Dissociation of Hadrons in Quark Matter Within a Finite-Temperature Field-Theory Approach on the Light Front

We present a relativistic three-body equation to investigate the properties of nucleons in hot and dense nuclear/quark matter. Within the light-front approach we utilize a zero-range interaction to study the three-body dynamics. The relativistic in-medium equation is derived within a systematic Dyson equation approach that includes the dominant medium effects due to Pauli blocking and self-energy corrections. We present the in-medium nucleon mass and calculate the dissociation of the three-body system.     

Correlations in Hot and Dense Quark Matter

 We present a relativistic three-body equation to investigate three-quark clusters in hot and dense quark matter. To derive such an equation we use the Dyson equation approach. The equation systematically includes the Pauli blocking factors as well as the self-energy corrections of quarks. Special relativity is realized through the light front form. Presently we use a zero-range force and investigate the Mott transition. Received October 29, 2001; accepted for publication November 12, 2001     

A New Method of Fractional Dynamics,i.e., Fractional Mei Symmetrical Method for Finding Conserved Quantity,and its Applications to Physics

In this paper, we present the fractional Mei symmetrical method of finding conserved quantity and explore its applications to physics. For the fractional generalized Hamiltonian system, we introduce the fractional infinitesimal transformation of Lie groups and, under the transformation, give the fractional Mei symmetrical definition, criterion and determining equation. Then, we present the fractional Mei symmetrical theorem of finding conserved quantity. As the fractional Mei symmetrical method’s applications, we respectively find the conserved quantities of a fractional general relativistic Buchduhl model, a fractional three-body model and a fractional Robbins–Lorenz model.     

Relativity from Light Front and Bethe–Salpeter Equations

We present some results of two independent relativistic approaches to the few-body problem: light-front dynamics and Bethe–Salpeter equation. We show that implementing relativistic invariance leads to new qualitative properties, and that, even driven by the same interaction Lagrangian, both approaches provide different quantitative results, especially in three-body systems. The case of Bethe–Salpeter equation for computing electromagnetic form factors is discussed.     

Relativity in the three-nucleon system

A Poincaré-invariant formulation of the three-body system is used. The two-body force embedded in the three-particle Hilbert space is generated out of the high-precision NN forces by solving a nonlinear equation. The solution of the relativistic 3N Faddeev equation for ³H reveals less binding energy than for the nonrelativistic one. The effect of the Wigner spin rotation on the binding energy is very small.     

Three-Body Force Effects on EOS of Asymmetric Nuclear Matter and Proton Fraction in Neutron Star Matter

The three-body force effects on the equation of state and its iso-spin dependence of asymmetric nuclearmatter and on the proton fraction in neutron star matter have been investigated within Brueckner-Hartree-Fock approachby using a microscopic three-body force. It is shown that, even in the presence of the three-body force, the empiricalparabolic law of the energy per nucleon vs. isospin asymmetry β＝ ( N - Z) /A is fulfilled in the whole asymmetry range0≤β≤1 and also up to high density. The three-body force provides a strong enhancement of symmetry energy at highdensity in agreement with relativistic approaches. It also shows that the three-body force leads to a much more rapidincreasing of symmetry energy with density in relatively high density region and to a much lower threshold density forthe direct URCA process to occur in a neutron star as compared to the predictions adopting only pure two-body force.     

Critical Temperature of Lequid-gas Phase Transition for Hot Nuclear Matter and Three-body Force Effect

The finite temperature Brueckner-Hartree-Fock (FTBHF) approach is extended by introducing a microscopic three-body force. Within the extended approach, the three-body force effects on the equation of state of hot nuclear matter and its temperature dependence have been investigated. The critical properties of the liquid-gas phase transition of hot nuclear matter have been calculated. It is shown that the three-body force provides a repulsive contribution to the equation of state of hot nuclear matter. The repulsive effect of the three-body force becomes more pronounced as the density and temperature increase and consequently inclusion of the three-body force contribution in the calculation reduces the predicted critical temperature from about 16MeV to about 13MeV. By separating the contribution originated from the 2σ-exchange process coupled to the virtual excitation of a nucleon-antinucleon pair from the full three-body force, the connection between the three-body force effect and the relativistic correction from the Dirac-Brueckner-Hartree-Fock has been explored. It turns out that the contribution of the 2σ-NN part is more repulsive than that of the full three-body force and the calculated critical temperature is about 11MeV if only the 2σ-NN component of the three-body force is included which is lower than the value obtained in the case of including the full three-body force and is close to the value predicted by the Dirac-Brueckner-Hartree-Fock (DBHF) approach. Our result provides a reasonable explanation for the discrepancy between the values of critical temperature predicted from the FTBHF approach including the three-body force and the DBHF approach.     

