Seminar über Physik der Starken Wechselwirkung, „QCD correlations functions, the axial anomaly, and some implications for hadron physics"

by Prof. Reinhard Alkofer (Universität Graz)

PH 3344 (Seminarraum Theorie) (TUM, Physik-Department)

PH 3344 (Seminarraum Theorie)

TUM, Physik-Department

James-Franck-Str. 1, Garching

Over the last two decades the behaviour of QCD propagators and vertex functions at sub-GeV scales has been determined by a variety of methods.
In this talk I will briefly review the current knowledge with an emphasis on correlation functions in the Landau gauge. These functions provide
input for calculating hadrons as bound states within a quantum-field-theoretical setting. The status of such calculations employing either the
Dyson-Schwinger--Bethe-Salpeter formalism or the Functional Renormalization Group / Dynamical Bosonization scheme are summarized.

As special applications of these formalisms I will discuss some implications of the non-Abelian and Abelian axial anomaly.
A mechanism to generate the $\eta^\prime$ mass and the $\eta$-$\eta^\prime$ mixing will be presented. Hereby, interesting relations between
quark confinement, dynamical chiral symmetry breaking and the axial anomaly arise. Another example, the decay of the neutral pion,
highlights the importance of the axial and the electromagnetic Ward-Takahashi-Green identities to describe on the one hand the anomaly and on
the other hand pions as a quark-antiquark bound states correctly. Last but not least, it is discussed how the anomalous process
$\pi \gamma \to \pi \pi$ is essential to experimentally verify or falsify the reliablity of the presented calculations.

The talk will end with a short summary of recent and an outlook on planned calculations within the above mentioned functional approaches
for hadron properties at time-like momenta.

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