Abstract
We compute the hadronic matrix element relevant to the physical radiative decay $\eta_{c}(2S)\to J/\psi\gamma$ by means of lattice QCD. We use the (maximally) twisted mass QCD action with Nf=2 light dynamical quarks and from the computations made at four lattice spacings we were able to take the continuum limit. The value of the mass ratio $m_{\eta_c(2S)}/m_{\eta_c(1S)}$ we obtain is consistent with the experimental value, and our prediction for the form factor is $V^{\eta_{c}(2S)\to J/\psi\gamma}(0)\equiv V_{12}(0)=0.32(6)(2)$, leading to $\Gamma(\eta_c (2S) \to J/\psi\gamma) = (15.7\pm 5.7)$ keV, which is much larger than $\Gamma(\psi (2S) \to \eta_c\gamma)$ and within reach of modern experiments.
Highlights
JHEP05(2015)014 non-relativistic QCD [12], lead to a very good agreement with lattice QCD results [13]
In this study, we focus on a subset of gauge field configurations considered in ref. [10] and study one value of the light sea quark mass per lattice spacing but we increase the statistics in order to be able to isolate the radially excited state from our correlation functions
In ref. [10] we showed that for the range of sea quark masses used in our simulation at β = 3.90 the results for the hyperfine splitting and the J/ψ → ηcγ form factor remain unchanged whether L = 24 or L = 32. (ii) In ref. [10] we showed that V11(0) remain independent on the sea quark mass. (iii) Our simulations are made with Nf = 2 dynamical light (u and d) quarks and the effects of the other sea quarks (s and c) contributing the QCD vacuum fluctuations is expected to be small
Summary
The hadronic matrix element governing the radiative decay ηc(2S) → J/ψγ∗ decay can be parameterized in terms of the form factor V12(q2) as,. In our previous paper we showed that the charmonium decays J/ψ → + − and J/ψ → ηcγ do not depend on the sea quark mass. [10] and study one value of the light sea quark mass per lattice spacing but we increase the statistics in order to be able to isolate the radially excited state from our correlation functions. We rely on the gauge field configurations produced by the ETM Collaboration [24, 25] in which the effect of Nf = 2 mass-degenerate dynamical light quarks has been included by using the maximally twisted QCD on the lattice [23]. Using the same action we compute the quark propagators and correlation functions needed for the physical problem discussed in this paper. Details concerning the lattice ensembles and the main results of this paper are listed in table 1
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