Local existence of the Borel transform in euclidean massless Φ 4 4

We extend the methods of [1] to prove large order estimates on the renormalized Feynman amplitudes of massless ₄ ⁴ euclidean field theory, at non-exceptional momenta. The Borel transform of the perturbative series is analytic in a disk centered at the origin of the complex plane. This result is a step towards the rigorous investigation of the infra-red singularities in the Borel plane, for theories containing massless particles, like the gauge theories.     

On the short-range order of amorphous Al−Au films

Al_100–x Au _x films (20x71) are produced by quench condensation. The analysis of electron diffraction patterns as well as resistivity measurements reveal the liquid-like structure of these films. In contrast to amorphous Al–Cu films the amorphous Al–Au filsm exhibit prepeaks in their interference functions. Atomic distances as large as the smallest Au–Au separations existing in the compound Al₂Au are responsible for these prepeaks. The CaF₂-type structure of this particular compound is due to an ionic bonding contribution in Al₂Au. This bonding contribution, probably caused by the large electronegativity difference between Al and Au, seems to be responsible for the pronounced chemical short-range order in amorphous Al–Au films.     

On the absolute efficiency of large neutron detectors for μCF

The absolute efficiency for a large organic scintillator neutron detector has been calculated via Monte Carlo simulation for neutrons of 14 MeV. The influence of the environmental geometry (source scattering, etc.) has been taken into account. Full differential cross-sections, including resonances, have been used. The calculated response function compares well with the measured one. This revised version was published online in August 2006 with corrections to the Cover Date.     

Construction and Borel summability of infrared Φ 4 4 by a phase space expansion

We construct the thermodynamic limit of the critical (massless) ⁴ model in 4 dimensions with an ultraviolet cutoff by means of a partly renormalized phase space expansion. This expansion requires in a natural way the introduction of effective or running constants, and the infrared asymptotic freedom of the model, i.e. the decay of the running coupling constant, plays a crucial rôle. We prove also that the correlation functions of the model are the Borel sums of their perturbation expansion.     

On the applicability of finite order perturbative QCD calculations of jet rates ine + e − annihilation

We have studied the measurement of α _s using exact second order QCD matrix element calculations of jet rates ine ⁺ e ^?→hadrons. We investigate the dependence of α _s (M _Z ² ), measured by experiments at theZ ⁰ resonance, on the choice of renormalisation scale in terms of the functional form of the three-jet matrix element. We find that only a restricted domain of the jet resolution parametery _c , $\Lambda _{\overline {MS} } $ , and scale gives a perturbation series which is well-behaved to second order, and that this domain is different for the various jet algorithms in current use.     

A Lipatov bound for Φ 4 4 Euclidean field theory

We bound the large order behavior of these pieces of the renormalized perturbation expansion for ₄ ⁴ which do not contain renormalons [1]. The bound we obtain has the form of the leading asymptotic behavior computed by the Lipatov method, with the exact value of the Lipatov constant. Therefore, this paper is a step towards the rigorous study of the large order behavior of ₄ ⁴ and towards a proof of existence of the first renormalon singularity which should prevent the theory from being Borel summable. Using the results of this paper and the techniques of [15], one can for instance improve [17] the estimate [18] on the finiteness of the radius of convergence of the Borel transform of renormalized ₄ ⁴ and obtain that this radius is at least the exact value conjectured in [1].Supported in part by the National Science Foundation under Grant PHY 85-13554     

Cluster expansion approach to the effective potential in Φ 2+1 4 -theory

We apply a truncated set of dynamical equations of motion for connected equal-time Green functions up to the 4-point level to the investigation of spontaneous ground state symmetry breaking in Φ ₂₊₁ ⁴ quantum field theory. Within our momentum space discretization we obtain a second order phase transition as soon as the connected 3-point function is included. However, an additional inclusion of the connected 4-point function still shows a significant influence on the shape of the effective potential and the critical coupling.     

On the scaling behavior of the chiral phase transition in QCD in finite and infinite volume

We study the scaling behavior of the two-flavor chiral phase transition using an effective quark–meson model. We investigate the transition between infinite-volume and finite-volume scaling behavior when the system is placed in a finite box. We can estimate effects that the finite volume and the explicit symmetry breaking by the current quark masses have on the scaling behavior which is observed in full QCD lattice simulations. The model allows us to explore large quark masses as well as the chiral limit in a wide range of volumes, and extract information about the scaling regimes. In particular, we find large scaling deviations for physical pion masses and significant finite-volume effects for pion masses that are used in current lattice simulations.     

