Improved lower bounds for the ground-state energy of many-body systems

New lower bounds for the binding energy of a quantum-mechanical system of interacting particles are presented. The new bounds are expressed in terms of two-particle quantities and improve the conventional bounds of the Hall-Post type. They are constructed by considering not only the energy in the two-particle system, but also the structure of the pair wave function. We apply the formal results to various numerical examples, and show that in some cases dramatic improvement over the existing bounds is reached.Comment: 29 pages, 5 figures, to be published in Phys. Rev.

Some Remarks on the Pade Unitarization of Low-Energy Amplitudes

We present a critical analysis of Pade-based methods for the unitarization of low energy amplitudes. We show that the use of certain Pade Approximants to describe the resonance region may lead to inaccurate determinations. In particular, we find that in the Linear Sigma Model the unitarization of the low energy amplitude through the inverse amplitude method produces essentially incorrect results for the mass and width of the sigma. Alternative sequences of Pades are studied and we find that the diagonal sequences (i.e., [N/N]) have much better convergence properties.Comment: 12 pages, 4 fig

O(p6)O(p^6) extension of the large--NCN_C partial wave dispersion relations

Continuing our previous work(JHEP 0706:030,2007), large--$N_C$ techniques and partial wave dispersion relations are used to discuss $\pi\pi$ scattering amplitudes. We get a set of predictions for $O(p^6)$ low-energy chiral perturbation theory couplings. They are provided in terms of the masses and decay widths of scalar and vector mesons.Comment: 7 page

Weakly-Bound Three-Body Systems with No Bound Subsystems

We investigate the domain of coupling constants which achieve binding for a 3-body system, while none of the 2-body subsystems is bound. We derive some general properties of the shape of the domain, and rigorous upper bounds on its size, using a Hall--Post decomposition of the Hamiltonian. Numerical illustrations are provided in the case of a Yukawa potential, using a simple variational method.Comment: gzipped ps with 11 figures included. To appear in Phys. Rev.

Unitary Standard Model from Spontaneous Dimensional Reduction and Weak Boson Scattering at the LHC

Spontaneous dimensional reduction (SDR) is a striking phenomenon predicted by a number of quantum gravity approaches which all indicate that the spacetime dimensions get reduced at high energies. In this work, we formulate an effective theory of electroweak interactions based upon the standard model, incorporating the spontaneous reduction of space-dimensions at TeV scale. The electroweak gauge symmetry is nonlinearly realized with or without a Higgs boson. We demonstrate that the SDR ensures good high energy behavior and predicts unitary weak boson scattering. For a light Higgs boson of mass 125GeV, the TeV-scale SDR gives a natural solution to the hierarchy problem. Such a light Higgs boson can have induced anomalous gauge couplings from the TeV-scale SDR. We find that the corresponding WW scattering cross sections become unitary at TeV scale, but exhibit different behaviors from that of the 4d standard model. These can be discriminated by the WW scattering experiments at the LHC.Comment: 38pp, Eur.Phys.J.(in Press); extended discussions for testing non-SM Higgs boson(125GeV) via WW scattering; minor clarifications added; references added; a concise companion is given in the short PLB letter arXiv:1301.457

Two-loop O(GF2MH4){\rm O}\left(G_F^2M_H^4\right) corrections to the fermionic decay rates of the Higgs boson

We calculate the dominant ${\rm O}\left(G_F^2M_H^4\right)$ two-loop electroweak corrections to the fermi\-onic decay widths of a heavy Higgs boson in the Standard Model. Use of the Goldstone-boson equivalence theorem reduces the problem to one involving only the physical Higgs boson $H$ and the Goldstone bosons $w^\pm$ and $z$ of the unbroken theory. The two-loop corrections are opposite in sign to the one-loop electroweak corrections, exceed the one-loop corrections in magnitude for $M_H>1114\ {\rm GeV}$, and increase in relative magnitude as $M_H^2$ for larger values of $M_H$. We conclude that the perturbation expansion in powers of $G_FM_H^2$ breaks down for $M_H\approx 1100\ {\rm GeV}$. We discuss briefly the QCD and the complete one-loop electroweak corrections to $H\rightarrow b\bar{b}, \,t\bar{t}$, and comment on the validity of the equivalence theorem. Finally we note how a very heavy Higgs boson could be described in a phenomenological manner.Comment: 24 pages, RevTeX file, 4 figures in a separate compressed uuencoded Postscript file or available by mail on request. Fig. 1 not included see Figs. 1, 2 in Phys. Rev. D 48, 1061 (1993