Chiral symmetry, the angular content of the vector current in QED and QCD, and the holographic description of hadrons

Details Chiral symmetry, the angular content of the vector current in QED and QCD, and the holographic description of hadrons Chiral symmetry, the angular content of the vector current in QED and QCD, and the holographic description of hadrons

2009-04-20

arxiv.org/abs/0904.3067v3

Phys.Rev.D80:057901,2009

Physics

High Energy Physics

High Energy Physics - Phenomenology

4 pp. The title has been changed. Implications for OPE and holographic description of mesons have been added. To appear in PRD

Scientific paper

10.1103/PhysRevD.80.057901

We perform a general chiral symmetry and unitarity based analysis of a local process of the fermion-antifermion creation from the vacuum by a high-energy photon as well as an explicit partial wave analysis of the vector current in QED and QCD. It turns out that such a local process proceeds necessarily via a certain superposition of the $S$- and $D$-wave contributions. These constraints from chiral symmetry and unitarity are confronted then with the well-known theoretical and experimental results on $e^+e^-\to\gamma\to e^+e^-$, $e^+e^-\to\gamma\to \mu^+\mu^-$, and $e^+e^-\to\gamma\to q\bar{q}$ in the ultrarelativistic limit. It is shown that these well-known results are consistent with the $S+D$-wave structure of the vertex and are inconsistent with the pure $S$-wave interpretation of the vertex. Then a free quark loop in the $1^{--}$ channel, representing the leading term in the Operator Product Expansion, contains both $S$-wave and $D$-wave contributions. This fact rules out the possibility that there is only one radial trajectory for the $\rho$-mesons with the fixed $S$-wave content. It also implies that all holographic models that assume a pure $S$-wave content of the $\rho$-meson have to fail to satisfy the matching conditions at the ultraviolet border $z=0$.

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