Particle Correlation in Quantum Field Theory

The paper deals with studies of the angular correlation of two mono-energetic particles produced in several fundamental processes in quantum field theory. The angular correlation is defined as the average (expectation value) of the cosine of the angle between the momenta of the two outgoing particles. A positive correlation indicates, in a statistical sense, that the particles tend to travel in the same directions (as in beam formation) while a negative one indicates that they tend to travel in opposing directions. The angular correlations for photons and electrons produced by sources, and in quantum eletrodynamics, to lowest order, γγ produced in e⁺e⁻ collision (annihilation), e⁺e⁻ pair production in γγ collision, and finally e⁺e⁻ pair production by a Nambu string are studied in detail.     

Angular correlation of photons ine + e − collision in QED: Planar processes

The angular correlation for two monochromatic photons produced ine ⁺ e ^– collision has been calculated to lowest order in the fine-structure constant in QED for planar processes. The angular correlation is defined as the average of the cosine of the angle between the directions of momenta of the two photons. This is done by computing, in the process, thee ⁺ e ^–-spin-momentum-averaged,-polarization-averaged conditional probability. In particular, we learn that for energies of the photons above a certain critical value, the angular correlation is strictly positive, for planar processes, indicating that the photons tend to travel in the same direction in a statistical sense for such processes.On sabbatical leave from Royal Military College, Kingston, Ontario, K7K 5LO, Canada.     

Defect structures in nematic liquid crystals around charged particles

We numerically study the orientation deformations in nematic liquid crystals around charged particles. We set up a Ginzburg-Landau theory with inhomogeneous electric field. If the dielectric anisotropy e₁ \varepsilon_{1}^{} is positive, Saturn-ring defects are formed around the particles. For e₁ \varepsilon_{1}^{} < 0 , novel “ansa” defects appear, which are disclination lines with their ends on the particle surface. We find unique defect structures around two charged particles. To lower the free energy, oppositely charged particle pairs tend to be aligned in the parallel direction for e₁ \varepsilon_{1}^{} > 0 and in the perpendicular plane for e₁ \varepsilon_{1}^{} < 0 with respect to the background director. For identically charged pairs the preferred directions for e₁ \varepsilon_{1}^{} > 0 and e₁ \varepsilon_{1}^{} < 0 are exchanged. We also examine competition between the charge-induced anchoring and the short-range anchoring. If the short-range anchoring is sufficiently strong, it can be effective in the vicinity of the surface, while the director orientation is governed by the long-range electrostatic interaction far from the surface.     

Recent experimental studies on 252Cf ternary fission

The rare ternary fission (TF) process was hitherto studied mainly by inclusive measurements of the energies and fractional yields of the light charged particles (LCPs) from fission, or by experiments on the angular and energy correlation between LCPs and fission fragments (FF). The present article briefly describes a series of recent correlation measurements on ²⁵²Cf(sf) TF that include either the registration of neutrons and γ rays with LCPs and FFs, or the coincident registration of two LCPs. The population of excited states in LCPs has been identified, as well as the formation of neutron-unstable nuclei as short-lived intermediated LCPs, the sequential decay of particle-unstable LCP species into charged particle pairs, and “quaternary” fission with the emission of two charged particles right at scission.     

Possible signature of charged Higgs particles in high energy e+e− annihilation

Possible indications of the existence of charged Higgs scalar particles are discussed in an SU(2)×U(1) model. Four-K and six-K final states at high energy e⁺e^? annihilation are suggested for the signature of the existence of the charged scalar particle.     

Photon-photon angular correlation ine +e− collision in QED

The angular correlation of two monochromatic photons produced ine ⁺e^– collision (annihilation), defined as the average of the cosine of the angle of separation between their outgoing momenta, is studied completely in momentum space to lowest order in the fine structure constant in QED. This is done from the expression of thee ⁺e^–-momentum-spin,-polarization-averaged conditional probability density for the angular distributions of the photons, given that the process has occurred. Although the density is in general nonvanishing for less than as well as greater than/2, the angular correlation is found to be strictly negative for all energies, indicating that the photons tend to travel in opposing directions in a statistical sense. The back-to-back motion, however, is very quickly unfavored as we move to higher energies.     

e − e + Production by a Nambu string

We analytically calculate the probability ofe ^– e ⁺ production with a given relative energy from a closed string arising from the Nambu action as a solution of a circularly oscillating string as, perhaps, the simplest generalization of the classic pointlike particle. A numerical analysis of the result is also given.     

