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Radiative and hadronic decays of vector mesons in the gauge model of quark-meson interactions
V.Beylin, V.Kuksa, G.Vereshkov
Southern Federal University

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An exact low energy hadron theory should be nonperturbative effective Lagrangian approach · Effective Lagrangians from fundamental theory (QCD) · Phenomenological Lagrangians from dynamical symmetries LM meson-meson and quark-meson interactions · VDM can be added
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QCD

SUL(2)x SUR(2)

· Bosonization procedure (see Volkov, Radzhabov, Phys-USP, 2006) · Current quarks constituent quarks, mq300 MeV, gluon substructures are included · EM and strong interactions are described by the gauge (vector) fields · Quark level -model (QM) hadron-level (NM)

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One of the simplest effective gauge approach is based on
U0(1) x U(1) x SU(2) · , , ­ gauge fields · EM and strong interactions are insensitive to the chirality, it should be localized diagonal sum of the global chiral SUL(2)x SUR(2) · Remained Higgs degrees of freedom can be associated with scalar mesons (a0, f0) · VDM is naturally realized in the gauge way
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The model Lagrangian

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In the model vector fields couplings are universal (see also R.Delbourgo, D.Liu, M.D.Scadron,1999)
· Diagonalization of V and S mass forms mass spectrum, (770), (782), , a0, f0 masses and decay properties can be described in the model due to free parameters in the S sector, see · In a tree approximation the vector boson physical states are

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Real tree level mass matrix and real gauge couplings zero relative phase in and

· ·

·

Phenomenologically, the complexity is resulted from superposition of pure isospin states |I> and |I> In the model the relative phase occurs due to couplings renormalization: tree parameters sin, cos correspond to abs values of renormalized mixings The phase value can be fixed due to free parameters (in the S sector)
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The final physical Lagrangian

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Here

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There are relations in the model

From

and

g2 and |s|

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The gauge scheme describes: · meson-meson interactions at the tree and loop levels · quark-meson interactions at the loop level

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Radiative decays and

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Differential width has the form

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Spectrum of photons in

2

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: with replacement

Due to loop contributions increase up to

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Processes via quark loops

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A consequence of a model separation of quark and gluon degrees of freedom in a hadron?
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Three-pion decays of light vector mesons

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Differential width is

theor( 3) = (8.2 ­7.4) MeV theor( 3) =(0.72 ­ 0.60)x10^(-3) MeV

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exp

( (

3)=(7.6 ­ 7.4) MeV 3)=(0.5 ­ 2.9)x10^(-3) MeV

exp

Due to we need in an exact integration procedure because the ratio is not small
see also J.L.Lucio M., M.Napsuciale,M.D.Scadron, V.M.Villanueva, 1999 with a "standard" quark mass
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Conclusions
· · · The gauge generalization of -model, including quark degrees of freedom explicitly, is considered. VDM occurs at the tree level. decays have been

calculated in a good agreement with experimental data as and · · and decays. The gauge model works well for the vector mesons three-pion decays also. · So, the gauge quantum field approach can be effectively used for the meson-meson and quark-meson interactions in the radiative and hadronic decay modes. · In principle, free Higgs degrees of freedom can be associated in the model with some known scalar mesons.
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-model can be realized in a various representations with 6 independent parameters Transformations of quark fields

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