On the uniqueness of the smooth zero mass limit for invariant amplitudes

The behavior of the invariant amplitudes for processes involving massive vector mesons is investigated in the limit as the mass goes to zero. The constraints of gauge invariance impose a definite structure on the amplitudes at k² = 0, and the question of the uniqueness of this structure is examined. It is shown that if the limit is smooth, the consequent relations between the massive and massless helicity amplitudes are unique, provided only that any additional dynamical assumptions are made consistently. Some of the implications of this result are discussed, with particular reference to the unambiguous covariant formulation of vector meson dominance for scattering amplitudes.     

Mass of nonrelativistic meson from leading twist distribution amplitudes

In this paper distribution amplitudes of pseudoscalar and vector nonrelativistic mesons are considered. Using equations of motion for the distribution amplitudes, relations are derived which allow one to calculate the masses of nonrelativistic pseudoscalar and vector meson if the leading twist distribution amplitudes are known. These relations can be also rewritten as relations between the masses of nonrelativistic mesons and infinite series of QCD operators, what can be considered as an exact version of Gremm-Kapustin relation in NRQCD.     

Vector meson electroproduction at next-to-leading order

The process of light neutral vector meson electroproduction is studied in the framework of QCD factorization in which the amplitude factorizes in a convolution of the nonperturbative meson distribution amplitude and generalized parton densities with perturbatively calculable hard-scattering amplitudes. We derive a complete set of hard-scattering amplitudes at next-to-leading order (NLO) for the production of vector mesons, V=ρ⁰, ω, ?.     

Enhanced electroweak penguin amplitude in B-->VV decays

We discuss a novel electromagnetic penguin contribution to the transverse helicity amplitudes in B decays to two vector mesons, which is enhanced by two powers of mB/Lambda relative to the standard penguin amplitudes. This leads to unique polarization signatures in penguin-dominated decay modes such as B-->rhoK* similar to polarization effects in the radiative decay B-->K*gamma and offers new opportunities to probe the magnitude and chirality of flavor-changing neutral current couplings to photons.     

Axiomatic Conformal Field Theory

A new rigourous approach to conformal field theory is presented. The basic objects are families of complex-valued amplitudes, which define a meromorphic conformal field theory (or chiral algebra) and which lead naturally to the definition of topological vector spaces, between which vertex operators act as continuous operators. In fact, in order to develop the theory, M?bius invariance rather than full conformal invariance is required but it is shown that every M?bius theory can be extended to a conformal theory by the construction of a Virasoro field. In this approach, a representation of a conformal field theory is naturally defined in terms of a family of amplitudes with appropriate analytic properties. It is shown that these amplitudes can also be derived from a suitable collection of states in the meromorphic theory. Zhu's algebra then appears naturally as the algebra of conditions which states defining highest weight representations must satisfy. The relationship of the representations of Zhu's algebra to the classification of highest weight representations is explained. Received: 22 October 1998 / Accepted: 16 July 1999     

Experimental research of the interference and phase structure of the power flux from a local source in shallow water

The paper studies the interference structure of low-frequency tonal and wideband signals in shallow water, received by four-component vector-scalar modules. The spatial amplitudes and phase characteristics of the scalar field are analyzed, as well as three components of the vibration velocity vector and the power flux vector. A relationship is established between the zone of interference maxima and minima and the phase gradient in the horizontal and vertical plane, the change in direction of the vertical and horizontal components of the vibration velocity vector, and the change in the depression angle of the power flux vector in the horizontal plane.     

矩形槽光栅的矢量模式理论

本文引进满足均匀矢量Helmholtz方程的矢量波函数作为基矢,对矩形槽光栅的槽内和槽外的光场分别进行矢量平面波展开和矢量模式展开,并由耦合条件导出了求解展开系数的方程组,可进行数值计算.该方法可研究入射场的方向和偏振任意时的衍射效率、偏振特性变化等问题.在p偏振和s偏振的特殊情况下所得到的公式与用标量模式理论得到的结果一致.     

Localized optical modes induced by point and extended defects in ionic crystals

It is shown that the vector character of the relative displacement of atoms in ionic crystals causes a nonexponential (power) law decay of localized optical mode amplitudes at large distances from point or linear defects.     

