Rigorous bounds for the complex dielectric constant of a two-component composite

Rigorous bounds are systematically derived for the bulk effective dielectric constant of a two-phase composite material ε_e under various assumptions about the available information. The bounds are drawn for some special cases in the complex ε_e-plane. The question of optimality of the bounds and their connection to solvable microgeometries is discussed. It is shown how linear programming theory can be used to aid in the derivation of these bounds.     

On the bounds for the Kℓ3 form factors

A complete solution is given to a mathematical problem encountered in the search for bounds on the K_?3 scalar form factor. Besides standard analyticity assumptions, the information used is, firstly, the Mathur-Okubo inequality derived from a chiral model, secondly the experimental low-energy $\text{I =}\text{1}\text{2}$, S-wave, Kπ phase shift. Upper and lower bounds are computed, compared with previous bounds, and found to be in agreement with recent experimental data.     

Bounds for Entanglement via an Extension of Strong Subadditivity of Entropy

Let ?? ₁₂ be a bipartite density matrix. We prove lower bounds for the entanglement of formation E_f(?? ₁₂) and the squashed entanglement E_sq(?? ₁₂) in terms of the conditional entropy S ₁₂ ? S ₁ and prove that these bounds are sharp by constructing a new class of states whose entanglements can be computed, and for which the bounds are saturated.     

Semi-phenomenological bounds for the pion-pion coupling constant

Upper and lower bounds on the Chew-Mandelstam ππ coupling constant λ are derived as functions of the D-wave scattering length a₂. The only information used is the axiomatic analyticity domain of the ππ scattering amplitude, and the crossing and unitarity properties. For a₂ = 7 × 10^?4, one obtains ?0.164<λ<0.162. This is compared with previous bounds.     

Z′ mass limits,masses and coupling of higgs bosons,and Z′ decays in an E6 superstring based model

We demonstrate that current phenomenological constraints on Z-Z′ mixing for an E₆ grand unified group with low energy gauge group SU(2)_L×U(1)_Y×U(1)_Y, allow only a narrow range of Higgs vacuum expectation values consistent with possibilities favored by renormalization group expectations. Modest improvements in bounds on this mixing will lead to substantial bounds on the Z′ mass if alternative renormalization group solutions are not found. We then explore the constraints upon relations between Higgs masses in this model. In addition we explore the couplings of these Higgs to the gauge particles of the theory and emphasize the associated implications for Higgs detection in decays of the Z′.     

Moments of structure functions and experimental tests of QCD

Simple assumptions which have little or no connection to quantum chromodynamics, lead to upper and lower bounds for the slope of the graph for log M_N′ versus log M_N, where M_N is the Nth moment of the deep inelastic structure function xF₃(x, q²). The published results of the CDHS and BEBC collaborations cover the entire range allowed by our bounds and therefore cannot be considered as evidence for the validity of QCD.     

S-matrix and unitarity bounds for three-channel systems,with application to low-energy photoproduction of pions from nucleons

A parametrization of the S-matrix for three-channel systems is given, where we state explicitly the unitarity bounds on the free parameters. The free parameters are directly related to measurable quantities. The results are applied to low-energy photoproduction of pions from nucleons, and lower bounds for the electric dipole amplitudes E₀₊ for π⁰ production are obtained. These lower bounds follow without using the Fermi-Watson final-state theorem.     

Lower bounds to the I = 0, I = 2 ππ s-wave scattering lenghts

Roy's exact partial wave equations allow us to find bounds for any linear combination of the isospin I = 0 and s-wave scattering lengths, with positive coefficients. The bound is a function of the quantity a_D = a₂⁽⁰⁾ + a₂⁽²⁾, where a₂^(I) are the D-wave sacttering lengths. Thus, we can draw on the (a₀⁽⁰⁾, a₀⁽²⁾) plane an allowed domain whose boundary is fairly close to the phenomenological region. For a value of a_D = 1.7×10^?3, we find the following particular bounds: a₀⁽⁰⁾??0.49, a₀⁽²⁾??0.29.     

Non standard weak bosons at HERA collider

We compare the effects of non-standard weak bosons (NSB) expected fromE ₆-superstrings (Z′), strong Higgs (V ₀) and composite (spin 0, 1, 2) models by using the classical inclusive deep-inelastic “ep” scattering at HERA energies. TheX ² associated to polarized and unpolarized cross-sections, as well as the six combinations of asymmetries, allow us to derive significant bounds on the masses of the new bosons of various spins associated to some composite models with exception of the excitedZ ^*. We have also obtained some lower bounds for spin one bosons of different models (Z′,V ₀,Z ^*) which are stronger than the present experimental limits.     

Nelson's symmetry and all that in the Yukawa2 and (φ4)3 field theories

We prove Guerra's theorem, φ bounds and Fröhlich bounds in the Y₂ and φ₃⁴ field theories. Among our technical results of interest is a proof that Z ≠ 0 in φ₃⁴ and that the spatially cutoff vacuum in Y₂ has a charge zero component. The two main inputs are Osterwalder-Schrader positivity in the spatial direction as well as in the time direction, and a finite renormalization of the “usual” partition function and Hamiltonian so that Euclidean and Hamiltonian counterterms match exactly.     

