The Ds1(2536)+ Decay Widths in the C3P0 Model

The Fock-Tani representation is a field theory formalism appropriated for the simultaneous treatment of composite particles and their constituents. The 3P0 model is a typical decay model which considers only OZI-allowed strong decays. The model considers a quark-antiquark pair created with the vacuum quantum numbers in the presence of the initial state meson. It is described as the non-relativistic limit of the pair creation Hamiltonian. Applying the Fock-Tani transformation to the microscopic Hamiltonian of the pair creation produces the characteristic expansion in powers of the wavefunction, where the 3P0 model is the lowest order in the expansion. The corrected 3P0 model (C3P0) is obtained from higher orders in the expansion, by the introduction of the bound state kernel ∆, called the bound state correction. The goal of this work is to study the application of the 3P0 model and C3P0 model in detail for the strange charmed meson sector (DSJ meson). In particular, we shall calculate the decay amplitudes and decay rates of the Ds1(2536).

The 3 P 0 model is a decay model that considers a quark-antiquark pair created with the vacuum quantum numbers which interact with a meson in the initial state, the pair creation Hamiltonian in this model (Ref. 5 ) is described in the nonrelativistic limit. When the Fock-Tani transformation is applied to this Hamiltonian it produces an expansion in powers of the wavefunction. The 3 P 0 model is the lowest order term in this expansion. The contribution of the higher orders terms in this expansion give origin to Corrected 3 P 0 model (C 3 P 0 ).
In this work we apply of C 3 P 0 model on the charming-strange sector (D SJ meson) and calculate the decay amplitudes and decay rates of the D s1 (2536) + → D * (2010) + K 0 up to first order correction.

The Meson in the Fock-Tani Formalism
In the Fock-Tani formalism we can write the meson creation operators in the following form where Φ µν α is the bound-state wavefunction for two-quarks respectively. The quark and antiquark operators obey canonical anti-commutation relations, but the composite meson operators do not satisfy canonical commutation relations. The idea of the Fock-Tani formalism is to make a representation change, of form that the composite particles operators are described by operators that satisfy canonical com- where m † α is the operators of the "ideal particles" creation. This can be done and lead to a set of Heisenberg-like equations for the basic operators m, M , q andq which can be solved order by order in function of the In this model we use the following Hamiltonian, inspired in the 3 P 0 approach, The quark field is respectively and γ = g 2mq , where m q is the mass of both produced quarks. Note that the operator gΨ † γ 0 Ψ leads to the decay (qq) A → (qq) B + (qq) C through the b † d † term. Introducing the following notation b → q; d →q; µ = ( p , s ) e ν = ( p, s), after the expansion one obtains where the sum (integration) is implied over repeated indexes and Applying the Fock-Tani transformation to H I one obtains the effective Hamiltonian Now considering the transition m γ → m α + m β , we are interested in to calculate the h f i (decay amplitude) that is given by where |i = m † γ |0 and |f = m † α m † β |0 .

The Meson Wavefunction
The meson wavefunction is defined as where χ is spin; f is flavor and C are color coefficients. The spatial parte is given by where Φ nl ( p i , p j ) is given by

Applications of the Corrected 3 P 0 Model
For this work we consider the decay process The full expressions for the decay amplitudes h f i has the following form where the coefficients C LS are polynomials which has a dependence on the P momentum and in β gaussian width of the mesons involved on the processes. The decay amplitude h f i can be combined with relativistic phase space to give the decay rate (Ref. 4 -5 ). We obtain in this work the decay rates for the processes studied. This decay rates are given in the following form The experimental values extracted from "Particle Data Group 2010" (PDG -Ref. 6 ) and the theoretical values obtained with C 3 P 0 model for this process are shown in the Tab. 1. Table 1. Experimental values of the total decay rates and branching ratios for the meson D * 2 (2460).

Conclusions
Here we present the Corrected 3 P 0 model applied for one meson decay process of the charming-strange sector. In this sector the decay process is D * SJ → D * K. The result is close to the experimental range, requiring a better fit with current pdg data.
The next step will be to consider the other D decay channels and higher-order corrections in the Corrected 3 P 0 model.