Reflective Scattering and Unitarity

Interpretation of unitarity saturation as reflective scattering is discussed. Analogies with optics and Berry phase alongside with the experimental consequences of the proposed interpretation at the LHC energies are considered.Comment: 4 pages, 1 figure, talk given by S. Troshin at Diffraction 2008, September 9-14, La Londe-les-Maures, Franc

Representation of Quantum Mechanical Resonances in the Lax-Phillips Hilbert Space

We discuss the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips $S$-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exactly exponential. The states corresponding to these resonances (eigenfunctions of the generator of the semigroup) lie in the Lax-Phillips Hilbert space, and therefore all physical properties of the resonant states can be computed. We show that the Lax-Phillips $S$-matrix is unitarily related to the $S$-matrix of standard scattering theory by a unitary transformation parametrized by the spectral variable $\sigma$ of the Lax-Phillips theory. Analytic continuation in $\sigma$ has some of the properties of a method developed some time ago for application to dilation analytic potentials. We work out an illustrative example using a Lee-Friedrichs model for the underlying dynamical system.Comment: Plain TeX, 26 pages. Minor revision

Prompt photon hadroproduction in the k_T-factorization approach

We study the production of prompt photons at high energy in the framework of the k_T-factorization approach. The amplitude for production of a single photon associated with quark pair in the fusion of two off-shell gluons is calculated. Theoretical results are compared with the Tevatron data.Comment: 4 pages, 3 figures, to be published in the Proceedings of Workshop "Diffraction 2008", La Londe-les-Maures, France, Sept. 9-14, 200

Global attractor for a nonlinear oscillator coupled to the Klein-Gordon field

The long-time asymptotics is analyzed for all finite energy solutions to a model U(1)-invariant nonlinear Klein-Gordon equation in one dimension, with the nonlinearity concentrated at a single point: each finite energy solution converges as time goes to plus or minus infinity to the set of all ``nonlinear eigenfunctions'' of the form \psi(x)e\sp{-i\omega t}. The global attraction is caused by the nonlinear energy transfer from lower harmonics to the continuous spectrum and subsequent dispersive radiation. We justify this mechanism by the following novel strategy based on inflation of spectrum by the nonlinearity. We show that any omega-limit trajectory has the time-spectrum in the spectral gap [-m,m] and satisfies the original equation. This equation implies the key spectral inclusion for spectrum of the nonlinear term. Then the application of the Titchmarsh Convolution Theorem reduces the spectrum of each omega-limit trajectory to a single harmonic in [-m,m]. The research is inspired by Bohr's postulate on quantum transitions and Schroedinger's identification of the quantum stationary states to the nonlinear eigenfunctions of the coupled U(1)-invariant Maxwell-Schroedinger and Maxwell-Dirac equations.Comment: 29 pages, 1 figur

The GDH Sum Rule and Related Integrals

The spin structure of the nucleon resonance region is analyzed on the basis of our phenomenological model MAID. Predictions are given for the Gerasimov-Drell-Hearn sum rule as well as generalized integrals over spin structure functions. The dependence of these integrals on momentum transfer is studied and rigorous relationships between various definitions of generalized Gerasimov-Drell-Hearn integrals and spin polarizabilities are derived. These results are compared to the predictions of chiral perturbation theory and phenomenological models.Comment: 15 pages LaTeX including 5 figure

Impact of D0-D0bar mixing on the experimental determination of gamma

Several methods have been devised to measure the weak phase gamma using decays of the type B+- --> D K+-, where it is assumed that there is no mixing in the D0-D0bar system. However, when using these methods to uncover new physics, one must entertain the real possibility that the measurements are affected by new physics effects in the D0-D0bar system. We show that even values of x_D and/or y_D around 10^{-2} can have a significant impact in the measurement of sin^2{gamma}. We discuss the errors incurred in neglecting this effect, how the effect can be checked, and how to include it in the analysis.Comment: 18 pages, Latex with epsfig, 8 figure

Information-theoretic significance of the Wigner distribution

A coarse grained Wigner distribution p_{W}(x,u) obeying positivity derives out of information-theoretic considerations. Let p(x,u) be the unknown joint PDF (probability density function) on position- and momentum fluctuations x,u for a pure state particle. Suppose that the phase part Psi(x,z) of its Fourier transform F.T.[p(x,u)]=|Z(x,z)|exp[iPsi(x,z)] is constructed as a hologram. (Such a hologram is often used in heterodyne interferometry.) Consider a particle randomly illuminating this phase hologram. Let its two position coordinates be measured. Require that the measurements contain an extreme amount of Fisher information about true position, through variation of the phase function Psi(x,z). The extremum solution gives an output PDF p(x,u) that is the convolution of the Wigner p_{W}(x,u) with an instrument function defining uncertainty in either position x or momentum u. The convolution arises naturally out of the approach, and is one-dimensional, in comparison with the two-dimensional convolutions usually proposed for coarse graining purposes. The output obeys positivity, as required of a PDF, if the one-dimensional instrument function is sufficiently wide. The result holds for a large class of systems: those whose amplitudes a(x) are the same at their boundaries (Examples: states a(x) with positive parity; with periodic boundary conditions; free particle trapped in a box).Comment: pdf version has 16 pages. No figures. Accepted for publ. in PR

Decay versus survival of a localized state subjected to harmonic forcing: exact results

We investigate the survival probability of a localized 1-d quantum particle subjected to a time dependent potential of the form $rU(x)\sin{\omega t}$ with $U(x)=2\delta (x-a)$ or $U(x)= 2\delta(x-a)-2\delta (x+a)$. The particle is initially in a bound state produced by the binding potential $-2\delta (x)$. We prove that this probability goes to zero as $t\to\infty$ for almost all values of $r$, $\omega$, and $a$. The decay is initially exponential followed by a $t^{-3}$ law if $\omega$ is not close to resonances and $r$ is small; otherwise the exponential disappears and Fermi's golden rule fails. For exceptional sets of parameters $r,\omega$ and $a$ the survival probability never decays to zero, corresponding to the Floquet operator having a bound state. We show similar behavior even in the absence of a binding potential: permitting a free particle to be trapped by harmonically oscillating delta function potential

What can we learn from a measurement of sin(2 beta + gamma)?

The constraints on the value of the CKM phase gamma that may be achieved by prospective measurements of sin(2 beta) and sin(2 beta + gamma) are discussed. Significant constraints require quite small errors, and may depend on assumptions about strong phases. The measurement of sin(2 beta + gamma) combined with other experiments could provide valuable limits on new physics in Bd-Bdbar mixing.Comment: 10 pages, 7 figures, RevTex 4, uses amsmath and graphic

Octet Quark Contents from SU(3) Flavor Symmetry

With the parametrization of parton distribution functions (PDFs) of the proton by Soffer \textit{et al.}, we extend the valence quark contents to other octet baryons by utilizing SU(3) flavor symmetry. We find the method practically useful. Fragmentation functions (FFs) are further obtained through the phenomenological Gribov-Lipatov relation at the $x \to 1$ region. Our results are compared with different models, and these different predictions can be discriminated by upcoming experiments.Comment: 6 pages, 5 figures, final version for journal publicatio