Higher Charmonia and X,Y,Z states with Screened Potential

Abstract: We incorporate the color-screening effect due to light quark pair creation into the heavy quark-antiquark potential, and investigate the effects of screened potential on the spectrum of higher charmonium. We calculate the masses, electromagnetic decays, and E1 transitions of charmonium states in the screened potential model, and propose possible assignments for the newly discovered charmonium or charmonium-like $"X,Y,Z"$ states. We find the masses of higher charmonia with screened potential are considerably lower than those with unscreened potential. The $\chi_{c2}(2P)$ mass agrees well with that of the Z(3930), and the mass of $\psi(4415)$ is compatible with $\psi(5S)$ rather than $\psi(4S)$. In particular, the discovered four $Y$ states in the ISR process, i.e., $Y(4008), Y(4260), Y(4320/4360), Y(4660)$ may be assigned as the $\psi(3S), \psi(4S), \psi(3D), \psi(6S)$ states respectively. The X(3940) and X(4160) found in the double charmonium production in $e^+e^-$ annihilation may be assigned as the $\eta_c(3S)$ and $\chi_{c0}(3P)$ states. Based on the calculated E1 transition widths for $\chi_{c1}(2P)\to \gamma J/\psi$ and $\chi_{c1}(2P)\to \gamma \psi(2S)$ and other results, we argue that the X(3872) may be a $\chi_{c1}(2P)$ dominated charmonium state with some admixture of the $D^0\bar{D}^{*0}$ component. Possible problems encountered in these assignments and comparisons with other interpretations for these $X,Y,Z$ states are discussed in detail. We emphasize that more theoretical and experimental investigations are urgently needed to clarify these assignments and other interpretations.

• The paper evaluates higher charmonium and X, Y, Z states using a screened potential model to account for color-screening effects due to light quark pair creation.
• A key finding is the assignment of various X, Y, Z states, such as Y(4260) to ψ(4S), within this screened potential framework.
• The study suggests that masses calculated with a screened potential are lower and better match experimental observations for states above the open-charm threshold, refining charmonium spectroscopy understanding.

Evaluation of Charmonium and X, Y, Z States Using a Screened Potential Model

The paper by Bai-Qing Li and Kuang-Ta Chao presents a comprehensive investigation into higher charmonium and charmonium-like X, Y, Z states using a screened potential model to account for the color-screening effect due to light quark pair creation. The authors propose that the masses of charmonium states calculated within a screened potential framework are substantially lower than those predicted by the traditional quenched potential model, particularly in regions above the open-charm threshold.

The main aspect of the study is the introduction of a screened potential characterized by a combination of a Coulomb term and a screened linear potential. This model addresses the limitations of the quenched potential models in predicting masses of higher charmonium states that significantly deviate from experimental results. In this paper, the authors provide estimated masses, electromagnetic decay widths, and E1 transition rates for these states, and contrast these with experimental observations and predictions from other theoretical models.

One of the salient findings is the assignment of various mysterious X, Y, Z states observed in experiments to specific excited charmonium states. For instance, Z(3930) is associated with χc2(2P), aligning closely with its observed mass, while Y(4260), traditionally a problematic state to classify in standard charmonium theory, is posited to correspond to the ψ(4S) state within the new framework, showing better agreement with experimental data than prior predictions.

The paper suggests the possibility that some of the recently observed Y states, namely Y(4008), Y(4260), Y(4320/4360), and Y(4660), can be assigned as ψ(3S), ψ(4S), ψ(3D), and ψ(6S) states, respectively. Furthermore, the X(3940) and X(4160) states found in e⁺e⁻ annihilation processes are interpreted as ηc(3S) and χc0(3P) states within the screened potential model.

Such detailed assignments have profound implications for understanding the spectroscopy of charmonium states, as well as the underlying dynamics dictated by the strong force in Quantum Chromodynamics (QCD). The results hold significant implications for the development of more accurate potential models that incorporate non-perturbative QCD effects such as string breaking and vacuum polarization due to light quark pair creation.

The findings promote a reevaluation of theoretical models for heavy-quark systems and highlight the need for further experimental and theoretical exploration, particularly into higher-energy states and their decay paths. Future studies could clarify these assignments and potentially refine the understanding of long-standing puzzles in the spectroscopy of mesons above open-charm thresholds.

In summary, this paper enhances the discourse on the complex interactions within charmonium systems and provides a framework for considering color-screening effects in extending potential models beyond the traditional constraints, impacting both practical computational models and the broader theoretical structure of heavy quarkonium physics. Further experimental support and theoretical refinements could substantially validate the proposed model, offering new insights into the complicated landscape of quantum chromodynamics.