Danilkin, I. V.

Leupold, S.

Lutz, M. F. M.

Terschlüsen, C.

GSI Repository

Photon-fusion reactions from chiral dynamics with vector fieldsI. V. Danilkin1,3, M. F. M. Lutz1, S. Leupold2, and C. Terschlu¨sen21GSI, Darmstadt, Germany; 2Uppsala Universitet, Sweden; 3ITEP, Moscow, RussiaPhoton-fusion reactions γγ → PP (with PP = π0π0,π−, K0K¯0, K+K−, ηη and π0η) play an importantrole in our understanding of non-perturbative QCD. As asystematic approach chiral perturbation theory (χPT) is ap-plied to describe these reactions at low energies [1]. Anextension of χPT to the resonance region can be achievedby recently proposed novel scheme [2], which implementsconstraints from micro-causality and coupled-channel uni-tarity.The cross sections of fusion processes are very sensitiveto hadronic final-state interactions. Therefore, a crucial in-put is a proper description of the Goldstone boson scatter-ing. This study has been performed in [3] within the novelunitarization scheme. The scalar resonances f0(980) and(980) are dynamically generated from coupled-channelPP ↔ PP interactions. An important ingredient of thesecalculations is the chiral Lagrangian supplemented withlight vector-meson degrees of freedom. The latter playsa crucial role in the hadrogenesis conjecture [4].In the case of photo-fusion reactions, the chiral La-grangian has five unknown parameters [5]. They parame-terize the strength of interaction terms involving two vectormeson fields. These parameters are fitted to γγ → π0π0,π−, π0η data and to the decay η → π0γγ, which islinked to γγ → π0η by crossing symmetry. For the de-cay amplitude we use the tree-level result, while for thereaction amplitudes we use the full rescattering formalismoutlined in [2]. The results are depicted in Figs. 1 and 2.The photon-fusion cross sections for the two-pion finalstates are in good agreement with the existing experimen-tal data from threshold up to about 0.9 GeV. The a0(980)	SSS[2S2[V4.VSV[ [/[8 [/e1Figure 1: The single-differential invariant-mass distribu-tion of the decay η → π0γγ.rUU469TT4r.rrrrstrγ→γγπγγ+γγ→oπrAγ.+ γ.n →.→6r444r.rrrγγrγπγ-γ[γ→oπrAγ.+ γ.n →.→6r444r.rrrrγrγπγ-γ[γ→oπrAγ.n γ.]σ →.π7#A$ rrrKsKtrγ→σ+γ-σ→oπrA→ →.→ →.π%769TT rrKγKγrγ→γπγ+γ→oπrA→ →.→ →.πrrr4rγ→.σ+-.σ→oπrA→.→ →.→σ →.πFigure 2: Total cross sections for the reactions γγ →π+π−, π0π0, π0η, K+K−, K0K¯0 and ηη.meson in the π0η channel is dynamically generated and anaccurate reproduction of the γγ → π0η data is achievedup to 1.2 GeV. Based on our parameter sets we predict theγγ →K0K¯0, K+K−, η η cross sections (see Fig. 2).References[1] J. Gasser, M. A. Ivanov and M. E. Sainio, Nucl. Phys. B 728(2005) 31; Nucl. Phys. B 745 (2006) 84[2] A. Gasparyan and M. F. M. Lutz, Nucl. Phys. A 848, 126(2010)[3] I. V. Danilkin, L. I. R. Gil and M. F. M. Lutz, Phys. Lett. B703 (2011) 504[4] M. F. M. Lutz and E. E. Kolomeitsev, Nucl. Phys. A 730(2004) 392; Nucl. Phys. A 700 (2002) 193[5] I. V. Danilkin, M. F. M. Lutz, S. Leupold and C. Terschlusen,arXiv:1211.1503 [hep-ph].GSI SCIENTIFIC REPORT 2012 PHN-HSD-THEORY-0325

Photon-fusion reactions from chiral dynamics with vector  fields

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Photon-fusion reactions from chiral dynamics with vector fields

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