Tests of quantum chromodynamics and a direct measurement of the strong coupling constant αs at √s=30 GeV

We report the measurement of the reaction e⁺ + e^? → hadronic jets at a center-of-mass energy √s=30 GeV using the MARK-J detector at PETRA. By measuring the energy and angular distribution of both neutrals and charged particles we were able to isolate unambiguously the three-jet events in a kinematic region where the backgrounds from q$\text{q}$ and phase space contributions and other processes are small. Various comparisons of the data with quantum chromodynamics were made. The relative yield of three-jet events and the shape distribution of the events enable us to determine α_s = 0.23 ± 0.02 (statistical error) with a systematic error of ± 0.04.     

Angular correlation in charmed particle production from e+e− and subsequent decays

In view of forthcoming experiments of greater statistics and accurate particle identification we have calculated the complete angular correlation in reactions of charmed particle (pseudo-scalar, vector, axial-vector) production from e⁺e^? and their subsequenc sequential decays, including possible photonic transitions.     

On the question of supersymmetric particles production in <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> annihilation

Some aspects of supersymmetric particles pair production in e ⁺ e ^?-annihilation in processes \(e^ + + e^ - \to \tilde l^ + + \tilde l^ -\), \(e^ + + e^ - \to \tilde \chi ^ + + \tilde \chi ^ -\) are studied. Aparatus, in which long-lived charged particles deceleraition and accumulation take place, is considered. Binding energy of a negatively charged particle with nucleus is obtained. Probability of β-decay of a nucleus bounded with a long-lived negatively charged particle is considered.     

Structure of final states with a high transverse momentum π0 in proton-proton collisions

We present a study of the final state structure in proton-proton collisions (√s = 53 GeV) where a large transverse momentum π⁰ (p_t > 2 GeV/c) is produced at an angle of 90°. Charged secondaries have been detected and momentum analysed in the split field magnet detector at the CERN Intersecting Storage Rings. The large angular coverage of this detector extends over ±2.5 units of rapidity and ±30° of azimuth with respect to the trigger π⁰, both towards and away from it. In each of these directions, where we observe similar strong correlations, we present charged particle distributions, in rapidity and momentum. In the hemisphere containing the trigger π⁰ we have measured the cross section for inclusive production of large transverse momentum ?^± mesons. In the opposite hemisphere the data exhibit several features predicted by hard scattering quark-parton models: coplanarity and short-range rapidity correlation for the large transverse momentum secondaries as well as a transverse momentum sharing distribution similar to that observed in deep inelastic electro-production and in e⁺e^? collisions.     

Quantum mechanics of relativistic spinless particles

A relativistic one-particle, quantum theory for spin-zero particles is constructed uponL ²(x, ct), resulting in a positive definite spacetime probability density. A generalized Schrödinger equation having a Hermitian HamiltonianH onL ²(x, ct) for an arbitrary four-vector potential is derived. In this formalism the rest mass is an observable and a scalar particle is described by a wave packet that is a superposition of mass states. The requirements of macroscopic causality are shown to be satisfied by the most probable trajectory of a free tardyon and a nontrivial framework for charged and neutral particles is provided. The Klein paradox is resolved and a link to the free particle field operators of quantum field theory is established. A charged particle interacting with a static magnetic field is discussed as an example of the formalism.     

Phase space dependence of the multiplicity distribution in π+ andpp collisions at 250 GeV/c

The charged particle multiplicity distribution has been studied for non-single-diffractive π⁺ p andpp collisions at \(\sqrt s = 22\) GeV, for full phase space as well as for intervals in rapidity, azimuthal angle and transverse momentum. In general, the multiplicity distribution is well described by a negative binomial. From comparison of the distribution for negative or positive particles to that of all charged particles, cascading is favoured as an interpretation over stimulated emission. Interesting consequences follow from a comparison of our results to those at collider energies and toe ⁺ e ^? data at comparable energy. Furthermore, evidence is given that the multiplicity distribution is not exactly of negative binomial type in every (connected or disconnected) phase space region.     

