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Photon-fusion reactions from the chiral Lagrangian with dynamical light vector mesons

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Abstract

We study the reactions γγ→π 0 π 0, π + π −, \(K^{0}\bar{K}^{0}\), K + K −, ηη and π 0 η based on a chiral Lagrangian with dynamical light vector mesons as formulated within the hadrogenesis conjecture. At present our chiral Lagrangian contains five unknown parameters that are relevant for the photon-fusion reactions. They parameterize the strength of interaction terms involving two vector meson fields. These parameters are fitted to photon-fusion data γγ→π 0 π 0, π + π −,π 0 η and to the decay η→π 0 γγ. In order to derive gauge invariant reaction amplitudes in the resonance region constraints from maximal analyticity and exact coupled-channel unitarity are used. Our results are in good agreement with the existing experimental data from threshold up to about 0.9 GeV for the two-pion final states. The a 0 meson in the π 0 η channel is dynamically generated and an accurate reproduction of the γγ→π 0 η data is achieved up to 1.2 GeV. Based on our parameter sets we predict the γγ→ \(K^{0}\bar{K}^{0}\), K + K −, ηη cross sections.

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Notes

  1. Note that in [12, 20] slightly different notations were used. The relations between e V , g D , g F , h P in [12, 20]—denoted by old—and f V , g 1, g 2, h P used here and in [21] are \(f_{V}= \frac{0.776~\mathrm{GeV}}{4e}e_{V}\), g 1=g D , g 2=g F and \(h_{P}=\frac{0.776~\mathrm{GeV}}{f_{V}}h_{P}[\mathit{old}]\).

  2. In the following we do not display any more the angular-momentum superscript J explicitly. Where not needed we also do not display the channel index ab.

  3. Usually the experimental results are limited to a range of |x|≤Z with x=cosθ. In this case the cross section is given by \(\sigma=2\int_{0}^{Z} \frac{d\sigma}{dx} \,dx\).

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Acknowledgements

The work of CT and SL has been supported by the European Community Research Infrastructure Integrating Activity “Study of Strongly Interacting Matter” (HadronPhysics3, Grant Agreement No. 283286) under the Seventh Framework Programme of the EU.

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Authors and Affiliations

  1. GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstraße 1, 64291, Darmstadt, Germany

    I. V. Danilkin & M. F. M. Lutz

  2. Institutionen för Fysik och Astronomi, Uppsala Universitet, Box 516, 75120, Uppsala, Sweden

    S. Leupold & C. Terschlüsen

  3. SSC RF ITEP, Bolshaya Cheremushkinskaya 25, 117218, Moscow, Russia

    I. V. Danilkin

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  1. I. V. Danilkin
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Correspondence to M. F. M. Lutz.

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Danilkin, I.V., Lutz, M.F.M., Leupold, S. et al. Photon-fusion reactions from the chiral Lagrangian with dynamical light vector mesons. Eur. Phys. J. C 73, 2358 (2013). https://doi.org/10.1140/epjc/s10052-013-2358-1

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