Electromagnetic trace anomaly in a generalized linear sigma model

Abstract

We build the electromagnetic trace anomaly effective term for a generalized linear sigma model with two chiral nonets, one with a quark-antiquark structure and the other one with a four-quark content. In the leading order of this framework, we study the decays into two photons of the lowest isosinglet scalar mesons. We find that the direct inclusion of underlying mixing among two-and four-quark components in the trace anomaly term is essential in order for the model prediction to agree with the available experimental data on the decay width of f 0 ð980Þ to two photons. Consequently, this sets a lower bound of 0.5 KeVon the decay with of f 0 ð500Þ to two photons.

Quark and glue spectroscopy of scalars and pseudoscalars in SU(3) flavor limit

“…Theoretical frameworks that aim to address the properties of scalar and pseudoscalar mesons up to around 2 GeV should be mindful of the glue contents in addition to quark-antiquarks and four-quark components. A generalized linear sigma model for understanding the properties of scalars and pseudoscalars, particularly their quark-antiquark and four-quark admixtures, was proposed in [40] and further developed in [41]- [49]. This model is formulated in terms of two chiral nonets (a quark-antiquark and a four-quark) and exhibits chiral symmetry and its breakdown, both spontaneously and explicitly through quark mass terms.…”

Standard Model Effective Potential from Trace Anomalies

“…It is worth mentioning that linear sigma models have long been a basic tool for some effective description for low energy QCD and were generalized to the more comprehensive global group (3) 퐿 × (3) 푅 [17][18][19][20] and also to include four quark states [21][22][23][24][25] that can accommodate two scalar and two pseudoscalar nonets. Moreover without the specific knowledge of the detailed interaction, one can add phenomenological terms that mock up the axial [26] and the trace anomalies [27] with significant role in the hadron properties and good agreement with the experimental data.…”

“…These decay widths as stated here depend on four parameters 2 , 2 , , and 耠 which in their turn depend on the top Yukawa and the gauge coupling constants. Again from low energy QCD [26,27], we learn that in the context of an effective theory one should not expect that the parameters that describe the effective widths should be directly related to those employed in standard tree level or one-loop calculations or to those employed in other types of models that describe the same processes. For a phenomenological model to be viable, it is necessary and sufficient only that the phenomenological result is aligned to the experimental data or other consistent theoretical results.…”

Generalized linear sigma model with two glueballs

“…Such model dependencies can be minimized if the framework is tested against various low-energy processes. In [39]- [48] we proposed and developed a generalized linear sigma model with two chiral nonets that satisfy approximately the low-energy chiral symmetry and the quantum anomalies of QCD. The model was able to describe the mass spectrum and some of the properties of 36 low lying scalar and pseudoscalar states with a good agreement with the experimental data.…”

“…The axial and trace anomalies in a linear sigma model refer both to the electromagnetic and the gluon fields. In [47,48] we studied the effect of the electromagnetic axial and trace anomalies on the decays to two photons of some of the scalar and pseudoscalar states. However the treatment of the gluon anomalies is somewhat different because the gauge invariant glueball states may behave as individual degrees of freedom which may be either integrated out from the Lagrangian or maintained as physical states.…”