Factorization method in the model of unstable particles with a smeared mass

The method of factorization, based on the model of unstable particles with a smeared mass, is applied to the processes with an unstable particle in the intermediate state. It was shown, that in the framework of the method suggested, the decay rate and cross section can be represented in the universal factorized form for an arbitrary set of particles. An exact factorization is caused by the specific structure of unstable particles propagators. We performed the phenomenological analysis of the factorization effect. The text was submitted by the authors in English.     

One-loop leading logarithms in electroweak radiative corrections

We discuss the evaluation of the collinear single-logarithmic contributions to virtual electroweak corrections at high energies. More precisely, we prove the factorization of the mass singularities originating from loop diagrams involving collinear virtual gauge bosons coupled to external legs. We discuss, in particular, processes involving external longitudinal gauge bosons, which are treated using the Goldstone-boson equivalence theorem. The proof of factorization is performed within the 't Hooft–Feynman gauge at one-loop order and applies to arbitrary electroweak processes that are not mass-suppressed at high energies. As basic ingredients we use Ward identities for Green functions with arbitrary external particles involving a gauge boson collinear to one of these. The Ward identities are derived from the BRS invariance of the spontaneously broken electroweak gauge theory. Received: 4 May 2001 / Published online: 6 July 2001     

Solutions of the factorization equations from Toda field theory

We apply the quantum inverse scattering method to a discretization of the generalized Toda field theory. In this way we get a family of solutions of the factorization equations. These solutions provide (i) a solvable many particle system with different types of particles interacting via non-relativistic complex potentials; (ii) a presumably solvable generalization of the six-vertex model in a planar lattice.     

Surface Emission of Quark Gluon Plasma at RHIC and LHC

Within the framework of a factorization model, we study the behaviour of nuclear modification factor in Au Au collisions at RHIC and Pb-Pb collisions at LHC. We find that the nuclear modification factor is inversely proportional to the radius of the quark-gluon plasma and is dominated by the surface emission of hard jets. We predict the nuclear modification factor R^LHC AA - 0.15 in central Pb-Pb collisions at LHC. The study shows that the factorization model can be used to describe the centrality dependence of nuclear modification factor of the high transverse momentum particles produced in heavy ion collisions at both RHIC and LHC.     

Factorization and transverse momentum for two-hadron production in inclusive e + e − annihilation

We study the factorization of processes involving two fragmentation functions in the case of very small transverse momenta. We consider two-hadron production in inclusive e ⁺ e ⁻ annihilation and demonstrate a new simple and illustrative method of factorization for such processes, including leading order α _s corrections. The text was submitted by the authors in English.     

QCD resummation for single spin asymmetries

We study the transverse momentum dependent factorization for single spin asymmetries in Drell-Yan and semi-inclusive deep inelastic scattering processes at one-loop order. The next-to-leading order hard factors are calculated in the Ji-Ma-Yuan factorization scheme. We further derive the QCD resummation formalisms for these observables following the Collins-Soper-Sterman method. The results are expressed in terms of the collinear correlation functions from initial and/or final state hadrons coupled with the Sudakov form factor containing all order soft-gluon resummation effects. The scheme-independent coefficients are calculated up to one-loop order.     

Total photoproduction cross section at very high energy

In this paper we apply to the photoproduction total cross section a model we have proposed for purely hadronic processes and which is based on QCD mini-jets and soft gluon re-summation. We compare the predictions of our model with the HERA data as well as with other models. For cosmic rays, our model predicts substantially higher cross sections at TeV energies than models based on factorization, but lower than models based on mini-jets alone, without soft gluons. We discuss the origin of this difference.     

On transverse-momentum dependent light-cone wave functions of light mesons

Transverse-momentum dependent (TMD) light-cone wave functions of a light meson are important ingredients in the TMD QCD factorization of exclusive processes. This factorization allows one conveniently resume Sudakov logarithms appearing in collinear factorization. The TMD light-cone wave functions are not simply related to the standard light-cone wave functions in collinear factorization by integrating them over the transverse momentum. We explore relations between TMD light-cone wave functions and those in the collinear factorization. Two factorized relations can be found. One is helpful for constructing models for TMD light-cone wave functions, and the other can be used for resummation. These relations will be useful to establish a link between two types of factorization.     

