Complex Regge poles and high energy scattering data

For the high energy data on σ_tot^pp the proton-proton total cross section, and on ?, the ratio of real to imaginary part of the forward elastic amplitude, including the recent ISR results, an excellent fit is obtained with P, P', ω Regge poles plus a pair of complex conjugate Regge poles. The complex poles describe the possible oscillatory behavior of the quantities σ_tot^pp and ?. The physical meaning of these complex poles and extrapolation to future measurements of the above quantities are discussed.     

Dependence on k2 of fixed pole residues in pion electroproduction

It is shown that different mechanisms leading to fixed poles in electroproduction of pions lead to a specific difference of the k²-dependence of the residues of these poles, k being the momentum transfer of the electrons.     

Duality,scaling and fixed poles in virtual compton scattering

J-plane fixed poles are considered in the lepton-hadron scattering amplitudes. A relation between the scale-invariant behaviour of the virtual Compton scattering structure W₂ and the J = 1 pole is established using the wrong signature FESR. A dual mechanism for the generation of fixed poles, leading to a number of interesting implications for a singular behaviour of the pole residue in the variable q² (photon mass square), is indicated.     

1N expansion and renormalization in quantum gravity

Gravity coupled to N massless fermions is expanded in powers of $\text{1}\text{N}$, keeping κ²N fixed. The resulting lowest order graviton propagator has (k⁴log k²)^?1 asymptotic behavior, and no tachyon or unphysical real bound state poles. There are, however, complex conjugate poles on the physical sheet. This leads to a unitary, and renormalizable, though “non-analytical” S-matrix.     

Regge poles in multiparticle scattering amplitudes

A study is made of the high-energy limits of multi-particle scattering amplitudes in a φ³ theory. A limited set of chekerboard diagrams dominate the asymptotic behavior .The diagrams sum to produce Regge poles. If N is the number of particles bound together, the trajectory functions of the leading Regge poles are given by α(N)=? (2N ? 3) +g²8π²m². Comparison is made with the generalized multiperipheral model of Auerbach, Aviv, Sugar and Blankenbecler in which the corresponding trajectories have the form α(N)=a?bN+cN².     

A critical study of finite energy sum rule difficulties in pion photoproduction

The difficulties that have emerged in recent phenomenological applications of pion photoproduction FESRs are surveyed and analysed. The main cause of failure, it is concluded, is the systematic lack of suitable cancellations among low-lying resonance poles, which are necessary to ensure the correct FESR reproduction of high-energy zeros. In order for such cancellations to hold, definite conspiracies among the relevant resonance poles should exist. Conspiracies of this type are indeed found to be an essential ingredient in the Veneziano model to have FESRs satisfied, and a number of instances of them are shown to actually occur in π^?p → π⁰n. The observed low-lying pole conspiracy default in pion photoproduction is traced back to spin complications which are higher in this process than in the FESR successful case of π^?p → π⁰n. Moreover, in general the interplay of FESRs and spin structure is shown to be far from trivial, and governed by rules (supposing that they exist) yet to be established.     

What can we learn about the Regge plane from pp cross sections?

We have analysed pp total and different cross sections from s = 10 (GeV)² upwards in terms of singularities in the Regge plane. The data can be fitted by poles alone but a considerably more continuous discontinuity structure is possible. An interpretation of the pole residues in terms of expected Regge poles runs into difficulties at some values of t.     

Analytic continuation of scattering data to the region of negative energies for systems that have one and two bound states

An exactly solvable potential model is used to study the possibility of deducing information about the features of bound states for the system under consideration (binding energies and asymptotic normalization coefficients) on the basis of data on continuum states. The present analysis is based on an analytic approximation and on the subsequent continuation of a partial-wave scattering function from the region of positive energies to the region of negative energies. Cases where the system has one or two bound states are studied. The α+d and α+¹²C systems are taken as physical examples. In the case of one bound state, the scattering function is a smooth function of energy, and the procedure of its analytic continuation for different polynomial approximations leads to close results, which are nearly coincident with exact values. In the case of two bound states, the scattering function has two poles—one in the region of positive energies and the other in the region of negative energies between the energies corresponding to the two bound states in question. Padéapproximants are used to reproduce these poles. The inclusion of these poles proves to be necessary for correctly describing the properties of the bound states.     

