Multi-quark interactions with a globally stable vacuum

It is shown that $U(3)_L\times U(3)_R$ eight-quark interactions stabilize the asymmetric ground state of the well-known model with four-quark Nambu -- Jona-Lasinio and six-quark 't Hooft interactions. The result remains when the reduced SU(3) f\mbox{}lavour symmetry is explicitly broken by the general current quark mass term with $\hat{m}_u\neq\hat{m}_d\neq\hat{m}_s$.Comment: LaTeX, 17 pages, 2 figures, version to appear in Phys. Lett.

Stable Multiquark Interactions

The necessity of adding higher order multiquark interactions to the three flavor NJL model with $U_A(1)$ breaking, in order to stabilize its vacuum, is discussed.Comment: 3 pages, 1 figure, prepared for the proceedings of Quark Confinement and the Hadron Spectrum VII, 2-7 Sep. 2006, Acores, Portuga

Effects of Quark Interactions on Dynamical Chiral Symmetry Breaking by a Magnetic Field

It is shown how the strong interaction dynamics of a multi-quark Lagrangian affects the catalysis of dynamical symmetry breaking by a constant magnetic field in (3+1) dimensions. Attention is drawn to the local minima structure of the theory.Comment: This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Lowering the critical temperature with eight-quark interactions

It is shown that eight-quark interactions, which are needed to stabilize the ground state of the combined three flavor Nambu -- Jona-Lasinio and 't Hooft Lagrangians, play also an important role in determining the critical temperature at which transitions occur from the dynamically broken chiral phase to the symmetric phase.Comment: 4 pages, 2 figure

Entanglement and scattering in quantum electrodynamics: S-matrix information from an entangled spectator particle

We consider a general quantum field relativistic scattering involving two half spin fermions, $A$ and $B$, which are initially entangled with another fermion $C$ that does not participate in the scattering dynamics. We construct general expressions for the reduced spin matrices for the out-state considering a general tripartite spin-entangled state. In particular we study an inelastic QED process at tree-level, namely $e^-e^+\rightarrow \mu^- \mu^+$ and a half spin fermion $C$ as an spectator particle which can be entangled to the $AB$ system in the following ways: W state, GHZ state, $|\text{A}^\alpha \rangle \otimes |\Psi^{\pm} \rangle_{\text{BC}}$ and $|\text{A}^\alpha \rangle \otimes |\Phi^{\pm} \rangle_{\text{BC}}$, where $\{|\Psi^{\pm} \rangle,|\Phi^{\pm} \rangle\}$ are the Bell basis states and $|\text{A}^\alpha \rangle$ is a spin superposition state of system $A$. We calculate the von-Neumann entropy variation before and after the scattering for the particle $C$ and show that spin measurements in $C$ contain numerical information about the total cross section of the process. We compare the initial states W and GHZ as well as study the role played by the parameter $\alpha$ in the evaluation of the entropy variations and the cross section encoded in the spectator particle.Comment: 12 pages, 10 figure

Effects of Quark Interactions on Dynamical Chiral Symmetry Breaking by a Magnetic Field

It is shown how the strong interaction dynamics of a multi-quark Lagrangian affects the catalysis of dynamical symmetry breaking by a constant magnetic field in (3+1) dimensions. Attention is drawn to the local minima structure of the theory

Effects of eight-quark interactions on the hadronic vacuum and mass spectra of light mesons

The combined effective low energy QCD Lagrangians of Nambu -- Jona-Lasinio (NJL) and 't Hooft are supplemented with eight-quark interactions. This work is a follow-up of recent findings, namely (i) the six quark flavour determinant 't Hooft term destabilizes the NJL vacuum, (ii) the addition of a chiral invariant eight-fermion contact term renders the ground state of the theory globally stable; (iii) stability constrains the values of coupling constants of the model, meaning that even in the presence of eight-quark forces the system can be unstable in a certain parameter region. In the present work we study a phenomenological output of eight-quark interactions considering the mass spectra of pseudoscalar and scalar mesons. Mixing angles are obtained and their equivalence to the two angle approach is derived. We show that the masses of pseudoscalars are almost neutral to the eight-quark forces. The only marked effect of the second order in the SU(3) breaking is found in the $\eta -\eta'$ system. The scalars are more sensitive to the eight-quark interactions. A strong repulsion between the singlet-octet members is the reason for the obtained low mass of the $\sigma$ state within the model considered.Comment: LaTeX, 46 pages, two figure