Stationary phase corrections in the process of bosonization of multi-quark interactions

The functional integration over the auxiliary bosonic variables of cubic order related with the effective action of the Nambu -- Jona-Lasinio model with 't Hooft term has recently been obtained in the form of a loop expansion. Even numbers of loops contribute to the action, while odd numbers of loops are assigned to the measure. We consider the two-loop corrections and analyse their effect on the low-lying pseudoscalar and scalar mass spectra, quark condensates and weak decay constants. The results are compared to the leading order calculations and other approaches.Comment: 22 pages, LaTeX, to appear in European Physics Journal

Light Quark Masses in Multi-Quark Interactions

We suggest and discuss in detail a multi-quark three flavor Lagrangian of the Nambu -- Jona-Lasinio type, which includes a set of effective interactions proportional to the current quark masses. It is shown that within the dynamical chiral symmetry breaking regime, the masses of the pseudo Goldstone bosons and their chiral partners, members of the low lying scalar nonet, are in perfect agreement with current phenomenological expectations. The role of the new interactions is analyzed.Comment: 8 pages, published versio

OZI violating eight-quark interactions as a thermometer for chiral transitions

This work is a follow-up of our recent observation that in the SU(3) flavor limit with vanishing current quark masses the temperature for the chiral transition is substantially reduced by adding eight-quark interactions to the Nambu - Jona-Lasinio Lagrangian with U_A(1) breaking. Here we generalize the case to realistic light and strange quark masses and confirm our prior result. Additionally, we demonstrate that depending on the strength of OZI violating eight-quark interactions, the system undergoes either a rapid crossover or a first order phase transition. The meson mass spectra of the low lying pseudoscalars and scalars at T=0 are not sensitive to the difference in the parameter settings that correspond to these two alternatives, except for the singlet-octet mixing scalar channels, mainly the sigma meson.Comment: LaTeX, 5 pages, 3 figure

One-Loop Determinant of Dirac Operator in Non-Renormalizable Models

We use proper-time regularizations to define the one-loop fermion determinant in the form suggested by Gasser and Leutwyler some years ago. We show how to obtain the polynomial by which this definition of ln det D needs to be modified in order to arrive at the fermion determinant whose modulus is invarinat under chiral transformations. As an example it is shown how the fundamental symmetries associated with the NJL model are preserved in a consistent way.Comment: 8 pages, LaTe

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

Aspects of U_A(1) breaking in the Nambu and Jona-Lasinio model

The six-quark instanton induced 't Hooft interaction, which breaks the unwanted U_A (1) symmetry of QCD, is a source of perturbative corrections to the leading order result formed by the four-quark forces with the U_L(3)X U_R(3) chiral symmetry. A detailed quantitative calculation is carried out to bosonize the model by the functional integral method. We concentrate our efforts on finding ways to integrate out the auxiliary bosonic variables. The functional integral over these variables cannot be evaluated exactly. We show that the modified stationary phase approach leads to a resummation within the perturbative series and calculate the integral in the ``two-loop'' approximation. The result is a correction to the effective mesonic Lagrangian which may be important for the low-energy spectrum and dynamics of the scalar and pseudoscalar nonets.Comment: 42 pages, 3 figures; concluding section and references adde

Long distance expansion for the NJL model with SU(3) and U_A(1) breaking

This work is a follow up of recent investigations, where we study the implications of a generalized heat kernel expansion, constructed to incorporate non-perturbatively the effects of a non-commutative quark mass matrix in a fully covariant way at each order of the expansion. As underlying Lagrangian we use the Nambu -- Jona-Lasinio model of QCD, with $SU_f(3)$ and $U_A(1)$ breaking, the latter generated by the 't Hooft flavour determinant interaction. The associated bosonized Lagrangian is derived in leading stationary phase approximation (SPA) and up to second order in the generalized heat kernel expansion. Its symmetry breaking pattern is shown to have a complex structure, involving all powers of the mesonic fields allowed by symmetry. The considered Lagrangian yields a reliable playground for the study of the implications of symmetry and vacuum structure on the mesonic spectra, which we evaluate for the scalar and pseudoscalar meson nonets and compare with other approaches and experiment.Comment: LaTeX, 30 pages, added discussions and references, title change, version to appear in Nucl. Phys.

Dynamical chiral symmetry breaking by a magnetic field and multi-quark interactions

Catalysis of dynamical symmetry breaking by a constant magnetic field in (3+1) dimensions is considered. We use the three flavour Nambu -- Jona-Lasinio type model with 't Hooft and eight-quark interaction terms. It is shown that the multi-quark interactions introduce new additional features to this phenomenon: (a) the local minimum of the effective potential catalyzed by the constant magnetic field is smoothed out with increasing strength of the field at the characteristic scale H~10^{19} G, (b) the multi-quark forces generate independently another local minimum associated with a larger dynamical fermion mass. This state may exist even for multi-quark interactions with a subcritical set of couplings, and is globally stable with respect to a further increase of the magnetic field.Comment: 6 pages, 3 figures, added discussion and references, version to appear in Phys.Lett.

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

The Rho-Meson as a Collective Excitation

A model of the rho-meson as a collective excitation of $q\bar{q}$ pairs in a system that obeys the modified Nambu--Jona-Lasinio Lagrangian is proposed. The rho emerges as a dormant Goldstone boson. The origin of the rho-meson mass is understood as a result of spontaneous chiral symmetry breaking. The low-energy dynamics of rho, pi, omega and gamma is consistently described in this new framework. The model accounts for the origin of the celebrated Kawarabayashi--Suzuki--Riazuddin--Fayyazuddin relation.Comment: 8 pages, plain LaTe