Charmonium spectrum with a Dirac potential model in the momentum space

Abstract

We study the charmonium spectrum using a complete one gluon exchange approach based on a phenomenological relativistic qq potential model with Dirac spinors in momentum space. We use phenomenological screening factors to include vacuum quantum effects. Our formulation does not rely on nonrelativistic approximations. We fit the lowest-lying charmonia (below the DD threshold) and predict the higher-lying resonances of the spectrum. In general, we reproduce the overall structure of the charmonium spectrum and, in particular, we can reasonably describe the X(3872) resonance mass as (mostly) a cc state. The numerical values of the free parameters of the model are determined taking into account also the experimental uncertainties of the resonance energies. In this way, we are able to obtain the uncertainties of the theoretical resonance masses and the correlation among the free parameters of the model.

Effects of heavy meson loops on higher charmonia radiative transitions

“…The ψ(4040) and ψ(4160) are widely accepted as the ψ(3S) state [67][68][69][70] and ψ(2D) state [67][68][69], respectively. In Ref.…”

“…[69], the author argue that the ψ(4260) state can be assigned as 4S charmonium state under the Dirac potential model. The ψ(4360) state was explained as a 3D state from a quark potential model calculation [71], while the ψ(4360) was explained to be the 4S state [69]. In Refs.…”

Chromo-Electric Field Energy in Quark Models

“…It is necessary to recall that the spectroscopy of hadronic systems (baryons and mesons) has been also successfully studied by means of various forms of Quark Models (QMs), partially related to QCD, that can be grouped in the following categories: Bag Models (BMs), see for example references [7][8][9][10][11]; Constituent Quark Models (CQMs), see for example, for charmonium and so-called higher quarkonia, referenes [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]; for baryons, see for example references [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]; Quark Diquark Models (QDMs), see for example references [47][48][49][50][51][52][53]…”

“…Also in this case, a variety of different theoretical interpretations has been proposed, including (as in the pentaquark case discussed above) kinematical effects related to rescattering. A careful discussion of this phenomenology is given in Molina et al [31], where the mass of these resonances is compared to the results of a fully relativistic Dirac quark model in which the theoretical uncertainties of the predicted masses are also taken into account.…”

“…Recalling that the interaction potential, W(r) = W qq (r) of Equation 26, only depends on the parameters α s and d, the condition E 0 = M cc allows to determine, for a given α s , the corresponding value of d. In the present CQM approch, α s represents a purely phenomenological parameter. For a rough orientation about some possible numerical values, see, for example, references [19,24,31]. Here we explore tentatively the interval 0.2 ≤ α s ≤ 1.0 and find the value of the parameter d (of the selected color charge distribution) that gives the fixed value of M cc .…”