Relativistic Descriptions of Few-Body Systems

A brief review of relativistic effects in few-body systems, of theoretical approaches, recent developments and applications is given. Manifestations of relativistic effects in the binding energies, in the electromagnetic form factors and in three-body observables are demonstrated. The three-body forces of relativistic origin are also discussed.     

Monopole Excitation of the Nucleon in a Relativistic Three-Quark Model

The densities and form factors of the proton andthe Roper monopole excitedstate resonance are calculatedusing a relativistic three-quark model. Small currentquark masses are used with the three-body Dirac equation solved in hypercentralapproximation. A QCD-based three-body potential,proportional to a minimum string length between thethree quarks, is used for confinement. The calculatedelectric form factor for the proton reproduces closelya dipole fit to the data. The proton density is morecompact than is the Roper resonance density. The centraldensity of the proton is about five times that for the Roper resonance. The hyperradial nodein the Roper resonance composite three-quark wavefunction shows up as a node in the transition densitybetween the proton and the Roper resonance. This node also causes the calculated transition formfactor to be larger than either the proton or Roperresonance form factors, all evaluated at the same valueof momentum transfer. The Roper resonance form factor is smaller than the proton form factor, asexpected, indicative of the Roper resonance being a morediffuse system than the proton.     

Relativistic three-body recombination with the QED vacuum

Electron-positron pair annihilation into a single photon is studied when a second free electron is present. Focussing on the relativistic regime, we show that the photon emitted in the three-lepton interaction may exhibit distinct angular distributions and polarization properties. Moreover, the process can dominate over two-photon annihilation in relativistic electron-positron plasmas of few-MeV temperature. An analogy with three-body recombination of electrons with ions is drawn.     

The light-baryon spectrum in a relativistic quark model with instanton-induced quark forces

This is the second of a series of three papers treating light-baryon resonances up to 3 GeV within a relativistically covariant quark model based on the three-fermion Bethe-Salpeter equation with instantaneous two- and three-body forces. In this paper we apply the covariant Salpeter framework (which we developed in the first paper, U. L?ring, K. Kretzschmar, B.Ch. Metsch, H.R. Petry, Eur. Phys. J. A 10, 309 (2001)) to specific quark model calculations. Quark confinement is realized by a linearly rising three-body string potential with appropriate spinorial structures in Dirac space. To describe the hyperfine structure of the baryon spectrum we adopt 't Hooft's residual interaction based on QCD-instanton effects and demonstrate that the alternative one-gluon exchange is disfavored on phenomenological grounds. Our fully relativistic framework allows to investigate the effects of the full Dirac structures of residual and confinement forces on the structure of the mass spectrum. In the present paper we present a detailed analysis of the complete non-strange-baryon spectrum and show that several prominent features of the nucleon spectrum such as, e.g., the Roper resonance and approximate “parity doublets” can be uniformly explained due to a specific interplay of relativistic effects, the confinement potential and 't Hooft's force. The results for the spectrum of strange baryons will be discussed in a subsequent paper, see U. L?ring, B.Ch. Metsch, H.R. Petry, this issue, p. 447. Received: 27 March 2001 / Accepted: 17 April 2001     

A three-body calculation of πd scattering

We present a theoretical treatment of the pion-deuteron system, meant specifically for the energy region below 100 MeV, and based on the Faddeev method for three-body scattering. This includes all orders of multiple scattering, two- and three-body unitarity (to a good approximation), nucleon recoil, deuteron d-state and a correct treatment of spin and isospin. For consistency with nuclear physics we treat the nucleons non-relativistically. However, relativistic kinematics are used for the pion. In order to obtain one-dimensional integral equations in the three-body system, we have constructed a set of separable πN t-matrices (with analytic form factors), which fit selected data up to 300 MeV. A comparison is made with existing π⁺d data at 48 MeV. This data tends to favour the Faddeev type of energy dependence for the πN t-matrix in the πd system. This could also be important in low-energy pion-nucleus scattering.     

