Orthogonality between scales and wavelets in a representation for correlation functions. The lattice dipole gas and (∇φ)4 models

Exact formulas for the correlation functions of lattice scalar field models in Z^d,d3, such as the dipole gas and anharmonic crystal are derived in terms of the effective action generated aftern applications of the block renormalization group transformation. Utilizing the orthogonality between different momentum scales (relations due to the wavelets implicit in the structure of the block renormalization group transformation), the formulas are quite simple, isolate the dominant term, and, in the thermodynamic andn limits, reduce the analysis to local estimates of the effective action. Based on a large-small field analysis, the two-point function is determined and it is shown how to extend the results to general correlations. The results proved here show the usefulness of the orthogonality-of-scales property for the study of correlation functions.     

Bounds on the decay of correlations for λ(∇φ)4 models

We consider models, with an abelian continuous group of symmetry, of the type: $$H = \sum\limits_x {\left[ {\frac{1}{2}(\nabla _x \phi )^2 + \frac{\lambda }{4}(\nabla _x \phi )^4 } \right].}$$ We generalize Brascamp-Lieb inequalities to get (λ-independent) bounds on the low momentum behaviour of general correlation functions when these are truncated into two clusters. We then use this result to derive an asymptotic expansion (up the second order in λ) of the dielectric constant of this system.     

Decay of the Bethe–Salpeter Kernel and Bound States for Lattice Classical Ferromagnetic Spin Systems at High Temperature

We consider lattice classical ferromagnetic spin systems at high temperature (1) with nearest neighbor interactions and even single-spin distributions (ssd). Associated with each system is an imaginary time lattice quantum field theory. It is known that there is a particle of mass m–ln in the energy-momentum spectrum. If s ⁴–3s ²²<0, where s ^k is the kth moment of the ssd, and is sufficiently small, we show that in the two-particle subspace there is no mass spectrum up to 2m. For >0 we show that the only mass spectrum in (m, 2m) is a bound state of mass m _b=2m+ln(1–)+O(), where =(+2s ²²)^–1. A bound on the decay of the kernel of a Bethe–Salpeter equation is obtained and used to prove these results.     

Molecular dynamics simulation of dielectric constant and cluster structure of liquid methanol: the role of cluster–cluster dipole correlations

A molecular dynamics simulation of liquid methanol at ambient conditions with two different three-site potential models was performed and the evaluated dielectric constant was discussed in the light of the cluster structure of the liquid. The distribution of the pair interaction energy of molecules and the cluster size distribution were calculated. An aggregation contribution to dielectric constant was defined and calculated as a function of the threshold H-bond energy using energetic criterion of H-bond. The structural information on dipole–dipole correlations of molecules incorporated in the size and structure distribution of aggregates proved to cover about 80% of the calculated dielectric constant of methanol. The other 20% should be attributed to the cluster–cluster dipole correlations.     

Borel summability of the perturbation series in a hierarchical λ(▽φ)4 model

We prove Borel summability of the perturbation series for the dielectric constant and the free energy density for the hierarchical ()⁴ lattice model. Our methods are based on nonperturbative renormalization group analysis of the model.On leave from the Department of Mathematical Methods of Physics, Warsaw University, Poland.Supported in part by the Center for Interdisciplinary Research, Bielefeld University, Germany.     

Phase structure of O(N)-symmetric φ63 models at small and intermediate N

To test on the occurrence of the non-trivial BMB fixed point we study the phase diagram of O(N)-symmetric φ⁶₃ models in the limit of infinite φ⁶-coupling. Our Monte Carlo results for N = 5, 10 and 30 confirm that the so-called BMB phenomenon could be a large-N effect.     

Lattice (Φ 4)4 effective potential giving spontaneous symmetry breaking and the role of the Higgs mass

We present a critical reappraisal of the available results on the broken phase ofλ(Φ ⁴)₄ theory, as obtained from rigorous formal analyses and from lattice calculations. All the existing evidence is compatible with Spontaneous Symmetry Breaking but dictates a trivially free shifted field that becomes controlled by a quadratic hamiltonian in the continuum limit. As recently pointed out, this implies that the simple one-loop effective potential should become effectively exact. Moreover, the usual naive assumption that the Higgs mass-squaredm _h ² is proportional to its “renormalized” self-couplingλ _R is not valid outside perturbation theory: the appropriate continuum limit hasm _h finite and vanishingλ _R . A Monte Carlo lattice computation of theλ(Φ ⁴)₄ effective potential, both in the single-component and in theO(2)-symmetric cases, is shown to agree very well with the one-loop prediction. Moreover, its perturbative leading-log improvement (based on the concept ofλ _R ) fails to reproduce the Monte Carlo data. These results, while supporting in a new fashion the peculiar “triviality” of theλ(Φ ⁴)₄ theory, also imply that, outside perturbation theory, the magnitude of the Higgs mass does not give a measure of the observable interactions in the scalar sector of the standard model.     