CP violation in correlated production and decay of unstable particles

We study resonant CP-violating Einstein-Podolsky-Rosen correlations that may take place in the production and decay of unstable scalar particles at high-energy colliders. We show that as a consequence of unitarity and CPT invariance of the S-matrix, in 2→2 scatterings mediated by mixed scalar particles, at least three linearly independent decay matrices associated with the unstable scalar states are needed to obtain non-zero CP-odd observables that are also odd under C-conjugation. Instead, for the correlated production and decay of two unstable particle systems in 2→4 processes, we find that only two independent decay matrices are sufficient to induce a net non-vanishing CP-violating phenomenon. As an application of this theorem, we present numerical estimates of CP asymmetries for the correlated production and decay of supersymmetric scalar top-anti-top pairs at the LHC, and demonstrate that these could reach values of order one. As a byproduct of our analysis, we develop a novel spinorial trace technique, which enables us to efficiently evaluate lengthy expressions of squared amplitudes describing the resonant scalar transitions.     

Real-time instantons and suppression of collision-induced tunneling

We consider tunneling processes in QFT induced by collisions of elementary particles. We propose a semiclassical method for estimating the probability of these processes in the limit of very high collision energy. As an illustration, we evaluate the maximum probability of induced tunneling between different vacua in a (1 + 1)-dimensional scalar model with boundary interaction.     

Thermonuclear Instabilities and Fueling in a Tokamak Reactor

The problem of fueling is of primary importance in the conceptual design of a fusion reactor. We consider a possible mechanism of supplying fresh fuel from a cold-plasma layer at the surface of the plasma. The existence of an energetic component of ions, viz, the alpha particles, may excite unstable collective oscillations of the plasma (called the thermonuclear instabilities). Such instabilities could give rise to microscopic processes which, in principle, would allow influx of fresh fuel while helping efflux of reaction products. A three-regime model is used to understand the nature of such fueling mechanisms and the possibility of using a cold-plasma layer as a surface fueling source.     

Recognition and classification of nonlinear chaotic signals

We propose a method of identifying and classifying signals generated by nonlinear, chaotic processes even when there are other signals and noise present. The method compares probability densities constructed from signals with a library of known densities. We note that there are many different invariant densities that can be constructed and that the characteristic functional of these densities factorizes into a product of characteristic functionals. Each member of the product is the characteristic functional of one of the signals present. This factorization provides a means of identifying the presence of a particular signal. Simple examples are given to demonstrate the method.     

Single Transverse Spin Asymmetries at Parton Level

Two factorization approaches have been proposed for single transverse spin asymmetries. One is the cofiinear factorization, the other is the transverse-momentum-dependent factorization. They have been previously derived in a formal way by using diagram expansion at hadron level. If the two factorizations hold or can be proven, they should also hold when we replace hadrons with patton states. We examine these two factorizations at patton level with massless partons. It is nontrivial to generate these asymmetries at parton level with massless patrons because the asymmetries require helicity-flip and nonzero absorptive parts in scattering amplitudes. By constructing suitable patton states with massless partons we derive the two factorizations for the asymmetry in Drell-Yan processes. It is found from our results that the collinear factorization derived at parton level is not the same as that derived at hadron level. Our results with massless partons confirm those derived with single massive parton state in our previous works.     