Comment Triton Binding Energy and Minimal Relativity

For relativistic three-body calculations, essentially two different approaches are in use: field theory and relativistic direct interactions. However, while results based upon relativistic field theory show an increase of the triton binding energy by about 0.3 MeV due to relativistic effects, calculations that claim to apply relativistic direct interactions obtain 0.3 MeV repulsion. In this paper, we discuss the origin of such a discrepancy. We show that the use of an invariant two-body amplitude increases the triton binding energy by about 0.3 MeV, consistent with the results from relativistic field theory. Furthermore, we point out that in calculations relying on the direct-interactions approach, indeed expansions are used, which may be a bad approximation and the reason for the discrepancy. Received November 4, 1996; revised January 15, 1998; accepted for publication January 19, 1998     

Relativistic oscillator model with spin for nucleon resonances

The relativistic three-body problem is approached via the extension of the SL(2, C) group to the Sp(4, C) one. In terms of Sp(4, C) spinors, a Dirac-like equation with three-body kinematics is composed. After introducing the linear in coordinates interaction, it describes the spin-1/2 oscillator. For this system, the exact energy spectrum is derived and then applied to fit the Regge trajectories of baryon N-resonances in the (E ², J) plane. The model predicts linear trajectories at high total energy E with some form of nonlinearity at low E.     

Bound states and scattering from bound states in the light-front field theory dynamics

Starting from the Weinberg rules we derive a covariant form of the relativistic Schrödinger equation and formulate the bound state problem in the light-front field theory dynamics. We present an explicit rule for embodying the two-body subsystem in the three-body space and demonstrate that the cluster decomposition property is explicitly preserved in the light front field theory dynamics. As an application of these results we write amplitudes forπd→nN ^*, πd→πpn, andπd→πd, in the impulse approximation, in terms of the internal bound state wave functions and two-body reducedt-matrix elements.     

A renormalized equation for the three-body system with short-range interactions

We study the three-body system with short-range interactions characterized by an unnaturally large two-body scattering length. We show that the off-shell scattering amplitude is cutoff independent up to power corrections. This allows us to derive an exact renormalization group equation for the three-body force. We also obtain a renormalized equation for the off-shell scattering amplitude. This equation is invariant under discrete scale transformations. The periodicity of the spectrum of bound states originally observed by Efimov is a consequence of this symmetry. The functional dependence of the three-body scattering length on the two-body scattering length can be obtained analytically using the asymptotic solution to the integral equation. An analogous formula for the three-body recombination coefficient is also obtained.     

Algebraic structure and Poisson integrals of a rotational relativistic Birkhoff system

We have studied the algebraic structure of the dynamical equations of a rotational relativistic Birkhoff system. It is proven that autonomous and semi-autonomous rotational relativistic Birkhoff equations possess consistent algebraic structure and Lie algebraic structure. In general, non-autonomous rotational relativistic Birkhoff equations possess no algebraic structure, but a type of special non-autonomous rotational relativistic Birkhoff equation possesses consistent algebraic structure and consistent Lie algebraic structure. Then, we obtain the Poisson integrals of the dynamical equations of the rotational relativistic Birkhoff system. Finally, we give an example to illustrate the application of the results.     

Microscopic three-body force for asymmetric nuclear matter

Brueckner calculations including a microscopic three-body force have been extended to isospin-asymmetric nuclear matter. The effects of the three-body force on the equation of state and on the single-particle properties of nuclear matter are discussed with a view to possible applications in nuclear physics and astrophysics. It is shown that, even in the presence of the three-body force, the empirical parabolic law of the energy per nucleon vs. isospin asymmetry β = (N - Z)/A is fulfilled in the whole asymmetry range 0≤β≤1 up to high densities. The three-body force provides a strong enhancement of the symmetry energy which increases with density in good agreement with the predictions of relativistic approaches. The Lane's assumption that proton and neutron mean fields linearly vary vs. the isospin parameter is violated at high density due to the three-body force, while the momentum dependence of the mean fields turns out to be only weakly affected. Consequently, a linear isospin split of the neutron and proton effective masses is found for both cases with and without the three-body force. The isospin effects on multifragmentation events and collective flows in heavy-ion collisions are briefly discussed along with the conditions for direct URCA processes to occur in the neutron star cooling. Received: 18 February 2002 / Accepted: 16 May 2002     

Three-Body Dynamics in One Dimension: A Test Model for the Three-Nucleon System with Irreducible Pionic Diagrams

 We formulate the three-body problem in one dimension in terms of the (Faddeev-type) integral equation approach. As an application, we develop a spinless, one-dimensional (1-D) model that mimics three-nucleon dynamics in one dimension. Using simple two-body potentials that reproduce the deuteron binding, we obtain that the three-body system binds at about 7.5 MeV. We then consider two types of residual pionic corrections in the dynamical equation; one related to the 2π-exchange three-body diagram, the other to the 1π-exchange three-body diagram. We find that the first contribution can produce an additional binding effect of about 0.9 MeV. The second term produces smaller binding effects, which are, however, dependent on the uncertainty in the off-shell extrapolation of the two-body t-matrix. This presents interesting analogies with what occurs in three dimensions. The paper also discusses the general three-particle quantum scattering problem, for motion restricted to the full line. Received March 5, 2002; accepted July 19, 2002