B. Hiller

Chiral anomaly and CPT invariance in an implicit momentum space regularization framework

This is the second in a series of two contributions in which we set out to establish a novel momentum space framework to treat field-theoretical infinities in perturbative calculations when parity-violating objects occur. Since no analytic continuation on the space-time dimension is effected, this framework can be particularly useful to treat dimension-specific theories. Moreover, arbitrary local terms stemming from the underlying infinities of the model can be properly parametrized. We (re)analyze the indeterminacy of the radiatively generated

Pion Observables in the Extended NJL Model with Vector and Axial-Vector Mesons☆

\mathrm{CPT}

Gauge invariance and the CPT and Lorentz violating induced Chern–Simons-like term in extended QED

violating Chern-Simons term within an extended version of

Comparing implicit, differential, dimensional, and Bogolubov-Parasiuk-Hepp-Zimmermann renormalization

{\mathrm{QED}}_{4}

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

and calculate the Adler-Bardeen-Bell-Jackiw triangle anomaly to show that our framework is consistent and general enough to handle the subtleties involved when a radiative correction is finite.

Four-point functions in quark flavor dynamics: meson-meson scattering

Abstract The momentum-space bosonization method of a Nambu and Jona-Lasinio type model with vector and axial-vector mesons is applied to ππ scattering. Unlike the case in earlier published papers, we obtain the ππ scattering amplitude using the linear and nonlinear realizations of chiral symmetry and fully taking into account the momentum dependence of meson vertices. We show the full physical equivalence between these two approaches. The chiral expansion procedure in this model is discussed in detail. Chiral expansions of the quark mass, pion mass and constant f π are obtained. The low-energy ππ phase shifts are compared to the available data. We also study the scalar form factor of the pion.

Strong and radiative meson decays in a generalized Nambu-Jona-Lasinio model☆

The radiative induction of the CPT and Lorentz violating Chern–Simons (CS) term is reassessed. The massless and massive models are studied. Special attention is given to the preservation of gauge symmetry at higher orders in the background vector bμ when radiative corrections are considered. Both the study of the odd and even parity sectors of the complete vacuum polarization tensor at one-loop order and a non-perturbative analysis show that this symmetry must be preserved by quantum corrections. As a complement we obtain the result that transversality of the polarization tensor does not fix the value of the coefficient of the induced CS term.

To \({d}\), or not to \({d}\): recent developments and comparisons of regularization schemes

We compare a momentum space implicit regularisation (IR) framework with other renormalisation methods which may be applied to dimension specific theories, namely Differential Renormalisation (DfR) and the BPHZ formalism. In particular, we define what is meant by minimal subtraction in IR in connection with DfR and dimensional renormalisation (DR) . We illustrate with the calculation of the gluon self energy a procedure by which a constrained version of IR automatically ensures gauge invariance at one loop level and handles infrared divergences in a straightforward fashion. Moreover, using the φ4 theory setting sun diagram as an example and comparing explicitly with the BPHZ framework, we show that IR directly displays the finite part of the amplitudes. We then construct a parametrization for the ambiguity in separating the infinite and finite parts whose parameter serves as renormalisation group scale for the Callan-Symanzik equation. Finally we argue that constrained IR, constrained DfR and dimensional reduction are equivalent within one loop order. Pacs:11.10.Gh, 11.25.Db, 11.15.Bt.

Medium effects on meson properties

Abstract 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 η – η ′ system. The scalars are more sensitive to the eight-quark interactions. A strong repulsion between the singlet and octet members is the reason for the obtained low mass of the σ state within the model considered.

Generalized proper-time approach for the case of broken isospin symmetry

Abstract We study pion-pion scattering in an extended version of the three-flavor Nambu-Jona-Lasinio model. We show that the leading order contributions of the ππ scattering amplitude agree with the standard current algebra results. We evaluate the various scattering lengths and amplitudes. For the regime of “barely broken” chiral symmetry, which is characterized by substantial non-linearities under the introduction of the current quark masses, we find a00=0.26 in agreement with the data. The threshold parameters in the other channels are also satisfactorily described.