The fundamental-electroweak scale hierarchy in the standard model

The multiple-point principle, according to which several vacuum states with the same energy density exist, is put forward as a fine-tuning mechanism predicting the ratio between the fundamental and electroweak scales in the Standard Model (SM). It is shown that this ratio is exponentially huge: ∼e ⁴⁰. Using renormalization group equations for the SM, we obtain the effective potential in the two-loop approximation and investigate the existence of its postulated second minimum at the fundamental scale. The investigation of the evolution of the top-quark Yukawa coupling constant in the two-loop approximation shows that, with initial values of the top-quark Yukawa coupling in the interval h(M _t )=0.95±0.03 (here, M _t is the top-quark pole mass), a second minimum of the SM effective potential can exist in the region ϕ_min2≈10¹⁶−10²² GeV. A prediction is made of the existence of a new bound state of six top quarks and six antitop quarks, formed owing to Higgs boson exchanges between pairs of quarks-antiquarks. This bound state is supposed to condense in a new phase of the SM vacuum. This gives rise to the possibility of having a phase transition between vacua with and without such a condensate. The existence of three vacuum states (new, electroweak, and fundamental) solves the hierarchy problem in the SM. The text was submitted by the authors in English.     

On Pointwise Decay of Linear Waves on a Schwarzschild Black Hole Background

We prove sharp pointwise t ⁻³ decay for scalar linear perturbations of a Schwarzschild black hole without symmetry assumptions on the data. We also consider electromagnetic and gravitational perturbations for which we obtain decay rates t ⁻⁴, and t ⁻⁶, respectively. We proceed by decomposition into angular momentum ℓ and summation of the decay estimates on the Regge-Wheeler equation for fixed ℓ. We encounter a dichotomy: the decay law in time is entirely determined by the asymptotic behavior of the Regge-Wheeler potential in the far field, whereas the growth of the constants in ℓ is dictated by the behavior of the Regge-Wheeler potential in a small neighborhood around its maximum. In other words, the tails are controlled by small energies, whereas the number of angular derivatives needed on the data is determined by energies close to the top of the Regge-Wheeler potential. This dichotomy corresponds to the well-known principle that for initial times the decay reflects the presence of complex resonances generated by the potential maximum, whereas for later times the tails are determined by the far field. However, we do not invoke complex resonances at all, but rely instead on semiclassical Sigal-Soffer type propagation estimates based on a Mourre bound near the top energy.     

Improved condition for the absence of bound states and converging analytic bounds to critical screening parameter

Converging lower bound to the critical screening parameterD _c associated with the ground state of a two-particle system interacting through a cut-off Coulomb potential is obtained analytically using an improved condition for the absence of bound states. The predicted numerical result for the lower bound is found to be within 10⁻³% of the exact result. On the other hand, a multi-parameter variational approach yields a tight upper bound, within 0.54% of the exact result. It is shown that the critical screening parameter for the exciteds-states can also be determined in an approximate way. We obtainD _c ^ms ≈ [0.764435n ⁻²+0.617737n ⁻³]⁻¹ wheren is the principal quantum number. The predictedD _c for various quantum states (n=1 to 8) are in good agreement with the values obtained numerically by Singh and Varshni.     

Production of relativistic antihydrogen atoms by pair production with positron capture and measurement of the Lamb shift

A beam of relativistic antihydrogen atoms — the bound state ( e⁺) — can be created by circulating the beam of an antiproton storage ring through an internal gas target. An antiproton which passes through the Coulomb field of a nucleus will create e⁺e⁻ pairs, and antihydrogen will form when a positron is created in a bound instead of continuum state about the antiproton. The cross section for this process is roughly 3Z ² pb for antiproton momenta about 6 GeV/c. A sample of 600 antihydrogen atoms in a low-emittance, neutral beam will be made in 1995 as an accidental byproduct of Fermilab experiment E760. We describe a simple experiment, Fermilab Proposal P862, which can detect this beam, and outline how a sample of a few-10⁴ atoms can be used to measure the antihydrogen Lamb shift to 1 %. Work supported in part by Department of Energy contract DE-AC03-76SF00515 (SLAC). Work supported by Fondo Nacional de Investigación Científica y Tecnológica, Chile.     

The missing-mass problem and the precession of perihelia

Summary From an analysis of data on the precession of perihelia we derive several constraints on the density of dark matter in the solar system and on the scales where the laws of celestial mechanics could be modified. For example, the bound on a uniform distribution is ρ_DM ≤ 6·10^-17 g/cm³ and a gravitational force of the form 1/r ²+1/r ₀ r can be excluded unlessr ₀ exceeds a few kpc.     