Spin Correlations in e+e? Pair Creation by Two-Photons and Entanglement in QED

Spin correlations of e ⁺ e ⁻ pair productions of two colliding photons are investigated and explicit expressions for their corresponding probabilities are derived and found to be energy (speed) dependent, for initially linearly and circularly polarized photons, different from those obtained by simply combining the spins of the relevant particles, for initially polarized photons. These expressions also depend on the angles of spin of e ⁺ (and/or of e ⁻), for initially linearly polarized photons, but not for circularly polarized photons, as a function of the energy. It is remarkable that these explicit results obtained from quantum field theory show a clear violation of Bell’s inequality of Local Hidden Variables theories at all energies beyond that of the threshold one for particle production, in support of quantum field theory in the relativistic regime. We hope that our explicit expression will lead to experiments, of the type described in the bulk of this paper, which can monitor energy (and speed) in polarization correlation experiments.     

Quantum effects in radiation on short bunches

The radiation caused by particles of one bunch in the collective electromagnetic field of the short oncoming bunch is studied. Quantum effects are calculated for the spectrum of radiated photons. Using this spectrum, the dependence of the relative energy loss δ on a quantum parameter K is discussed. It is shown that the behaviour of δ changes considerably with the increase of that parameter. In the classical regime (K ? 1) the energy loss is proportional to the incoming particle energy, while in the extreme quantum regime (K ? 1) the energy loss becomes a constant. The coherent e⁺e^? pair production for γe colliders as cross-channel to CBS is considered.     

Proton and α sequential emission in the 16O + 58Ni deep inelastic reaction: A semi-classical approach

The 132 MeV ¹⁶O + ⁵⁸Ni reaction has been experimentally investigated by using coincident charged particle techniques. A closed-form theoretical approach, describing in a simple picture the non-equilibrium component and the evaporative one of the angular correlation between light particles and reaction residues emitted in a peripheral heavy-ion collision, is applied — in the hypotesis of a sequential process — to the (C,N,O)-α and (C,N,O)-p differential multiplicities for the ¹⁶O + ⁵⁸Ni at 8.25 MeV/A deep inelastic collision. From this analysis some reaction mechanism information is deduced.     

Precise measuring mass and spin of dark matter particles at ILC via singularities in the single lepton energy spectrum

We consider models, in which stability of Dark Matter particles D is ensured by the conservation of the new quantum number, called D-parity here. Our models contain also charged D-odd particle D ^±. We propose method for precision measuring masses and spin of D-particles via the study of energy distribution of single lepton (e or μ) in the process e ⁺ e ^? → D ⁺ D ^? → DDW ⁺ W ^? with the observable state dijet + μ (or e) + nothing. It is shown that this distribution has kinematically determined singular points (upper edge and kinks or peak). Measuring of their positions allow to determine precisely masses of D and D ^±. After this, even a rough measuring of corresponding cross section allows to determine the spin of D particles.     

Origin of complex fragments from32S+natAg reaction at 37.5 A·MeV

Fragment emission from collisions of³²S with^natAg at 37.5 A·MeV has been studied with the 4π multi-detector AMPHORA. Production of intermediate mass and heavy fragments as well as of light charged particles has been measured. The total charged particle multiplicity and polar angular distributions have been used to select various classes of collisions. Analysis of angular and energy distributions of fragments and light particles in central collisions indicates the formation of a hot source (excitation energy of≈4.4 A·MeV) with an additional contribution from a preequilibrium process at more forward angles. Azimuthal angle correlations of He-Li, Li-Li, B-B, and C-C pairs have been used as a tool to study the origin of complex fragments. Data at backward angles are well described by considering a thermalized emitter with an angular momentum around 70? and a fragment emission time of the order of 200 fm/c. A microscopic approach of BNV type confirms these emission times and angular momenta indicating the persistence of an incomplete fusion process responsible for the emission of complex fragments at backward angles.     

Triple correlation in the 10B(n, αγ)7Li reaction

The formally T-odd triple correlation between the directions of the momenta of α particle and γ quantum and the polarization pseudovector of a thermal neutron was examined for the ¹⁰B+n=⁷Li+⁴He+γ reaction. Such T-odd correlations can be directly used for checking time reversal invariance in the elastic scattering of particles. In more complex reactions, this correlation can occur as a result of particle interactions in the entrance and exit channels of the reaction and, being a background effect, requires correct theoretical or direct experimental estimation. Our experiments gave an upper limit of 3.2×10^?4 (90% confidence level) for the possible T-odd asymmetry parameter in the reaction under study.