On the consistent solution of the gap-equation for spontaneously brokenλΦ 4-theory

We present a self-consistent solution of the finite temperature gap-equation for ⁴ theory beyond the Hartree-Fock approximation using a composite operator effective action. We find that in a spontaneously broken theory not only the so-called daisy and superdaisy graphs contribute to the resummed mass, but also resummed non-local diagrams are of the same order.herby@lapphpl.in2p3.fr     

The critical behavior of φ 1 4

The eigenvalues, eigenfunctions, and Schwinger functions of the ordinary differential operator $$H(\lambda ,m) = \tfrac{1}{2}\{ p^2 + \lambda q^4 + (m^2 - \lambda m^{ - 2} )q^2 \} $$ are studied as λ → ∞. It is shown that the scaling limit of the Schwinger functions equals the scaling limit of a one dimensional Ising model. Critical exponents ofH(λ,m) are shown to equal critical exponents of the Ising model, while critical exponents of the renormalized theory are shown to agree with those of a harmonic oscillator.     

On the Equivalence of Regularization Schemes

We illustrate via the sunset diagram that dimensional regularization “deforms“ the nonlocal contents of multi-loop disgrams with its equivalence to cutoff regularization scheme recovered only after sub-divergence was subtracted.Then we employed a differential equation approach for calculationg loop diagrams to verify that dimensional regularization deforms the low energy contents before subtraction.The virtues of the differential equation approach are argued especially in nonperturbative perspective.     

Asymptotics of the cut discontinuity and large order behaviour from the instanton singularity: The case of lattice Schrödinger operators with exponential disorder

We discuss the relation between the singularity structure of the Borel transform, the asymptotics of the cut discontinuity and the large order behaviour of perturbation theory. In an explicit example — a tight binding model with exponential disorder — we show how to obtain the first instanton singularity from a cluster expansion in the Borel variable, and as an application we determine the exact decay of the density of states asE . The method opens some perspectives for similar problems arising from different models of Mathematical Physics.     

On the structure of Σ-hypernuclei

We investigate the-nucleus potential in the framework of a relativistic mean field approximation. As input for the elementaryN interaction we supplement the-repulsion by the exchange of an effective, complex-meson to account for theN N conversion. As the main result we find that the strength of ths absorptive central potential is smaller than the corresponding real part, whereas in the spin-orbit interaction, which is expected to be much weaker than for a nucleon, the imaginary component dominates.This work was partially supported by CNPq, FINEP (Brazil) and by the Bilateral Cooperation W. Germany — Brazil (KFA — CNPq).     

On the longitudinal electromagnetic coupling of the Δ

The relativistic corrections, corresponding to the transverse and longitudinal excitation of the Δ, are included in the original Blomqvist-Laget model. They are calibrated against the pion photoproduction data. The measurement of the transverse-longitudinal interference cross sections of the (e, e′ π⁰) reaction is the most promising way to study the longitudinal coupling of the Δ.     

Special features of the long-range order – short-range order phase transition in FCC-based alloys

Results of x-ray analysis of the long-range order in FCC-based alloys with L1₂, L1₂(M), L1₂(MM), and D1_a superstructures are generalized. Regularities of the behavior of the long-range order parameter and average size of the thermal and periodic antiphase boundaries (APB) are traced, main mechanisms of temperature order-disorder phase transition are elucidated, and influence of the thermal and periodic APB on the special features of the order-disorder phase transition is revealed. The character of change of the periodic antiphase boundary density determines the special features of the order-disorder phase transition in alloys with longperiod superstructures.     

An upgraded analysis of ɛ′/ɛ at the next-to-leading order

An upgraded analysis of ,x _d and /, using the latest determinations of the relevant experimental and theoretical parameters, is presented. Using the recent determination of the top quark mass,m _t =(174±17) GeV, our best estimate is /=(3.1±2.5)×10^–, which lies in the range given by E731. We describe our detemination of / and make a comparison with other similar studies. A detailed discussion of the matching of the full theory to the effective Hamiltonian, written in terms of lattice operators, is also given.     

The effect of non-mesogenic biphenyl impurity on the orientational order parameter of 4-cyano-4′-n-octyl-biphenyl (8CB)

The role of non-mesogenic impurities on a mesogen and the consequent alteration of mesogenic properties have always been of great interest in the tailoring of mesogenic behaviour. In the present work the effect of rigid, non-polar, nonmesogenic solute ‘biphenyl’ on the optical properties of the mesogen 4-cyano-4′-n-octyl-biphenyl (8CB) has been reported. The phase transitions and thermal variations of the refractive index, polarisability and order parameter ?P₂? of the 8CB–biphenyl systems of various concentrations have been investigated using a He–Ne laser beam. The results have been compared with ?P₂? of pure 8CB. It has been observed that biphenyl lowers both smecticA–nematic and nematic–isotropic transition temperatures by an amount that depends on impurity concentration.