Lattice study of form factors for charmonium
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Regular Article - Theoretical Physics
Lattice study of form factors for charmonium Ning Lia , Chao-Chen Liu, Ya-Jie Wu School of Science, Xi’an Technological University, Xi’an 710032, People’s Republic of China
Received: 2 June 2020 / Accepted: 13 September 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Communicated by William Detmold
Abstract Form factors for ηc and χc0 have been simulated based on N f = 2 Twisted Mass Lattice Quantum Chromodynamics (Lattice QCD) gauge configurations. We construct particle interpolation operators by variational method that can significantly improve signal-to-noise ratio of correlation functions. We apply twisted boundary conditions to compute corresponding correlation functions which make us obtain form factors with more small four-momentum transfer. Furthermore, we fit charge radius for ηc and χc0 , respectively. The results obtained in this simulation could be considered as a ground test to calculate branch ratio decay width of χc0,1,2 → γ J/ψ on lattice in future.
1 Introduction Charmonium Physics has been considered as an ideal research topics to precisely test Quantum Chromodynamics(QCD) since they are in the intermediate energy scale of Quantum Chromodynamics, where both perturbative and nonperturbative effect are present. Until now, Lattice QCD defined on discrete Euclidean space-time provides a best framework to study non-perturbative QCD. Through the simulation of corresponding correlation functions and suitable extrapolations, one can readily extract physical quantities [1,2]. In theories, studying radiative transitions between various charmonium states is particularly interesting in charmonium physics. Since most charmonium ground states lie ¯ and the suppression below the threshold of hadron states D D, of Okubo-Zweig-Iizuka (OZI) rule exist, these charmonium states usually have rather narrow widths. Therefore, radiative decays among charmonium mesons become the dominant decay modes. Thus, precisely studying radiative transitions
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between charmonium states is an important way to explore the internal structure of heavy quark bound state [3,4]. In experiments, to further explore the physical properties of charmonium-like, exotic and hybrid states, BESIII collaboration will precisely measure quantities for radiative decay modes from Ψ (3686). In particular, the expected sensitivity on branching fraction for χc0,1,2 → γ J/ψ reaches 1 × 10−6 [5]. Thus, studying radiative transitions between χc0,1,2 and the vector mesons in theory is of great significance. However, it is difficult to create χc0,1,2 from vacuum on lattice since that they are nearly degenerate P-wave states. In the previous study, we have used variational method to calculate two-photon decay width of ηc and χc0 , where the overlap between particle state and vacuum state is significantly enhanced and the signal-to-noise ratio of correlation functions is well improved [6]. In this si
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