Model calculations forI=0 andI=2S-wave pion-pion scattering

Several simple models for theS-waves in isospinI=0 andI=2 pion-pion scattering are constructed. These models are based on unitarity, analyticity in the complexq-plane (q=c.o.m. momentum), approximate crossing symmetry, and the assumption that the forces acting in theS-waves are mainly due to exchange ofρ-mesons,fmesons and a strongI=0S-wave. These models contain between one and three parameters, which are being used to obtain a best fit to Walker'sI=0 data. Our best fits are associated with anI=0 scattering lengtha ₀=0.53 μ^?1. Having fixed the parameters from theI=0 data, predictions are obtained for theI=2S-wave. Our predictions are generally characterized by a very small positiveI=2 scattering lengtha ₂? 0.08 μ^?1 and a zero of the phase shift just above threshold, at a total c.o.m. energy of 320 to 360 MeV. The cause for this behaviour is shown to be the strongS-wave in the crossedI=0 channels. Various reasons are discussed, why we might expect this zero to occur at somewhat larger or at smaller energies, even below threshold. Although because of the crudeness of these models the significance of our results is mainly qualitative, certain internal contradictions in the Walker data seem to be indicated.     

The effective potential and symmetry breaking in theO(N) xO(N) model

We compute the finite temperature effective potential in theO(N)xO(N) symmetric model for largeN in spacetime dimensionsd=4, 3, 2 and discuss the spontaneous symmetry breaking patterns. Ford=3 we find that the symmetry, if broken at zero temperature is restored at arbitrarily small nonzero temperature. Ford=4 the model is plagued by an intrinsic instability; in particular, there is no stable ground state at high temperature.     

Quantization and confinement effects in superconducting nanostructures

The confinement of the flux lines by a lattice of submicron holes (‘antidots’) has been studied in nanostructured superconducting Pb/Ge multilayers. By introducing regular arrays of sufficiently large antidots, multi-quanta vortex lattices have been stabilized. Sharp cusp-like magnetization (M) anomalies, appearing at matching fieldsH_m=mφ₀/Sin superconducting films with the antidot lattices having a unit cell areaS, are successfully explained. These anomalies are, analogues of the well-knownM(H) cusp atH_c1, but for the onset of multi-quanta (m+1)φ₀-vortices penetration at each subsequent matching fieldH_m. It is shown that theM(H) curve between the matching fieldsH_m<H<H_m+1follows a simpleM∝ln(H−H_m) dependence. These experimental observations have revealed an unusual expansion of validity of the London limit in superconductors with lattices of relatively large antidots. The successful high quality fit of theM(H,T) curves convincingly demonstrates that a new type of the critical stateB=const (‘single-terrace critical state’) can be realized in superconductors with the antidot lattices.     

Asymptotic perturbation expansion in theP(φ)2 quantum field theory

In theP(φ)₂ model it is proved that the perturbation series for the infinite volume Schwinger functionsS(λ) are asymptotic in the limit as the coupling constant λ goes to zero. We also give conditions which imply smoothness ofS(λ) at arbitrary λ.     

Vacuum insertion and nonperturbative effects for exclusive nonleptonic decays of charmed mesons and kaons

We re-examine QCD sum rules forS-wave charmonium. Dimension 6, 8 contributions for both³ S ₁,¹ S ₀ waves are taken into account using the factorisation model and found to be reasonably small. A good fit to the data requires the confinement parameterφto be much bigger than the generally accepted value.     

Finite temperature QCD corrections to lepton-pair formation in a quark-gluon plasma

We discuss theO(α _S ) corrections to lepton-pair production in a quark-gluon plasma in equilibrium, assuming the quarks are massless at zero temperature. The corrections are found to be very small in the domain of interest for ultrarelativistic heavy ions collisions. Interesting effects, however, appear at the annihilation threshold of the thermalized quarks where the correction factor has a (1/α _S ) behavior.     