A quantum cascade laser-based optical feedback cavity-enhanced absorption spectrometer for the simultaneous measurement of CH4 and N2O in air

Optical feedback cavity-enhanced absorption spectroscopy (OF CEAS) has been demonstrated with a thermoelectrically cooled continuous wave distributed feedback quantum cascade laser (QCL) operating at wavelengths around 7.84 μm. The QCL is coupled to an optical cavity which creates an absorption pathlength greater than 1000 m. The experimental design allows optical feedback of infra-red light, resonant within the cavity, to the QCL, which initiates self-locking at each TEM₀₀ cavity mode frequency excited. The QCL linewidth is narrowed to below the mode linewidth, greatly increasing the efficiency of injection of light into the cavity. At the frequency of each longitudinal cavity mode, the absorption coefficient of an intracavity sample is obtained from the transmission at the mode maximum, measured with a thermoelectrically cooled detector: spectral line profiles of CH₄ and N₂O in ambient air were recorded simultaneously and with a resolution of 0.01386 cm^?1. A minimum detectable absorption coefficient of 5.5×10^?8 cm^?1 was demonstrated after an averaging time of 1 s for this completely thermoelectrically cooled system. The bandwidth-normalised limit for a single cavity mode is 5.6×10^?9 cm^?1?Hz^?1/2 (1σ).     

Stochastic evolution of Schwarzschild black hole in a radiation heat bath

The mass of a Schwarzschild black hole in equilibrium with black-body radiation is shown to undergo a random drift with a diffusion coefficient D ～ M^-3. This follows from the master equation for the radiation in a stochastically bistable system of a black hole in an isolating cavity.     

Derivation and implications of rigorous absolute bounds for ππ partial waves up to 1 GeV

Generalized dispersion relations and axiomatic results are used to derive absolute upper bounds for the ππ partial waves in a complex energy domain containing the physical region up to 1 GeV. As applications, a new lower bound for the π⁰π⁰ S-wave scattering length is given and some ambiguities in the connection between resonances and second sheet poles are removed.     

S-Wave Shape Resonances in the Ps− System

We have investigated the S-wave shape resonance states of the positronium negative ion (Ps^?) system. The resonance poles are traced from H^? system to Ps^? by systematically varying the mass of the positively charged particle from infinitely heavy to one unit of the electron mass. The shape resonances that associated with and lying above the Ps(N = 2, 3, 4 and 5) thresholds are located by employing the complex-coordinate rotation method with highly correlated Hylleraas-type wave functions. It has been shown that the Ps^?(N = 3) shape resonance lies at an energy which is higher than the Ps(N = 4) thresholds and even the Ps^?(N = 4) shape resonance. An explanation was given to shed light on such phenomena.     

Mode splitting of a cavity with a high-density birefringence rubidium vapor in the superstrong coupling regime

The mode splitting in a system with Doppler-broadened high-density two-level atoms in the presence of magnetic field inside a relatively long optical cavity is studied in the superstrong coupling regime(atoms-cavity coupling strength g√N is near or larger than the cavity free-spectral range?FSR).The effect of a magnetic field applied along the quantization axis is used to break the polarization degeneracy of the cavity and thereby introduce birefringence(or Faraday rotation)into the medium.The cavity modes are further split in the presence of the magnetic field compared with the normal case of the multi-normal-mode splitting of the two-level system near the D2 line of87Rb.The dependence of the mode splitting on the magnetic field and the temperature is studied.The theoretical analysis according to the linear dispersion theory can provide a good explanation.     

