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Register a new userSearching for the $X(3872)$ and $Z_c^+(3900)$ on HISQ lattices
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Song-haeng Lee
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We present preliminary simulation results for the I = 0 charmonium state $X(3872)(1^{++})$ and the I = 1 charmonium state $Z_c^+(3900)(1^{+-})$. The study is performed on gauge field configurations with 2+1+1 flavors of highly improved staggered sea quarks (HISQ) with clover (Fermilab interpretation) charm quarks and HISQ light valence quarks. Since the $X(3872)$ lies very close to the open charm $D bar D^*$ threshold, we use a combination of $bar c c$ and $D bar D^* + bar D D^*$ interpolating operators. For the $Z_c^+(3900)$ we use a combination of $J/psi pi$ and $D bar D^* + bar D D^*$ channels. This is the first such study with HISQ sea quarks and light valence quarks. To this end, we describe a variational method for treating staggered quarks that incorporates both oscillating and non-oscillating components.
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In this exploratory study, near-threshold scattering of $D$ and $bar{D}^*$ meson is investigated using lattice QCD with $N_f=2+1+1$ twisted mass fermion configurations. The calculation is performed within the coupled-channel Luschers finite-size formalism. The study focuses on the channel with $I^G(J^{PC})=1^+(1^{+-})$ where the resonance-like structure $Z_c(3900)$ was discovered. We first identify the most relevant two channels of the problem and the lattice study is performed within the two-channel scattering model. Combined with a two-channel Ross-Shaw theory, scattering parameters are extracted from the energy levels by solving the generalized eigenvalue problem. Our results on the scattering length parameters suggest that, at the particular lattice parameters that we studied, the best fitted parameters do not correspond to a peak behavior in the elastic scattering cross section near the threshold. Furthermore, within the zero-range Ross-Shaw theory, the scenario of a narrow resonance close to the threshold is disfavored beyond $3sigma$ level.
The decay $Z_c(3900)^pmtoomegapi^pm$ is searched for using data samples collected with the BESIII detector operating at the BEPCII storage ring at center-of-mass energies $sqrt{s}=4.23$ and $4.26$~GeV. No significant signal for the $Z_c(3900)^pm$ is found, and upper limits at the 90% confidence level on the Born cross section for the process $e^+e^-to Z_c(3900)^pmpi^mptoomegapi^+pi^-$ are determined to be $0.26$ and $0.18$ pb at $sqrt{s}=4.23$ and 4.26 GeV, respectively.
Assuming the newly observed $Z_c(3900)$ to be a molecular state of $Dbar D^*(D^{*} bar D)$, we calculate the partial widths of $Z_c(3900)to J/psi+pi;; psi+pi;; eta_c+rho$ and $Dbar D^*$ within the light front model (LFM). $Z_c(3900)to J/psi+pi$ is the channel by which $Z_c(3900)$ was observed, our calculation indicates that it is indeed one of the dominant modes whose width can be in the range of a few MeV depending on the model parameters. Similar to $Z_b$ and $Z_b$, Voloshin suggested that there should be a resonance $Z_c$ at 4030 MeV which can be a molecular state of $D^*bar D^*$. Then we go on calculating its decay rates to all the aforementioned final states and as well the $D^*bar D^*$. It is found that if $Z_c(3900)$ is a molecular state of ${1oversqrt 2}(Dbar D^*+D^*bar D)$, the partial width of $Z_c(3900)to Dbar D^*$ is rather small, but the rate of $Z_c(3900)topsi(2s)pi$ is even larger than $Z_c(3900)to J/psipi$. The implications are discussed and it is indicated that with the luminosity of BES and BELLE, the experiments may finally determine if $Z_c(3900)$ is a molecular state or a tetraquark.
The spin and parity of the $Z_c(3900)^pm$ state are determined to be $J^P=1^+$ with a statistical significance larger than $7sigma$ over other quantum numbers in a partial wave analysis of the process $e^+e^-to pi^+pi^-J/psi$. We use a data sample of 1.92 fb$^{-1}$ accumulated at $sqrt{s}=4.23$ and 4.26 GeV with the BESIII experiment. When parameterizing the $Z_c(3900)^pm$ with a Flatte-like formula, we determine its pole mass $M_textrm{pole}=(3881.2pm4.2_textrm{stat}pm52.7_textrm{syst})textrm{MeV}/c^2$ and pole width $Gamma_textrm{pole}=(51.8pm4.6_textrm{stat}pm36.0_textrm{syst})textrm{MeV}$. We also measure cross sections for the process $e^+e^-to Z_c(3900)^+pi^-+c.c.to J/psipi^+pi^-$ and determine an upper limit at the 90% confidence level for the process $e^+e^-to Z_c(4020)^+pi^-+c.c.to J/psipi^+pi^-$.
Using data samples collected with the BESIII detector operating at the BEPCII storage ring at center-of-mass energies from 4.178 to 4.600 GeV, we study the process $e^+e^-rightarrowpi^{0}X(3872)gamma$ and search for $Z_c(4020)^{0}rightarrow X(3872)gamma$. We find no significant signal and set upper limits on $sigma(e^+e^-rightarrowpi^{0}X(3872)gamma)cdotmathcal{B}(X(3872)rightarrowpi^{+}pi^{-}J/psi)$ and $sigma(e^+e^-rightarrowpi^{0}Z_c(4020)^{0})cdotmathcal{B}(Z_c(4020)^{0}rightarrow X(3872)gamma)cdotmathcal{B}(X(3872)rightarrowpi^{+}pi^{-}J/psi)$ for each energy point at $90%$ confidence level, which is of the order of several tenths pb.
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