Gell-Mann-Low function in the ϕ4 theory

An algorithm is proposed for the determination of the asymptotics of a sum of a perturbation series from the given values of its coefficients in the strong-coupling limit. When applied to the ?⁴ theory, the algorithm yields the β(g)∝g ^α behavior with α≈1 at large g for the Gell-Mann-Low function.     

Analyticity of scattering for the ϕ4 theory

We consider scattering for the equation (+m ²)+³=0 on four-dimensional Minkowski space. Form>0, one-to-one and onto wave operatorsW _± :HH are known to exist for all 0, whereH denotes the Hilbert space of finite-energy Cauchy data. We prove that the maps (,u)W _± (u) and (,u)(W _± )^–1 (u) are continuous from [0, )×H toH, and extend to real-analytic functions from an open neighborhood of {0}×H×{0}×H to the Hilbert spaceH _–1 of Cauchy data with Poincaré-invariant norm. Form=0, wave operatorsW _± are known to exist as diffeomorphisms ofH for all 0, where hereH denotes the Hilbert space of finite Einstein energy Cauchy data. In this case we prove that the maps (,u)(W _± ) (u) and (,u)(W _± )^–1 (u) extend to real-analytic functions from a neighborhood of [0, )×H×H toH.     

A new proof of the existence and nontriviality of the continuum ϕ 2 4 and ϕ 3 4 quantum field theories

We use Schwinger-Dyson equations combined with rigorous “perturbation-theoretic” correlation inequalities to give a new and extremely simple proof of the existence and nontriviality of the weakly-coupled continuum ? ₂ ⁴ and ? ₃ ⁴ quantum field theories, constructed as subsequence limits of lattice theories. We prove an asymptotic expansion to order λ or λ² for the correlation functions and for the mass gap. All Osterwalder-Schrader axioms are satisfied except perhaps Euclidean (rotation) invariance.     

States on Effect Algebras That Have the ϕ-Symmetry Property

The relationship between the property of havinga full set of states and the archimedean property in thecase of -symmetric effect algebra is explored, andequivalent conditions are obtained.     

Search for the ϕ → π+π−γγ and ϕ → π+π−η decays with the CMD-2 detector

The ? → π⁺π^?γγ and ? → π⁺π^?η decays are sought in the experimental data obtained with the CMD-2 detector in the region of the ?-meson resonance. Upper limits ?(? → ππγγ)< 1.2 × 10^?4 and ?(? → ππη) < 6.1 × 10^?5 (both at a C.L. of 90%) are determined for the branching ratios of these decays.     

Hadronic ϕ production and the lund model for lowp T interactions

Experimental results on inclusive ? production are compared with the Lund model for lowp _T hadronic interactions. The data is based on a sample of 600,000 ? mesons in the kinematic rangep _T <1.0 (GeV/c)² and 0.0<x _F<0.4, produced in π^±,K ^±,p and \(\bar p\) Be interactions at 100 GeV/c and 120 GeV/c incident momentum. The Lund model reproduces the shapes of the longitudinal differential cross sections reasonably well, but the relative cross sections for incident, π,K andp show a discrepancy with the data.     

Borel summability of the mass and theS-matrix in ϕ4 models

We show that in the ₂ ⁴ theory, the physical mass and the two-bodyS-matrix are Borel summable in the coupling constant at =0.     

Large deviation estimates in the stochastic quantization ofϕ 2 4

We study in the small noise limit the behaviour of field trajectories for the process constructed by the authors in connection with the stochastic quantization of ₂ ⁴ . Due to the presence of infinite renormalization the usual large deviation techniques do not apply immediately and a new strategy has to be developed. We prove some estimates analogous to the Freidlin-Ventzel inequalities. From these it follows that the field trajectories suitably smeared in space over a scaler ₀ behave, when the noise is small, as the projection on the same scale of a field obeying a regularized stochastic equation with a large cut-off. However the estimates are not uniform in the cut-off and an interesting feature of the problem is that the scale over which the field is smeared determines whether the noise is sufficiently small for the estimates to apply.Laboratoire associé au CNRS UA 280     

Compactification and spontaneous symmetry breaking in the λϕ4 theory with Kaluza-Klein background

We obtain a one-loop effective action for the ⁴ theory in the space M₄×S_N.We study the questions of compactification and spontaneous symmetry breaking due to the one-loop effective action of the ⁴ theory. We show how the vacuum quantum effects of the scalar field induce the 4-dimensional Einstein-Cartan theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 9–14, September, 1988.The author is grateful to I. L. Bukhbinder, I. V. Tyutin, A. A. Tseitlin, and B. L. Spokoinyi for useful discussions.     

Inclusive ϕ meson production,the parton fusion model and strange quark structure functions

The parton fusion model is used to describe the longitudinal differential cross section (dσ/dx _F ) of hadronic ? production. Thedσ/dx _F for ? production in π^± p, \(\mathop p\limits^{( - )} p\) andK ^± p interactions is evaluated in the model by using structure functions for the constituents of the interacting particles. A comparison between the model and high statistics data in the Feynmanx range 0.0<x _F (?)<0.4 allows the determination of the strange valence quark distribution inK mesons and the strange sea quark distribution in π mesons, which appears to be harder than the light sea quark distribution. The comparison also shows that a significant part of inclusive ? production is due to the OZI allowed fusion of strange quarks, while the OZI inhibited fusion diagrams are strongly suppressed.     

Search forN ϕ (1960) baryon

In the experiments at the SPHINX facility in the 70 GeV proton beam of the IHEP accelerator the diffractive production reactionsp+N[(1385)⁰ K ⁺] +N andp+N[(1385)⁰ K ⁺]+N+ (neutral particles) were studied. In the effective mass spectra of the [(1385)⁰ K ⁺] system in these processes there were no signals from the anomalously narrow baryon stateN (1960) which had been observed earlier in the measurement at the BIS-2 setup.SPHINX Collaboration (IHEP-ITEP)     

Leading RG logs in ϕ4 theory

We find the leading RG logs in ϕ⁴ theory for any Feynman diagram with 4 external edges. We obtain the result in two ways. The first way is to calculate the relevant terms in Feynman integrals. The second way is to use the RG invariance based on the Lie algebra of graphs introduced by Connes and Kreimer.     

Higher order corrections to the Lipatov asymptotics in the ϕ<Superscript>4</Superscript> theory

Higher orders in perturbation theory can be calculated by the Lipatov method [1]. For most field theories, the Lipatov asymptotics has the functional form ca ^N Γ(N+b (N is the perturbation theory order); relative corrections to this asymptotics have the form of a power series in 1/N. The coefficients of higher order terms of this series can be calculated using a procedure analogous to the Lipatov approach and are determined by the second instanton in the field theory in question. These coefficients are calculated quantitatively for the n-component ?⁴ theory under the assumption that the second instanton is (i) a combination of elementary instantons and (ii) a spherically asymmetric localized function. A technique of two-instanton computations, as well as the method for integrating over rotations of an asymmetric instanton in the coordinate state, is developed.     

Search for Scalar Resonance in the ωϕ System in the Pion-Nuclear Interaction at Momentum of 29 GeV/c

Physics of Atomic Nuclei - The charge-exchange reaction $${{\pi }^{ - }}p \to n\omega (783)\phi (1020)$$ , $$\omega \to {{\pi }^{ + }}{{\pi }^{ - }}{{\pi }^{0}}$$ , $$\phi \to {{K}^{ + }}{{K}^{ -...