Relativistic resonances as non-orthogonal states in Hilbert space

We analyze the energy-momentum properties of relativistic short-lived particles with the result that they are characterized by two 4-vectors: in addition to the familiar energy-momentum vector (timelike) there is an energy-momentum `spread vector' (spacelike). The wave functions in space and time for unstable particles are constructed. For the relativistic properties of unstable states we refer to Wigner's method of Poincaré group representations that are induced by representations of the space-time translation and rotation groups. If stable particles, unstable particles and resonances are treated as elementary objects that are not fundamentally different one has to take into account that they will not generally be orthogonal to each other in their state space. The scalar product between a stable and an unstable state with otherwise identical properties is calculated in a particular Lorentz frame. The spin of an unstable particle is not infinitely sharp but has a `spin spread' giving rise to `spin neighbors'. This opens the possibility of a non-zero scalar product between states with unequal spin. - A first practical application of non-orthogonal states is seen in diffraction dissociation reactions whose large cross-sections are attributed to interference of states that are `partially identical'. Received: 28 June 2002 / Revised version: 13 November 2002 / Published online: 14 March 2003 RID="a" ID="a" e-mail: walter.blum@cern.ch RID="b" ID="b" e-mail: hns@mppmu.mpg.de     

The Virasoro vertex algebra and factorization algebras on Riemann surfaces

This paper focuses on the connection of holomorphic two-dimensional factorization algebras and vertex algebras which has been made precise in the forthcoming book of Costello–Gwilliam. We provide a construction of the Virasoro vertex algebra starting from a local Lie algebra on the complex plane. Moreover, we discuss an extension of this factorization algebra to a factorization algebra on the category of Riemann surfaces. The factorization homology of this factorization algebra is computed as the correlation functions. We provide an example of how the Virasoro factorization algebra implements conformal symmetry of the beta–gamma system using the method of effective BV quantization.     

Fading out of J/ψ color transparency in high energy heavy ion peripheral collisions

We provide predictions for the J/ψ coherent production in the peripheral heavy ion collisions at LHC and RHIC using the leading twist model of nuclear shadowing based on the QCD factorization theorem for diffraction and the HERA hard diffraction data. We demonstrate that for LHC kinematics this model leads to a bump-shape distribution in rapidity which is suppressed overall as compared to the expectations of the color transparency regime by a factor 6. This is a significantly larger suppression than that expected within the impact parameter eikonal model. Thus we show that the interaction of spatially small wave package for which the total cross section of interaction with nucleons is small is still strongly shadowed by nuclear medium in high energy processes.     

Investigation of the unstable flow phenomenon in a pump turbine

Instability of pump turbine with S-shaped curve is characterized by large fluctuations of rotational speed during the transient processes.For investigating this phenomenon,a numerical model based on the dynamic sliding mesh method(DSSM)is presented and used to numerically solve the 3D transient flow which is characterized by the variable rotation speed of runner.The method is validated by comparison with measured data for a load rejection process in a prototype pump turbine.The results show that the calculated rotation speed agrees well with the experimental data.Based on the validated model,simulations were performed for the runaway process using an artificially assumed operating condition under which the unstable rotation speed is expected to appear.The results confirm that the instability of runner rotational speed can be effectively captured with the proposed method.Presented results include the time history profiles of unit flow rate and unit rotating speed.The internal flow characteristics in a typical unstable period are discussed in detail and the mechanism of the unstable hydraulic phenomenon is explained.Overall,the results suggest that the method presented here can be a viable alternative to predict the dynamic characteristics of pump turbines during transient processes.     

Particle spectrum and geometrical symmetry

The spectrum of unstable particles is studied on a model meeting the requirement of geometrical symmetry expressed by the restricted Lorentz groupL _r, which is represented by an unstable model particle described by the invariant tensor or spintensor of the groupL _r satisfying the Klein-Gordon equation. The problem of the spectrum of model particles is formulated and treated as a certain eigenvalue problem invariant with regard toL _r. The calculated spectrum of the reduced levels mass/width of the model particles is spin independent, agrees with the observed spectrum of resonances and shows that the model employed represents certain laws manifesting themselves in the observed spectrum of unstable particles.In conclusion the author would like to thank Dr. J. Fischer for fruitful discussions on this work and Dr. K. Kunc for performing some numerical computations on the computer.