Finite size scaling for O(N) φ4-theory at the upper critical dimension

A finite size scaling theory for the partition function zeroes and thermodynamic functions of O(N) φ⁴-theory in four dimensions is derived from renormalization group methods. The leading scaling behaviour is mean-field like with multiplicative logarithmic corrections which are linked to the triviality of the theory. These logarithmic corrections are independent of N for odd thermodynamic quantities and associated zeroes and are N dependent for the even ones. Thus a numerical study of finite size scaling in the Ising model serves as a non-perturbative test of triviality of φ⁴₄-theories for all N.     

A finite size scaling analysis of the O(4)-invariant lattice δ4 theory

The critical behaviour of the three- and four-dimensional N=4 vector model is investigated by means of a Monte Carlo simulation on lattices with size between 4³ and 16³, and between 4⁴ and 12⁴, respectively. For obtaining information about some critical properties of the model, we use a method due to Binder which is based on the theory of finite size scaling. For the three-dimensional model we get estimates of the critical exponents ν and η which are compatible with estimates obtained from the ϵ-expansion. In four dimensions we study for two different values of the bare self-coupling λ (λ=1 in our normalization, and λ=∞) the scaling behaviour of some Green function ratios at the phase boundary. In both cases we find compatibility with the “predicted” scaling behaviour at the gaussian fixed point. This is another independent numerical hint that the continuum limit of the four-dimensional O(4)-invariant lattice δ⁴-model is a free field theory.     

The CP violation of theB→Kϕ decay at γ(4s) in the non-standard models

The CP violating asymmetry in theB→K? decay is studied in both supersymmetric model and three Higgs doublets model. The absorptive part of the penguin amplitude leads to the CP violating asymmetry in theB _u ^+- →K ^±? decays, which is at most 3% due to the GIM mechanism in the standard model. However, the asymmetry could be relatively large if there exists a new source of the imaginary component in the decay amplitude. In the supersymmetric model, the contributions of the imaginary part of the super-penguin and the super-box processes rather suppress the magnitude of the asymmetry, whereas in the three Higgs doublets model, that of the charged Higgs-penguin process could significantly enhance it.     

Study of the Λ(1405) Resonance Through its Neutral and Charged Decay Channels by AMADEUS at DAΦNE

The AMADEUS collaboration has the goal to perform unprecedented measurements in the field of the low-energy charged kaons-nuclei interactions, by implementing the existing KLOE detector with a dedicated setup in the inner region. The KLOE detector at DAΦNE represents a unique opportunity to perform a complete study of the Λ(1405) resonance through all its three Σπ decay channels. The importance of these measurements relies on the possibility to compare the different results for the various decay channels, investigating their contributions to the final resonance shape. In particular, one of the main differences between the neutral and charged Σπ channels is the presence of a second resonance, the Σ(1385), whose contribution to the final Λ(1405) spectra has to be evaluated and subtracted. Very promising preliminary results have been already obtained for the Σ ⁰π⁰ decay channel to which, for isospin selection rules, the Σ(1385) resonance can not decay, and for the Σ ⁺π^? decay channel analysis, and will be presented in this work.     

Accurate ab initio potential of CO(XΣ) at low cost via correlation scaling and extrapolation method

The potential energy curve (PEC) for the ground state of CO(X¹Σ⁺) has been investigated by the highly accurate valence internally contracted multi-reference configuration interaction with the Davidson correction (MRCI+Q) method in combination with a series of correlation-consistent basis sets of Dunning and co-workers. The scheme proposed by Varandas, which enables high-quality molecular potentials to be obtained from small basis set calculations via scaling and extrapolation of the electron correlation to the complete basis set limit plus extrapolation to the complete basis set limit of the complete-active-space self-consistent field energy, has been applied to the system under consideration here. The present results are compared with the other theoretical and experimental data, and show that the present methods are credible and accurate.     

Existence of Tensor Glueball ξ(2230) and Its Mass, Spin, and Decay Width

In order to solve the current experimental controversy on the existence of the tensor glueball ξ(2230), we examine whether the conclusion from Seth's experimental measurement, which rejects existence of ξ(2230), is reliable. We claim that the non-observation of the resonance structure by Seth is not a sound ground for rejecting the existence of ξ(2230) but it may just indicate that ξ(2230) has a broad width. We also study the tensor glueball properties: the mass, spin, and decay width. Our theoretical predictions of the mass and the spin of the ξ(2230) using QCD sum rule are about 2.23 GeV and J=2, respectively. Our theoretical results also evidently show that the ξ(2230) must have a total decay width of about 100 MeV, which is much broader than the reported 20 MeV but a small partial decay width of 2 MeV into pp decay channel.     

