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( D$_{sJ}$ (2860) has been assigned to the s$_{ℓ}$ = 5 2 doublet, with a question mark since confirmation is needed). 

Some indications about the masses of these states come from potential model calculations. For example, in Ref.[11] the spectrum of heavy-light mesons is computed in the framework of a relativistic quark model (RQM), with results: 

Notice that, if the identification of D$_{sJ}$ (2860) as the J P s$_{ℓ}$ = 3 − 5 / 2 state were experimentally confirmed, this would disfavor the assignment of D$_{sJ}$ (3040) to its spin partner D ∗′ s 2 with J P s$_{ℓ}$ = 2 − 5 / 2 , since a mass inversion in a spin doublet seems unlikely. For a similar reason, one would also disfavor the identification of D$_{sJ}$ (3040) with D$_{s}$$_{2}$ , although in that case the two mesons would belong to different doublets. 

The four classifications for D$_{sJ}$ (3040) in Table I can be discussed computing the allowed strong decays. To this purpose, we work in the heavy quark limit in which the various spin doublets are described by effective fields: H$_{a}$ for s P ℓ = 1 2 − ( a = u, d, s is a light flavour index); S$_{a}$ and T$_{a}$ for s P ℓ = 1 2 + and s P ℓ = 3 2 $^{+}$, respectively; X$_{a}$ and X ′ a for the doublets corresponding to orbital angular momentum ℓ = 2, i.e. s P ℓ = 3 2 − and s P ℓ = 5 2 $^{−}$: 

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with the various operators annihilating mesons of four- velocity v which is conserved in strong interaction pro- cesses (the heavy field operators contain a factor √ m$_{P}$ and have dimension 3 / 2). 

Let us consider decays with the emission of a light pseudoscalar meson. The octet of light pseudoscalar mesons is introduced considering the fields: ξ = e i M f π , Σ = ξ $^{2}$, and the matrix M containing π, K and η fields ( f$_{π}$ = 132 MeV): 

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light meson momentum expansion, the decays F → HM ( F = H, S, T, X, X ′ and M a light pseudoscalar meson) are described by the Lagrangian interaction terms [12]: 

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