Constructal design of T-shaped cavity for several convective fluxes imposed at the cavity surfaces

The purpose here is to investigate, by means of the constructal principle, the influence of the convective heat transfer flux at the cavity surfaces over the optimal geometry of a T-shaped cavity that intrudes into a solid conducting wall. The cavity is cooled by a steady stream of convection while the solid generates heat uniformly and it is insulated on the external perimeter. The convective heat flux is imposed as a boundary condition of the cavity surfaces and the geometric optimization is achieved for several values of parameter a = (2hA^1/2/k)^1/2. The structure of the T-shaped cavity has four degrees of freedom: L₀/L₁ (ratio between the lengths of the stem and bifurcated branches), H₁/L₁ (ratio between the thickness and length of the bifurcated branches), H₀/L₀ (ratio between the thickness and length of the stem), and H/L (ratio between the height and length of the conducting solid wall) and one restriction, the ratio between the cavity volume and solid volume (φ). The purpose of the numerical investigation is to minimize the maximal dimensionless excess of temperature between the solid and the cavity. The simulations were performed for fixed values of H/L = 1.0 and φ = 0.1. Even for the first and second levels of optimization, (L₁/L₀) _○○ and (H₀/L₀)_○, the results revealed that there is no universal shape that optimizes the cavity geometry for every imposed value of a. The T-shaped cavity geometry adapts to the variation of the convective heat flux imposed at the cavity surfaces, i.e., the system flows and morphs with the imposed conditions so that its currents flow more and more easily. The three times optimal shape for lower ratios of a is achieved when the cavity has a higher penetration into the solid domain and for a thinner stem. As the magnitude of a increases, the bifurcated branch displaces toward the center of the solid domain and the number of highest temperature points also increases, i.e., the distribution of temperature field is improved according to the constructal principle of optimal distribution of imperfections.     

Two-body hypercharge-exchange reactions in K−p and π+p interactions at 10 and 16 GeV/c

Cross-section values or upper limits are presented for twenty-five two-body hypercharge-exchange reactions in K^?p and π⁺p interactions at 10 and 16 GeV/c. The 16 GeV/c results are compared with some predictions of line-reversal plus exchange-degenerate Regge poles, of SU(3) and of the additive quark model. Agreement is found in all cases.     

Phenomenological characteristics of absorption in charge- and hypercharge-exchange reactions

We try to explain in a unique framework charge- and hypercharge-exchange reactions above 3 GeV/c. Our approach is based on exchange degenerate and SU(3) symmetric Regge poles to which absorption corrections are applied.In the absence of a firm theoretical basis for these corrections we adopt the approach of fixing the Regge poles through theoretical and phenomenological considerations; we then determine what kind of absorption we should apply. At intermediate energy (around 5 GeV/c our results indicate complete absorption of the s-wave amplitude. Of the two terms 1 and e^?iπα of the Reggesignature factor, the latter should be more strongly absorbed. This effect may explain especially the breaking of line-reversal symmetry for hypercharge-exchange reactions, π^?p→π⁰n polarization data, and the difference of peripherality of ??ω and A₂?f₀ contributions.In addition, K-exchange in $\text{p}\text{p}\text{→}\text{Λ}\text{Λ}$ has been studied.     

Finite size effects for the Ising model on random graphs with varying dilution

We investigate the finite size corrections to the equilibrium magnetization of an Ising model on a random graph with N nodes and N^γ edges, with 1<γ≤2. By conveniently rescaling the coupling constant, the free energy is made extensive. As expected, the system displays a phase transition of the mean-field type for all the considered values of γ at the transition temperature of the fully connected Curie-Weiss model. Finite size corrections are investigated for different values of the parameter γ, using two different approaches: a replica based finite N expansion, and a cavity method. Numerical simulations are compared with theoretical predictions. The cavity based analysis is shown to agree better with numerics.     

Movement of gas-filled cavities in alkalihalide crystals produced by external force fields

The migration of gas-filled cavities in KBr, NaCl, LiF single-crystals is investigated experimentally in an electric field and a temperature gradient.It is shown, that migration in an electric field is strongly dependent on the surface purity, due to its influence on matter transport along cavity surface. It is found that the velocity of cavity (v), having a ‘dirty’ surface follows a V～1/R dependence. (R—cavity size). In case of a ‘pure’ cavity surface. V is independent of R. Different types of V-vs-R dependence result in intermediate regions.Migration in a temperature gradient is also sensitive to surface purity. When the state of surface purity is determined, an appropriate critical size (R^*) exists such that if R is smaller than R^*, V～R and if R is larger than R^*, V is independent of R.Some constants of investigated process are determined from obtained experimental data.