439-1439-1439-1transitions: model-independent bounds on invariant form factors

In this note we report on some model-independent bounds involving the transition form factors for Ω_b → Ω_c and Ω_b → Ω _c ^* transitions and the nonperturbative matrix elements of the Ω_b system. The bounds are derived by using operator product expansion (OPE) methods in heavy quark effective theory.     

Improved rigorous upper bounds for transport due to passive advection described by simple models of bounded systems

The work of J. A. Krommes and R. A. Smith on rigorous upper bounds for the turbulent transport of a passively advected scalar is extended in two directions: (1) For their reference model, improved upper bounds are obtained by utilizing more sophisticated two-time constraints which include the effects of cross-correlations up to fourth order. Numerical solutions of the model stochastic differential equation are also obtained; they show that the new bounds compare quite favorably with the exact results, even at large Reynolds and Kubo numbers. (2) The theory is extended to take account of afinite spatial autocorrelation lengthL _c. As a reasonably generic example, the problem of particle transport due to statistically specified stochastic magnetic fields in a collisionless turbulent plasma is revisited. A bound is obtained which reduces for smallL _c to the quasilinear limit and for largeL _c to the strong turbulence limit, and which provides a reasonable and rigorous interpolation for intermediate values ofL _c.     

Searching for effects of neutrino magnetic moments at reactors and accelerators

The sensitivity of the νe elastic scattering experiments to possible effects of nonzero neutrino magnetic moment (μ) is analyzed and the optimal experimental condition under which such effects are relatively enhanced are found. New, somewhat more restrictive than the previously derived bounds on μ, are obtained on the basis of existing data by the use of selfconsistent statistical analyses: μ_νe < 1.52 × 10^?10e/2m_e and μ_νμ < 1.19 × 10^?9e/2m_e. These bounds are expected to be improved approximately by an order of magnitude in experiments planned to be performed in the near future.     

Constraining the low-energy pion electromagnetic form factor with spacelike data

The pionic contribution to the g-2 of the muon involves a certain integral over the modulus squared of F_π(t), the electromagnetic form factor of the pion. We extend techniques that use cut-plane analyticity properties of F_π(t) in order to account for present day estimates of the pionic contribution and experimental information at a finite number of points in the spacelike region. Using data from several experiments over a large kinematic range for |t|, we find bounds on the expansion coefficients of F_π(t), sub-leading to the charge radius. The value of one of these coefficients in chiral perturbation theory respects these bounds. Furthermore, we present a sensitivity analysis to the inputs. A brief comparison with results in the literature that use observables other than the g-2 and timelike data is presented.     

Neutrino mixing and the mw/mz mass ratio

A comparison of neutral and charged current data according to the standard model provides bounds on neutrino mixing parameters, independently of the number of fermions. The mixing may also affect the determination of sin² θ and m_w/m_z.     

Unitarity and approach to scaling at the SPS collider

We use variable-t ₁ bounds on preliminary SPS Collider data to show that these data saturate the unitarity bounds over a wide range oft. The bounds can be used to normalize different sets of data and to estimate reliably a self-consistent set of values for global quantities such as the total and the elastic cross-sections and the forward elastic slope. The approach to scaling is argued to be non-uniform int.     

Experimental constraints on weak mixing angles in the six quark scheme

Experimental results on charm production by neutrinos and onB meson decays are used to derive bounds on the quark mixing anglesθ ₂ andθ ₃ in the six quark model of Kobayashi and Maskawa.     

Bounds on enhanced turbulent flame speeds for combustion with fractal velocity fields

Rigorous upper bounds are derived for large-scale turbulent flame speeds in a prototypical model problem. This model problem consists of a reaction-diffusion equation with KPP chemistry with random advection consisting of a turbulent unidirectional shear flow. When this velocity field is fractal with a Hurst exponentH with 0<H<1, the almost sure upper bounds suggest that there is an accelerating large-scale turbulent flame front with the enhanced anomalous propagation lawy=C _H t ^1+H for large renormalized times. In contrast, a similar rigorous almost sure upper bound for velocity fields with finite energy yields the turbulent flame propagation law within logarithmic corrections. Furthermore, rigorous theorems are developed here which show that upper bounds for turbulent flame speeds with fractal velocity fields are not self-averaging, i.e., bounds for the ensemble-averaged turbulent flame speed can be extremely pessimistic and misleading when compared with the bounds for every realization.     

Young's modulus of NbSe3

Using the Barmatz vibrating reed technique we have measured the Young's modulus of NbSe₃. An anomaly is observed at T₁ (142 K) but not at T₂ (58 K). Taken together with published specific heat data our results provide upper (lower) bounds for the anisotropy of the transition-temperature-stress-dependence at T₁ (T₂).