Cohesive properties of (Cu,Ni)–(In,Sn) intermetallics: Database,electron-density correlations and interpretation of bonding trends

This paper presents a systematic and comparative study of the composition and volume dependence of the cohesive properties for a large group of Me–X intermetallic phases (IPs) with Me=Cu,Ni and X=In,Sn, which are of interest in relation with the design of lead-free soldering (LFS) alloys. The work relies upon a database with total-energy versus volume information developed by using projected augmented waves (PAW) calculations. In previous papers by the current authors it was shown that these results account satisfactorily for the direct and indirect experimental data available. In the present work, the database is further expanded to investigate the composition dependence of the volume (V₀), and the composition and volume dependence of the bulk modulus (B₀) and cohesive energy (E_coh). On these bases, an analysis is performed of the systematic effects of replacing Cu by Ni in several Me–X phases (Me=Cu,Ni and X=In,Sn) reported as stable and metastable, as well as various hypothetical compounds involved in the thermodynamic modeling of IPs using the Compound-Energy Formalism. Moreover, it is shown that the cohesion-related quantities (B₀/V₀)^½ and (E_coh^½/V₀) can be correlated with a parameter expressing the number of valence electrons per unit volume. These findings are compared in detail with related relations involving the Miedema empirical electron density at the boundary of the Wigner–Seitz cell. In view of the co-variation of the cohesive properties, E_coh is selected as a key property and its composition and structure dependence is examined in terms of a theoretical view of the bonding which involves the hybridization of the d-states of Cu or Ni with the s and p-states of In or Sn, for this class of compounds. In particular, a comparative analysis is performed of the DOS of various representative, iso-structural Me–X compounds. Various effects of relevance to understand the consequences of replacing Cu by Ni in LFS alloys are highlighted and explained microscopically for the first time.     

J/ψ(ψ') production at the Tevatron and LHC at O(α(s)4v4) in nonrelativistic QCD

We present a complete evaluation for J/ψ(ψ') prompt production at the Tevatron and LHC at next-to-leading order in nonrelativistic QCD, including color-singlet, color-octet, and higher charmonia feeddown contributions. The short-distance coefficients of 3P(J)([8]) at next-to-leading order are found to be larger than leading order by more than an order of magnitude but with a minus sign at high transverse momentum p(T). Two new linear combinations of color-octet matrix elements are obtained from the CDF data, and used to predict J/ψ production at the LHC, which agrees with the CMS data. The possibility of (1)S(0)([8]) dominance and the J/ψ polarization puzzle are also discussed.     

Magnetic penetration depths of (BiPb)-2212 and (TlPb)-1212 — Universal correlations revisited

A systematic study of the dependence of the critical temperature on the superconducting carrier density, as measured by ⁺SR, was carried out for a variety of cuprate oxides. We have shown that substitution of Pb for Bi and La for Sr result in well pinned vortex lattices in Bi₂Sr₂CaCu₂O_x, and studied (BiPb)-2212 from the underdoped to the slightly overdoped regime. We also found that Tl-1212 samples, which have optimal maximumT _c=108 K, trace a separate line with parameters comparable to overdoped Tl-2223 at the maximum. These data, together with data on Y-124/247, Tl-2201 and other cuprates result in an larger set of universal correlations between T_c and(0) n _s /m ^* for the high temperature superconductors.     

Graded orthosymplectic geometry and OSp (4;1)-invariant fermionic σ models

A geometry based on the fundamental 4+N-dimensional linear representation of the extended super-de Sitter group OSp(4;N) is considered. For N=1 two OSp(4;1)-invariant fermionic models are discussed.On leave of absence from Institute of Theoretical Physics, University of Wrocaw, Wrocaw, Poland.     

Multi-oriented moiré superstructures of graphene on Ir(111): experimental observations and theoretical models

Six types of moiré superstructures of graphene on Ir(111) with different orientations (labeled as R0, R14, R19, R23, R26 and R30) are investigated by low-energy electron diffraction, scanning tunneling microscopy and first-principles calculations. The moiré superstructure of R0 graphene has remarkable diffraction spots and deeper corrugation than that of the other superstructures. A high-order commensurate (HOC) method is applied to produce a list of all possible graphene moiré superstructures on Ir(111). Several useful structural data including the precise matrices of the moiré patterns are revealed. Density functional theory based first-principles calculations that include van der Waals interactions reveal the differences of the geometric environment and electronic structures of carbon atoms with respect to the underlying Ir(111) lattices for all the observed moiré patterns. The further calculations of electronic properties at the graphene-Ir interfaces show that the electron transfers for all superstructures are small and of the same order of magnitude, which demonstrates a weak interaction between graphene and the Ir(111) substrate, leading to the coexistence of multi-oriented moiré superstructures.     

Decay properties of D and D_s mesons in coulomb plus power potential (CPP_ν)

The decay properties of the D and D s mesons are computed in a nonrelativistic phenomenological quark-antiquark potential of the type V (r) =-4 3 α s r+ Ar ν with different choices of ν.Numerical method to solve the Schrdinger equation has been used to obtain the spectroscopy of qQ mesons.The numerically obtained radial solutions are employed to obtain the decay constant and leptonic decay widths.It has been observed that predictions of the ground state masses and the decay widths are consistent with other model predictions as well as with the known experimental values.