A relativistic quark model for mesons based on numerical solutions of the Bethe-Salpeter equation

A study is made to determine if the results of the nonrelativistic quark model can be reproduced by a fully relativistic model of deeply bound $\text{spin}\text{-}\text{1}\text{2}$ quarks. It is found that the relativistic model does not reproduce the nonrelativistic results, even when the quarks have nonrelativistic momenta. However, the model is rather successful in accounting for the known properties of mesons.Numerical solutions to the Bethe-Salpeter equation are obtained for pseudoscalar and vector bound states of equal mass quark-antiquark pairs, with either a scalar, pseudoscalar, or neutral vector exchange interaction. The interaction function corresponds to single particle exchange, with the addition of either one or two regulating terms. It is found that the second regulator allows the internal quark momentum to be nonrelativistic, but that the spinor structure of the wave function remains highly relativistic.Only the scalar interaction can account for the observed spectrum of states. The pseudoscalar interaction yields a vector state of lower mass than the pseudoscalar state, and the vector interaction leads to a vector state which lies approximately one quark mass above the pseudoscalar state. The λ quark is taken as slightly heavier than the p and n, and the perturbation treatment of the mass difference leads to a quadratic mass formula.The decay amplitudes for π, K → μν are calculated, and it is found, independent of parameters, that $\text{?}{}_{\mathrm{\pi }}\text{≈ ?}{}_{\mathrm{K}}$ for either a scalar or vector interaction, in agreement with experiment and in contrast with the nonrelativistic model. The amplitudes for ?^o, ω, φ → e⁺e^?, μ⁺μ^? are also calculated, but in this case the ratios (again parameter independent) are in minor discrepancy with experiment.The question of the additivity of quark amplitudes is examined by calculating (with significant restrictions) the magnetic moments of the vector mesons and the amplitudes for magnetic transitions such as ω → π^oγ. The magnetic moments of the vector mesons have the same (trivial) ratios to each other as in the nonrelativistic model, but they are strongly enhanced over the sum of the quark magnetic moments. The amplitude for magnetic transitions, however, is related to the quark magnetic moments in approximately the same ratio as in the nonrelativistic model.The model is also used to obtain parameter dependent predictions for the masses and decay amplitudes. These predictions are not experimentally correct, but are generally well within an order of magnitude for a wide range of the parameters.The most significant defect discovered of the model is the presence of ghost states (the daughters of the vector mesons, with J^PC = 0^+?) with masses of about 2 BeV.     

Reciprocal space-time and momentum-space singularities in the narrow resonance approximation

A general scheme is proposed which makes explicit the relationship between the singularities of off-shell amplitudes in position-space and momentum-space in the narrow resonnace approximation. In some ways this may be viewed as a duality scheme for amplitudes involving external quarks, in which narrow resonances in certain channels build the Fourier transform of power singularities in x² (x^μ being a position vector). This scheme is made precise by dual string off-shell amplitudes. As well as highlighting possible connections between the general dual framework and the structure of confined field theories we are able to pinpoint certain grave shortcomings of present dual models.     

Polarization Phenomena for Vector-Meson Production Induced by Neutron-Proton Collisions in Collinear Kinematics

 Polarization phenomena for vector meson production in neutron-proton collisions, , with , are studied for collinear kinematics when the vector mesons are produced at angles or 180° with respect to the momentum of the incoming beam. It is shown that the spin structure of the matrix elements can be parametrized in terms of five independent complex scalar amplitudes whose symmetry properties follow from the isotopic invariance of the strong interaction and from which specific polarization properties can be deduced. The polarization structure functions, calculated in terms of these five independent scalar amplitudes, allow to analyze one and two spin polarization observables in a model independent way. Received July 3, 1998; accepted for publication January 30, 1999     

矩孔光栅的矢量模式理论

本文引入满足均匀矢量亥姆霍兹（Ｈｅｌｍｈｏｌｔｚ）方程的矢量波函数作为基矢，对矩孔光栅的孔内外光场分别进行矢量模式展开和矢量平面波展开，并由耦合条件导出了求解展开系数的方程组，从方程组中求解出相应的振幅系数，可研究光栅的衍射场分布，该方法可研究入入射扬方向和偏振任意时的衍射效率和偏振特性等问题。     

Corrections to VMD in the photoproduction of vector mesons I: Mass dependence of amplitudes

We study the dependence of the vector meson scattering amplitudes on the external masses, assuming that the most important effects arise from the coupling of the vector mesons to low mass intermediate states which mediate the scattering. The consequence is that the amplitudes for ?⁰ and ø photoproduction are modified by approximately + 10% and ?15% respectively. This result is equivalent to naively using the coupling constants from the e⁺e^- decay widths and ignoring the mass variation effects. The analysis also calls attention to residual uncertainties at the several percent level.     