<Superscript>4</Superscript>He<Superscript>3</Superscript>H<Superscript>2</Superscript>H three-body model of the <Superscript>9</Superscript>Be nucleus

Within the framework of the single-channel approximation, an {αtd} model of the ⁹ Be nucleus is presented. A comparative analysis of the t ⁶ Li wave functions describing relative motion of bound states constructed in {ααn} and {αtd} cluster representations is carried out on the example of calculations of the ⁹ Be(γ,t₀)⁶ Li process characteristics. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 85–89, January, 2008.     

Strong reaction channels at barrier energies in the system 6Li + 208Pb

Large cross-section reaction channels were measured in the systems ⁶Li( ⁷Li) + ²⁰⁸Pb with high statistical accuracy at 5(3) energies around the Coulomb barrier from 29 to 39 MeV. These channels were assigned (mainly) to the breakup of ⁶Li, very loosely bound, into α + d and to the breakup of ⁵Li, produced by n-transfer to the target, into α + p and to similar processes with ⁷Li beam. The cross-sections with ⁶Li, S _α = 1.475 MeV, are systematically larger than the ⁷Li ones. This reflects, most likely, the higher binding energy of ⁷Li, S _α = 2.468 MeV. Theoretical predictions for the ⁶Li + ²⁰⁸Pb system which include for ⁶Li breakup to continuum states within a continuum discretized coupled-channels approach (CDCC) and resonant breakup plus n-transfer with DWBA reproduce the angular distribution shapes but still underestimate the cross-sections by a factor ∼ 3. Received: 15 January 2001 / Accepted: 3 March 2001     

Improved unitarity bounds for inclusive reactions of particles with spin

A comprehensive discussion of the unitarity bounds on inclusive angular distributions, given the elastic amplitudes and the integrated inelastic cross section, is presented. The role played by the latter constraint in improving the bound is studied in detail. Calculations are made forπ ^± p →p (inclusive) at 6 GeV/c.     

Fermion states on domain-wall junctions and the flavor number

In this paper we address the problem of localizing fermion states on stable domain-wall junctions. The study focus on the consequences of intersecting six independent 8d domain walls to form 4d junctions in a ten-dimensional spacetime. This is related to the mechanism of relaxing to three space dimensions through the formation of domain-wall junctions. The model is based on six bulk real scalar fields, the φ ⁴ model in its broken phase, the prototype of the Higgs field, and is such that the fermion and scalar modes bound to the domain walls are the zero mode and a single massive bound state, which can be regarded as a two-level system, at least at sufficiently low energy. Inside the junction, we use the fact that some states are statistically more favored to address the possibility of constraining the flavor number of the elementary fermions.     

Influence of vertex coulomb effects on peripheral partial amplitudes for the consecutive transfer of two protons in A(X,Y)B peripheral nuclear reactions induced by light loosely bound (exotic) nuclei at low energies

The amplitude for the consecutive transfer of two protons in A(X, Y)B peripheral nuclear reactions induced by loosely bound light (exotic) nuclei and described by a nonrelativistic square Feynman diagram in which the first transferred proton is loosely bound while the second one in tightly bound is considered. It is shown that the inclusion of three-ray Coulomb vertex effects in the square diagram leads to the appearance of an additional “Coulomb” singularity in the variable cos θ (here, θ is the c.m. scattering angle), this singularity being closer to the physical domain, −1 ≤ cos θ ≤ 1, than the well-known “triangle” singularities corresponding to the amplitude of the square diagram in which the internal line is contracted. The asymptotic behavior of the partial-wave amplitudes for l ≫ 1 that are generated by the aforementioned singularities is found explicitly. A comparative analysis of the resulting partial-wave amplitudes for l ≫ 1 is performed for specific peripheral nuclear reactions induced by ⁸B and ¹²N ions at various energies.     

The CVC prediction for the τ−→h −π0 v τ branching ratio

We present the branching ratio predictions of an isospin statistical model forτ decays to four, five and six pions. Limits on the branching ratios of the three possible six pionτ decay modes using the Conserved Vector Current (CVC) Hypothesis and thee ⁺ e ⁻→6π cross section data are also presented. We find that the isospin model prediction is in good agreement with the well-measured four pion decay modes and consistent with the five pion decay modes. However, we find that some of the recent six pionτ measurements do not agree with the isospin model and the CVC prediction.     