Investigation of203, 205Hg with the (d,pγ) reaction — Identification of thei 13/2 neutron hole state in205Hg

Low lying levels in²⁰³Hg and²⁰⁵Hg were studied with the (d, p) deuteron break-up reaction atE _d=14 and 18 MeV. Gamma-rays and conversion-electrons were measured in coincidence with protons. In addition delayed spectra were recorded with us and ms beam pulsing. Thei _13/2 neutron hole state was identified in²⁰⁵Hg and confirmed in²⁰³Hg. The known level structure of²⁰⁵Hg below 2 MeV is confirmed and extended. For²⁰³Hg we observe theγ-decay of several levels below 1.5 MeV, which were previously known from transfer reactions.     

J/ψ+η′ Production ine + e −-annihilation: A perturbative QCD calculation

The cross section for the reactione ⁺ e ^?→³S₁+¹S₀ is calculated in the framework of perturbative QCD, using the nonrelativistic approximation for the³S₁ and¹S₀ bound states. The model is applied toJ/Ψ plus η,η,η′, andl production. We find extremely small rates in contrast to previous estimates based on vector meson dominance and discuss possible reasons for this difference.     

High precision hyperfine structure measurements in185Re and187Re

The hyperfine structure of the atomic levels 5d ⁵ 6s ^{2 6} S _5/2 and⁴ P _5/2 in¹⁸⁵Re and¹⁸⁷Re has been studied with high precision by atomic-beam magnetic-resonance. Additional measurements were performed in the 5d ⁵ 6s ^{2 4} G _5/2 and 5d ⁶ 6s ⁶ D _9/2 states of¹⁸⁷Re. For the interpretation of the results eigenvectors in intermediate coupling have been derived by a least squares fit of all known levels of the configurations (5d+6s)⁷. The ratioB(¹⁸⁵Re)/B(¹⁸⁷Re) is the same for the⁶ S _5/2 and the⁴ P _5/2 state within the error limits of 6 parts in 10⁵. Combining the present results with the known hyperfine structure data of¹⁸⁶Re and¹⁸⁸Re we find the magnetic-dipole hyperfine anomalies for the isotopic series^185?188Re.     

KaonB parameter with static cavity QCD corrections

The kaonB parameter is computed in a framework in which static cavity QCD loop corrections to the weak interactions of hadrons are included by extending the Fock state wavefunction to includeO(g) bremsstrahlung and vacuum fluctuation states. Since the QCD corrections are inherent in the calculation of the matrix elements of the bare effective weak ΔS=2 Hamiltonian between hadronic states the scale matching problem of the standard short distance analysis is alleviated. The modified static cavity model used is characterised by four parameters; the effective quarkgluon coupling constant, the confinement pressure, the zero-point energy and a parameter governing the centre-of-mass corrections. These parameters are fitted to the π and ? masses and the charge radii of π andK. Results are given for the ultra-relativistic (m _u=m _d=0) sector and for a region (m _u=m _d≈140 MeV) where the ΔI=1/2 rule is uniquely reproduced. For the parameter set which describes the ΔI=1/2 rule we findB _K=0.58 at a basis size ofN _B=6.     

A comment on octet enhancement in the ΔI=1/2 rule

We apply vacuum background fields method to correct the coefficient functions of theO ₊ andO _? operators in ΔS=1 effective weak Hamiltonian responsible forK→2π decays. The additional relative octet enhancement factor of 2–3 is obtained by accounting for the gluon condensate corrections if the scale parameterπ ²x is set below 1 GeV₂.     

Nonperturbative contribution to the fermion propagator and dynamical electroweak symmetry breaking

We examine the field-theoretical contribution of fermion-antifermion condensates arising from a weak-SU(2) doublet of condensing fermions to electroweak vacuum polarization functions. For the custodial-SU(2) case of equal condensates and masses, we find that the condensate contributions to vacuum polarization functions uphold the electroweak signature relationm _w=m _zcosθ_w, and that these contributions are decoupled entirely from oblique radiative corrections. If only the upper member of the doublet forms a fermion-antifermion condensate, the relationm _w=m _zcosθ_w is again upheld in the limit that the mass of the lower member of the doublet is small compared to that of the upper member. For this case, the upper-member's fermion-antifermion condensate is shown to enter oblique radiative corrections. In the absense of an explicit Higgs mechanism, identification of this doublet with (t, b) is shown to be excluded by present empirical bounds onS, T, andU parameters. Further phenomenological consequences of fermion-antifermion condensate contributions to theW-Z mass matrix are discussed, both in the absense and in the presence of an explicit Higgs mechanism.     

