Speaker
Description
The ground-state positive-parity charmonia $\chi_{c0}(1P)$, $\chi_{c1}(1P)$, $h_c(1P)$, and $\chi_{c2}(1P)$ [1] are generally well described in static (``quenched'') quark models [2], in which dynamical effects of actual or virtual strong decay are neglected. Since these states lie below their lowest OZI-allowed decay thresholds of pairs of open-charm mesons, the resulting real, negative mass shifts can largely be accounted for by redefining the parameters of the confining interaction only, leaving e.g. the typical ratio $\left\{M({}^{3\!}P_2)-M({}^{3\!}P_1)\right\}/\!\left\{M({}^{3\!}P_1)-M({}^{3\!}P_0)\right\}$ almost unchanged [3].
In contrast, the five observed [1] candidates for $P$-wave charmonia around roughly 3.9 GeV, probably including the first radial excitations of the above ones, display a totally different pattern of masses. For instance, the $\chi_{c1}(3872)$ (formerly called $X(3872)$ [4]) is even lighter than the $\chi_{c0}(3915)$. Moreover, alongside the latter scalar meson, the additional $\chi_{c0}(3860)$ further complicates the picture. Note, however, that all these five charmonia have been seen to decay to one or more final states of two open-charm mesons, thus turning them into resonances of wildly varying widths, depending on the precise location of their lowest decay thresholds. The estimates of real mass splittings
given in Ref. [3] are no longer valid for these resonances, subject to complex mass shifts upon unquenching, owing to strong decay.
In this talk I shall present results for the first radial excitations of $P$-wave charmonia obtained with the Resonance-Spectrum Expansion [5], including all OZI-allowed decay channels of ground-state charm-meson pairs. Employing the generalised scheme of computing coupling constants for decays based on the ${}^{3\!}P_0$ model as developed in Ref. [6] ensures that no distortion of the spectra will occur due to the different classes of permitted decay channels for the various positive-parity charmonia.
[1] S. Navas et al. [Particle Data Group], Phys. Rev. D 110 (2024) 030001.
[2] S. Godfrey and N. Isgur, Phys. Rev. D 32 (1985) 189.
[3] T. J. Burns, Acta Phys. Polon. Supp. 8 (2015) 31 [arXiv:1411.2485].
[4] S. Coito, G. Rupp, and E. van Beveren, Eur. Phys. J. C 71 (2011) 1762 [arXiv:1008.5100]; 73 (2013) 2351 [arXiv:1212.0648]; M. Cardoso, G. Rupp, and E. van Beveren, Eur. Phys. J. C 75 (2015) 26 [arXiv:1411.1654].
[5] E. van Beveren and G. Rupp, Annals Phys. 324 (2009) 1620 [arXiv:0809.1149].
[6] E. van Beveren, Z. Phys. C 17 (1983) 135 [arXiv:hep-ph/0602248].