Symmetric and antisymmetric vector solitons for the fractional quadric-cubic coupled nonlinear Schrödinger equation

The fractional quadric-cubic coupled nonlinear Schrödinger equation is concerned, and vector symmetric and antisymmetric soliton solutions are obtained by the square operator method. The relationship between the Lévy index and the amplitudes of vector symmetric and antisymmetric solitons is investigated. Two components of vector symmetric and antisymmetric solitons show a positive and negative trend with the Lévy index, respectively. The stability intervals of these solitons and the propagation constants corresponding to the maximum and minimum instability growth rates are studied. Results indicate that vector symmetric solitons are more stable and have better interference resistance than vector antisymmetric solitons.     

On W±, Z0, γ self-interactions: High energy behaviour and tree unitarity bounds

We analyze the high-energy behaviour of vector boson scattering amplitudes within the framework of a recently suggested lagrangian model based on global weak isospin symmetry broken by electromagnetism. Requiring vanishing of the most strongly (as s²) rising contribution to vector boson scattering amplitudes leads to vector boson self-interactions dependent on a single parameter, for which the anomalous W^± magnetic moment, κ, can be chosen. Tree unitarity is violated at about 2 TeV for arbitrary κ as in the SU(2)_L × U(1)_Y theory for m_H → ∞. The model is well suited for significant tests of the vector boson sector of the SU(2)_L × U(1)_Y electroweak theory in processes such as e⁺e⁻ → W⁺W⁻.     

光子扫描隧道显微镜的角谱传递函数

用傅里叶角谱衍理论推导了光子扫描隧道显笛镜的标量和矢量角谱传递函数。表明,光子扫描隧道显微镜的角谱传递鲜明地分成两个区,即远场区和近场区。随首探针榈间距增大,近场区内的角谱其振幅迅速衰减,频率越高衰减越快,而相位保持不变;相反远场区内的角谱内的角谱其振幅保持不变,而相位非均匀线性均匀线性增加,频率越低增加越快。光子扫描隧道显微镜对近场角谱的采集能力是其皮瑞利衍射极限的关键。坦 步根据角谱传递函数计     

Indefinite charge for the classical spinor field

We define a conserved Lorentz vector for a two-component spinor field that obeys the Klein-Gordon equation and interpret it as a charge-current density. The corresponding total charge can take negative as well as positive values, which is not the case for the usual charge of the Dirac field. We consequently can define probability amplitudes for a relativistic quantum mechanics, and we solve the inhomogeneous equation by means of the causal Green function. This vector is not invariant under gauge transformations of the spinor field, and we cannot generalize the equation by the gauge invariant substitution to obtain the interaction with an electromagnetic field. In the limit of a massless field that obeys the Weyl equation, the charge vanishes.     

Chiral symmetry and diffractive neutral pion photo- and electroproduction

We show that diffractive production of a single neutral pion in photon-induced reactions at high energy is dynamically suppressed due to the approximate chiral symmetry of QCD. These reactions have been proposed as a test of the odderon-exchange mechanism. We show that the odderon contribution to the amplitude for such reactions vanishes exactly in the chiral limit. This result is obtained in a nonperturbative framework and by using PCAC relations between the amplitudes for neutral pion and axial vector current production.     

对称型闪耀光栅的矢量模态理论

本文将满足均匀矢量亥姆霍兹方程的标准矢量波函数作为基矢对对称型闪耀光栅槽内、外的电磁场分别进行矢量模式和矢量平面波展开。然后通过在槽内外分界面上的场耦合条件得到一组振幅系数方程组。从方程组中求解出相应的振幅系数,就可研究光栅的衍射场分布。该方法适用于对称型闪耀光栅对任意入射方向、任意偏振态入射场衍射问题的研究。在K_2=0入射情况下,其振幅方程组与已发表的文献[6]相同。