The Radiative Decay Of Y(4260)�'X(3872)+γ In The Unitarized Meson Model

The radiative decay of Y（4260）(J^PC =1--)�' X（3872）(J^PC =1++) + γ is studied by the unitarized meson model （UMM）, which was proposed by the Nijmegen group. The basic idea of this theory is that the heavy quarkonia is not a purely structure of quark-antiquark pair, but a coupling of a quark-antiquark pair with multi-channel meson-meson pairs （there are egiht channels for heavy flavor quarkonium MM , MM", M*M*（L₁,S₁）, M*M*（L₂,S₂）, MsMs, MsMs*, Ms*Ms* （L₁,S₁）, Ms*Ms* （L₂,S₂））. In the simplified model, the interaction between quark and antiquark is taken as the harmonic oscillator （HO） confining potential in the quark-antiquark channel, and the coupling of the quark-antiquark pair channel to the meson-meson channel is considered as a delta-shell interaction gδ（δ-a）, and the mesons in the meson-meson channel is recognized to be free. In the UMM, there are two kinds of decay trasitons: qq�'qq+γy and （MM）�' （MM） + γ, and the processes like MM’�'MM + γ is negligible. Since the masses of Y（4260） and X（3872） are several ten MeV below the DXD and DD* thresholds, respectively, Y（4260） can be treated as the hybrid of cc （43S₁ state）and D1D （S-state） and X（3872） as a hybrid of cc （23P1 state） and DD* （S-state）. The decay width of Y（4260）�'X （3872） + γ can be easily calculate in this model. The radiative decay consists of two parts: One process is DD1 （1-- ）�' DD* （1++ ） +γ which is equivalent to the process D1 （1+ ）�'D* （1-） +γ ; Another process is cc （41--）�'cc（21++）+γ . The first process involves the change of internal strcucture of mesons and therefore is igonored in the UMM, while this process is taken into account in the present work. The second process is a reduced UMM and there is noly one channel left, it is a very simple radiative decay process. In order to get the radiative decay width of Y（4260） �'X（3872） +γy, one needs the radial wave function of Y（4260） and X（3872）, where we obtain these wave functions by solving the coupling channel Schrodinger equation with the hamiltonians of Hqq and HMM. Last the obtained radiative decay width is 0<Γ（Y�'>X+γ）<23 keV for free parameter 1GeV-1≤a≤4GCV-1, which is discussed and compared to that of other theoretical works.