On some properties of the neutron in the statistical model

Using the statistical model to arrive at |ψ(r)|² the square modulus of theS state wavefunction of the neutron, the electric dipole moment |d _n ^e | of the neutron as well as its baryon number violating lifetime have been estimated. The baryon asymmetry of the universe depending on |d _n ^e | has also been studied in this context.     

Stark effect,hyperfine structure and isotope shifts in highly excited states of BaI and CaI

The electric dipole polarizabilities of 9 even-parity barium states (6s8s ¹ S ₀,³ S ₁; 6s7d ¹ D ₂,³ D _1,2; 5d7s ¹ D ₂ and 6p ^{2 3} P _0,1,2) in the interval 33,800–35,800 cm^?1 have been measured with high resolution laser-atomic-beam spectroscopy. Simultaneously, values of isotope shifts and hyperfine coupling constants for theJ=1 states have been obtained. Comparison of the experimental polarizabilities with calculated values as well as inspection of the data on isotope shifts and hyperfine structure from the present and earlier work strongly suggests erroneous assignments of theJ=2 states, with an exception for the 5d 7s ¹ D ₂ state. The influence of an electric field on the 3d ^{2 3} P _0,1,2 states of calcium has also been studied. A marked departure from a quadratic Stark effect has been observed at relatively small field strengths. This can be attributed to the large polarizabilities of neighbouring Rydberg states. The low field data allow the determination of admixtures of Rydberg states into the 3d ^{2 3} P-states as small as 0.02%.     

A simple relationship between chandrasekha's S and T functions

Chandrasekhar's equations for the functions S and T which represent the diffuse scattering and the diffuse transmission, respectively, of a beam of radiation by a planar atmosphere are invariant under the transformations S(τ₁; μ, φ - μ₀), φ₀) exp (-τ₁/μ₀) = T(τ₁; μ, φ; μ₀, φ₀) and T(τ₁; μ, φ; -μ₀, φ₀) exp(-τ_t/μ₀) = S(τ₁; μ, φ; μ₀, φ₀). This relationship reflects the physical symmetry of radiative transfer in a planar atmosphere. It offers a simple method for obtaining the expression for S (T) when an analytical expression for T (S) exists. However, it does not appear to ofter any simplification of numerical solutions.     

Contribution of higher gluon condensates to light-quark vacuum polarization

A method of classifying quark operators in QCD sum rules is suggested. The expansion coefficients of all thed≦8 bilinear quark condensates in gluon condensates are calculated. The coefficient functions at the gluon operators withd≦8 in the polarization operator ∏(q ²) of the light-quark vector current are obtained. A comparison is performed with the calculations in the covariantly constant fields and self-dual fields. The results obtained can be used in the sum rules for the ρ, ω and ? families.     

Optical theorem in curved space-time quantum field theory

A structural analysis is given of the optical theorem in theS-matrix approach to mutually interacting quantum fields in classical Robertson-Walker universes. As a case study, theφψ ²-interaction of conformally coupled massive (φ) and massless (φ) Klein-Gordon particles is studied. Based on the outgoing massless particles as indicator configuration, the physical interpretation is reduced to the corresponding added-up probabilities. Several examples are discussed in an in-in scheme which has the advantage that only a few non-Minkowskian in-in Feynman diagrams are involved.     

Alternative scaling hypothesis forSU(2) andSU(3) lattice gauge theories

High precision data from a variety of sources forSU(2) andSU(3) Wilson action lattice gauge theory are analyzed with respect to the hypothesis of the possible existence of a zero temperature deconfining phase transition, in analogy with theU(1) theory. The internal energy, specific heat, string tension, and Wilson line, fit well to correlation length scaling laws associated with a finite order transition occurring at the weak coupling end of the crossover region for both theories. TheSU(2) theory is consistent with a correlation length exponent ν=2/3 and critical pointβ _c ≈2.47. ForSU(3) the data fit well to ν=1 andβ _c ≈6.69. Additional indirect evidence for the existence of such phase transitions is discussed, as is the possible crucial role of light dynamical fermions in the confinement mechanism.