X(3872) as virtual companion pole of the charm–anticharm state χc1(2P)

Abstract

We study the spectral function of the axial-vector charmonium state χc1(2P ) coupled to DD * mesons, by employing a quantum field theoretical approach: a pronounced enhancement close to the D 0 D * 0 threshold, to be identified with the X(3872), emerges. In the complex plane we find two poles: a pole for the broad seed state χc1(2P ), and -in the easiest scenario-a virtual pole for the X(3872). Thus, our approach describes both the seed state and the dynamically generated X(3872) simultaneously. In particular, it explains the most prominent, both molecular-like and quarkoniumlike, features of the X(3872): its very small width (the decay into D 0 D * 0 is predicted to be about 0.5 MeV), the enhanced radiative decay into ψ(2S)γ w.r.t. ψ(1S)γ, and the isospin breaking decay into J/ψρ (thanks to DD * loops mediating this decay channel). At the same time, we aim to determine the pole position and the properties of the charmonium seed state: quite interestingly, even if a pole is always present, it is possible that there is no peak corresponding to this state in the spectral function, thus potentially explaining why the corresponding resonance could not yet be seen in experiments.X(3872). This result is achieved naturally by the mesonic quantum fluctuations dressing the bare state and without considering explicitly the Fock space with bothqq and molecular components. It is important to stress that there is only one spectral function, correctly normalized to 1, hence strictly speaking there is only 'one object'. However, the shape of this spectral function is non-trivial and two (relevant) poles on the complex plane are present. Quite interestingly, for certain sets of parameters, the spectral function shows only one peak close to threshold and no peak corresponding to the seed state, thus possibly explaining why thecc seed state could not yet be experimentally measured.Moreover, our study can easily explain why the strong decay into D 0 D * 0 is dominant (predictions for this decay width are evaluated to be about 0.5 MeV). Moreover, one can understand why radiative decays are in agreement with the charmonium assignment: since X(3872) is part of the spectral function of the whole state χ c1 (2P ) (originally acc seed state dressed by DD * loops), the coupling constants are basically the same (see later for details), hence the decay into ψ(2S)γ is larger than the decay into ψ(1S)γ. For the very same reason, the prompt production of the X(3872) in heavy ion collisions is quite natural. However, due to the close threshold and dressing, various 'molecular-like' properties also emerge: the ratio X(3872) → J/ψω → J/ψπ + π − π 0 over X(3872) → J/ψρ → J/ψπ + π − can be correctly described by taking into account the small difference between the D 0 D * 0 and D + D * − loop functions.In the end, it should be stressed that within our approach the very existence of the X(3872) is not possible without the seed charmonium state. If one sends the mass of the latter to infinity and/or reduce the interaction strength to DD * mesons, the...

Decays of X(3872) to χcJπ0 and Zhou1, Yu2, Xiao3 2019Phys. Rev. D

“…The theoretical basis of this work is that the Xð3872Þ state automatically emerges in the extended Friedrichs scheme and can be expressed as the combination of the cc components and the continuum components such as DD Ã , in which the DD Ã component is dominant [19]. This picture has proved successful in obtaining the mass and width and the isospin-breaking effects of the Xð3872Þ decays [25], and another calculation with the similar spirit also indicates the reasonability of this scheme [26]. This approach can be extended to discuss the decays to χ cJ π 0 processes by considering one of the final states as being a P-wave state.…”

Relativistic Friedrichs–Lee model and quark-pair creation model

“…From recent experience in studying the exotic heavy quarkonium-like states like X (3872), it is also demonstrated that by coupling the QCD fundamental qq states with the continuum, not only can the fundamental state itself be modified from the potential model predictions, but also new states can be dynamically generated. This idea was successfully used in explaining the generation of the X (3872) [3,4,[21][22][23][24][25][26]. Actually, this kind of idea has already been widely used in studying the charmonium state [1] and the low lying scalar mesons [27][28][29][30] with some successes.…”

Density of states of a coupled-channel system

“…A good example of this is the X(3872) system. Previous works have focused on the single-channel phase shift [14,79]. Our study here suggests that analyzing the structure of det S may yield a better understanding for characterizing the density of states.…”