy of all external states is large compared to the string tension. We argue that the amplitudes are naturally complex analytic in the matter central charge $c$ and we propose to define the amplitudes for arbitrary value of $c$ by analytic continuation. We show that the high energy limit is dominated by a saddle point that can be mapped onto an equilibrium electro-static energy configuration of an assembly of $N$ pointlike (Minkowskian) charges, together with a density of charges arising from the Liouville field. We argue that the Liouville charges accumulate on segments of curves, and produce quadratic branch cuts on the worldsheet. The electro-statics problem is solved for string tree level in terms of hyper-elliptic integrals and is given explicitly for 3- and 4-point functions. We show that the high energy limit should behave in a string-like fashion with exponential dependence on the energy scale for generic values of $c$.

hep-th↗
arXiv1995

1+1 dimensional QCD with fundamental bosons and fermions

We analyze the properties of mesons in 1+1 dimensional QCD with bosonic and fermionic ``quarks'' in the large $\nc$ limit. We study the spectrum in detail and show that it is impossible to obtain massless mesons including boson constituents in this model. We quantitatively show how the QCD mass inequality is realized in two dimensional QCD. We find that the mass inequality is close to being an equality even when the quarks are light. Methods for obtaining the properties of ``mesons'' formed from boson and/or fermion constituents are formulated in an explicit manner convenient for further study. We also analyze how the physical properties of the mesons such as confinement and asymptotic freedom are realized.

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arXiv1994

Triviality, perturbation theory and $Z\to b \overline b$

We compute the large-$m_t$ contributions to the $Zb\overline b$ vertex in the Standard Model non-perturbatively using both the $1/\nc$ and the $1/\nf$ expansions. Triviality and its consequences for the perturbative result are systematically analyzed. In particular, we point out that the effect of triviality is already important at the two-loop level for a heavy Higgs ($600\gev<M_H<1\tev$) even when the top mass is below $200\gev$.

hep-ph↗
arXiv1993

Large--order behavior of non--decoupling effects and triviality

We compute some non--decoupling effects in the standard model, such as the $ρ$ parameter, to all orders in the coupling constant expansion. We analyze their large order behavior and explicitly show how it is related to the non--perturbative cutoff dependence of these non--decoupling effects due to the triviality of the theory.

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arXiv1993

Effects of new physics to the the $ρ$--parameter in the supersymmetric standard model

The contribution to the $ρ$--parameter of the quark--Higgs sector of the supersymmetric standard model is computed non--perturbatively using the large--$\nf$ expansion for the case tan$β$=0. An explicit formula is found for the $ρ$--parameter which is ill-defined unless the triviality cutoff is taken into account. The cutoff dependence of the $ρ$--parameter is found to be large if and only if the top mass is larger than $2v$ so that the cutoff scale is of the order of the electroweak scale. These non--universal effects are the reflections at low energies of the physics beyond the supersymmetric standard model. By also considering the effects of the soft--breaking terms, cutoff effects in both decoupling and non--decoupling effects are analyzed.

hep-ph↗
arXiv1993

Boson--fermion bound states in two dimensional QCD

We derive the boson--fermion bound state equation in a two dimensional gauge theory in the large--$\nc$ limit. We analyze the properties of this equation and in particular, find that the mass trajectory is linear with respect to the bound state level for the higher mass states.

hep-th↗
arXiv1993

Geometrical origin of integrability for Liouville and Toda theory

We generalize the Lax pair and Bäcklund transformations for Liouville and Toda field theories as well as their supersymmetric generalizations, to the case of arbitrary Riemann surfaces. We make use of the fact that Toda field theory arises naturally and geometrically in a restriction of so called $W$--geometry to ordinary Riemannian geometry. This derivation sheds light on the geometrical structure underlying complete integrability of these systems. (Invited talk presented at the 877th meeting of the American Mathematical Society, USC, November 1992 and at the YITP workshop ``Directions on Quantum Gravity", Kyoto, November 1992.)

hep-th↗
arXiv1992

Non--decoupling, triviality and the $ρ$ parameter

The dependence of the $ρ$ parameter on the mass of the Higgs scalar and the top quark is computed non--perturbatively using the $1/N_F$ expansion in the standard model. We find an explicit expression for the $ρ$ parameter that requires the presence of a physical cutoff. This should come as no surprise since the theory is presumably trivial. By taking this cutoff into account, we find that the $ρ$ parameter can take values only within a limited range and has finite ambiguities that are suppressed by inverse powers of the cutoff scale, the so called ``scaling--violations". We find that large deviations from the perturbative results are possible, but only when the cutoff effects are also large.

hep-ph↗
arXiv1992

Non--perturbative evidence for non--decoupling of heavy fermions

We investigate, using a $1/N$ expansion, the behavior of a parameter in the scalar--fermion sector of the standard model that shows perturbative non--decoupling as the fermion becomes heavy. This low energy parameter is related to the $S$ parameter defined through the $W_3-B$ vacuum polarization tensor. We obtain the leading $1/N$ contribution to this parameter that, if expanded perturbatively, collapses to its constant one--loop result; remarkably all the higher--order terms in the series vanish. Non--perturbatively, however, we find that as the mass of the fermion approaches the built--in cutoff scale of the theory --- the triviality scale --- the parameter is highly dependent on the implementation of the cutoff; it is non--universal, and shows non--decoupling.

hep-ph↗
arXiv1991

On the Liouville Approach to Correlation Functions for 2-D Quantum Gravity

We evaluate the three point function for arbitrary states in bosonic minimal models on the sphere coupled to quantum gravity in two dimensions. The validity of the formal continuation in the number of Liouville screening charge insertions is shown directly from the Liouville functional integral using semi-classical methods.

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