Searching for a bound state with the decay

Lianrong Dai; Genaro Toledo; Eulogio Oset

doi:10.1140/epjc/s10052-020-8058-8

EPJ

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2020) 80: 510
https://doi.org/10.1140/epjc/s10052-020-8058-8

Regular Article - Theoretical Physics

Searching for a $D {\bar{D}}$ bound state with the $\psi (3770) \rightarrow \gamma D^0 {\bar{D}}^0$ decay

Lianrong Dai¹^,2^*, Genaro Toledo³^,4 and Eulogio Oset⁴

¹ School of Science, Huzhou University, Huzhou, 313000, Zhejiang, China
² Department of Physics, Liaoning Normal University, Dalian, 116029, China
³ Instituto de Física, Universidad Nacional Autónoma de México, AP 20-364, Mexico City, Mexico
⁴ Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC Institutos de Investigación de Paterna, Aptdo.22085, 46071, Valencia, Spain

^* e-mail: dailianrong68@126.com

Received: 17 April 2020
Accepted: 16 May 2020
Published online: 8 June 2020

Abstract

We perform a calculation of the mass distribution in the $\psi (3770) \rightarrow \gamma D {\bar{D}}$ decay, studying both the $$D^+ D^- $$ and $D^0 {\bar{D}}^0$ decays. The electromagnetic interaction is such that the tree level amplitude is null for the neutral channel, which forces the $\psi (3770) \rightarrow \gamma D^0 {\bar{D}}^0$ transition to go through a loop involving the $D^+ D^- \rightarrow D^0 {\bar{D}}^0$ scattering amplitude. We take the results for this amplitude from a theoretical model that predicts a $D {\bar{D}}$ bound state and find a $D^0 {\bar{D}}^0$ mass distribution in the decay drastically different than phase space. The rates obtained are relatively large and the experiment is easily feasible in the present BESIII facility. The performance of this experiment could provide an answer to the issue of this much searched for state, which is the analogue of the $$f_0(980)$$ resonance.