M. Beyer

Two-fermion bound states within the Bethe-Salpeter approach

To solve the spinor-spinor Bethe-Salpeter equation in Euclidean space we propose a novel method related to the use of hyperspherical harmonics. We suggest an appropriate extension to form a new basis of spin-angular harmonics that is suitable for a representation of the vertex functions. We present a numerical algorithm to solve the Bethe-Salpeter equation and investigate in detail the properties of the solution for the scalar, pseudoscalar and vector meson exchange kernels including the stability of bound states. We also compare our results to the nonrelativistic ones and to the results given by light-front dynamics.

The

Abstract Among the light nuclear clusters the α -particle is by far the strongest bound system and therefore expected to play a significant role in the dynamics of nuclei and the phases of nuclear matter. To systematically study the properties of the α -particle we have derived an effective four-body equation of the Alt–Grassberger–Sandhas (AGS) type that includes the dominant medium effects, i.e. self energy corrections and Pauli-blocking in a consistent way. The equation is solved utilizing the energy dependent pole expansion for the subsystem amplitudes. We find that the Mott transition of an α -particle at rest differs from that expected from perturbation theory and occurs at approximately 1/10 of nuclear matter densities.

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Abstract We present the form factors of the B→π,ρ transitions induced by the b→u quark currents at all kinematically accessible q2. Our analysis is based on the spectral representations of the form factors within the constituent quark picture: we fix the soft meson wave functions and the constituent quark masses by fitting A1(q2) and T2(q2) to the lattice results at small recoils ( 17≲q 2 ≲20 GeV2). We then calculate the B→π,ρ transition form factors down to q2=0. For the B→π case the region q2≲20 GeV2 however does not cover the whole kinematically accessible range. Due to the smallness of the pion mass the region of small recoils is close to the nearby B ∗ (5234) resonance. We develop a parametrization which includes the B ∗ dominance of the form factors f+ and f− at small recoils and numerically reproduces the results of calculations at q 2 ≲20 GeV2. We find Γ(B→πlν)=8.0+0.8−0.2|Vub|2ps−1 and Γ(B→ρlν)=15.8±2.3|Vub|2ps−1.

-particle in nuclear matter

Within a microscopic statistical description of heavy ion collisions, we investigate the effect of the medium on the formation of light clusters. The dominant medium effects are self-energy corrections and Pauli blocking that produce the Mott effect for composite particles and enhanced reaction rates in the collision integrals. Microscopic description of composites in the medium follows the Dyson equation approach combined with the cluster mean-field expansion. The resulting effective few-body problem is solved within a properly modified Alt-Grassberger-Sandhas formalism. The results are incorporated in a Boltzmann-Uehling-Uhlenbeck simulation for heavy ion collisions. The number and spectra of light charged particles emerging from a heavy ion collision changes in a significant manner in effect of the medium modification of production and absorption processes.

Form-factors of exclusive b -> u transitions

Abstract We analyse pionic couplings of heavy mesons combining PCAC with the dispersion quark model to calculate the relevant transition form factors. Ground states and radial excitations are considered. For the ground state coupling constants the values g =0.5±0.02 in the heavy quark limit, and g B ∗ Bπ =40±3 , g D ∗ Dπ =16±2 are obtained. A sizable suppression of the coupling constants describing the pionic decays of the radial excitations is observed.

Medium corrections in the formation of light charged particles in heavy ion reactions

We derive three-body equations valid at finite densities and temperatures. These are based on the cluster mean field approach consistently including proper self energy corrections and the Pauli blocking. As an application we investigate the binding energies of triton and determine the Mott densities and momenta relevant for a many particle description of nuclear matter in a generalized Beth-Uhlenbeck approach. The method, however is not restricted to nuclear physics problems but may also be relevant, e.g., to treat three-particle correlations in weekly doped semiconducters or strongly coupled dense plasmas.

Pionic coupling constants of heavy mesons in the quark model

We investigate the nonrelativistic reduction of the Bethe-Salpeter amplitude for the deuteron electrodisintegration near threshold energies. To this end, two assumptions have been used in the calculations: 1) the static approximation and 2) the one iteration approximation. Within these assumptions it is possible to recover the nonrelativistic result including a systematic extension to relativistic corrections. We find that the so-called pair current term can be constructed from the

Three-body properties in nuclear matter at thermal equilibrium

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Isovector meson exchange currents in the Bethe-Salpeter approach

-wave contribution of the deuteron Bethe-Salpeter amplitude. The form factor that enters into the calculation of the pair current is constrained by the manifestly gauge independent matrix elements.

Light-front versus Bethe-Salpeter forms of two nucleon amplitudes ∗

Abstract. We discuss the relation between the two-nucleon Bethe-Salpeter amplitude and the light-front wave functions. Both approaches provide a covariant description for the deuteron bound state and the two-nucleon scattering state. A comparison is done for the spin-orbit functions as well explicit integrals are given on the basis of the Nakanishi integral-representation method.