C M ? C N D -computable state

The notions of D-computable state and D-concurrence are generalized to the C ^M ⊗ C ^N system. A class of D-computable state on C ^M ⊗ C ^N is given and the calculating method of the lower bound of D-concurrence is provided. The obvious expression of the lower bound of D-concurrence for the state mixed by two D-pure states is derived. Supported by the National Natural Science Foundation of China (Grant No. 60433050) and the Key Project of the Science Foundation of Xuzhou Normal University (Grant No. 06XLA05)     

Symmetry and boundness of four-particle coulomb systems

The problem of boundness of a ⁺ b ⁺ c ⁻ d ⁻ four-particle Coulomb systems (quadrions) is studied versus the masses of the particles involved. Inequalities that make it possible to deduce that, if some reference quadrions form a bound state, the same is true for a large number of quadrions formed by particles having various masses were derived. A compendium of calculations for energies of reference systems that possess various symmetries [positronium molecules (e ⁺ e ⁺ e ⁻ e ⁻) and quadrions of the a ⁺ b ⁺ b ⁻ b ⁻, a ⁺ b ⁺ a ⁻ b ⁻, and a ⁺ a ⁺ b ⁻ c ⁻ types] is given, and groups of bound asymmetric quadrions corresponding to them are determined. An inequality for kinetic energies of particles that makes it possible to find out, by using asymmetric reference systems, whether specific quadrions are bound is obtained. It is shown that the boundness of many quadrions is ensured by the boundness of respective three-particle systems. The entire body of the present results permits proving that, of the total number of 406 quadrions containing electrons, muons, pions, kaons, protons, deuterons, and tritons and their antiparticles, 227 quadrions are bound.     

Existence of exotic proton-kaon four particle system

Existence of the exotic proton-kaon four particle system p ⁺ k ⁻ p ⁻ k ⁺ is investigated. The Rayleigh-Riyz variational technique is used in calculations. The system tested is found to exist as bound state and its binding energy is calculated.     

The A(K-stop,Λd )A'' reaction, a tool to observe [ˉNNN] clusters

This work presents experimental results obtained from a study of the K ^- _stop A → ΛdA' reaction, where A = ⁶ Li . The study concerns the distributions of the Λd invariant mass, which allows us to determine the structure of bound [K ^- ppn] systems in nuclei. A candidate of such clusters is identified in the present measurement, and its mass (binding energy), decay width and yield are reported. The experiment was performed at the DAΦ NE φ -facility (LNF) by using the FINUDA spectrometer. The study depended on the capability of FINUDA to reconstruct the traces of all the particles involved in the decay of the nuclear cluster.     

Top quark search beyond theW mass at tevatron collider energy

The upgraded Tevatron collider, with an expected integrated luminosity of 100 pb⁻¹, shall push up the top quark discovery limit from 80 to 200 GeV. The distinctive signature of the signal vis-a-vis background are analysed for this mass range of top. The ratio ofW andZ widths, measured indirectly by the UA1 and UA2 experiments, has been shown to favourm _t <60 GeV [8]. But the experimental errors are too large to derive any meaningful upper bound form _t [2]     

The Kowalewski and Hénon-Heiles motions as Manakov geodesic flows onSO(4) — a two-dimensional family of Lax pairs

The invariant surfaces for the Kowalewski top, the Hénon-Heiles system and the Manakov geodesic flow onSO(4) complete into Abelian surfacesA, by adjoining, in each case, a divisorD of arithmetic genus 9; these divisors belong to the same linear system onA and they each define a polarization (2,4). Therefore there are rational maps transforming the Kowalewski top and the Hénon-Heiles system into Manakov's geodesic flow onSO(4). This paper deals with the precise geometric relationship between these three problems; it is based on the splitting of the 8-dimensional space of sections ofD (theta-functions) into an even and an odd part and also on a normal form for the six quadrics describingA, as embedded in ⁷. As a byproduct, we get a 2-dimensional family of Lax pairs for both the Kowalewski top and the Hénon-Heiles system.The support of a National Science Foundation grant #84-03136 is gratefully acknowledged     

Fine structure of the muonic <Superscript>4</Superscript>He ion

On the basis of quasi-potential approach to the bound state problem in QED we calculate the vacuum polarization, recoil and structure corrections of orders α⁵ and α⁶ to the fine splitting interval ΔE ^fs = E(2P _3/2) − E(2P _1/2) in muonic ₂⁴He ion. The resulting value ΔE ^fs = 146180.68 μeV provides reliable guideline in performing a comparison with the relevant experimental data.     

Resonance behavior of a K S K S system near the mass 1775 MeV

The preliminary results of an investigation of a system of two K _S mesons in the mass interval 1600–1950 MeV are reported. The events were obtained on a 6-m magnetic spark spectrometer at ITEP in π ⁻ p interactions at 40 GeV, using a neutral trigger which suppressed both charged particles and γ rays. A peak of width ≃30 MeV with statistical significance not lower than six standard deviations is observed with momentum transfer selection |tu|0.23 GeV² near the mass 1775 MeV of the K _S K _S system. The observed phenomena can be interpreted as the existence of one resonance with the indicated parameters, or two narrower resonances. In the latter case, their masses are 1768±1.5 and 1787±1.5 MeV. The widths of these states are comparable to the mass resolution of the spectrometer (∼5 MeV). Estimates of the product σ ⋅BR(K _S K _S ) give ∼1.5 and 2.5 nb, respectively, for the first and second states. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 10, 727–731 (25 November 1998)