D-wave excited tetraquark states with and *

Abstract We study the mass spectra of D -wave excited tetraquark states with J^{PC}=1^{++} and 1^{+-} in both symmetric \mathbf{6}_{cs}\otimes\bar{\mathbf{6}}_{\bar{c}\bar{s}} antisymmetric \bar{\mathbf{3}}_{cs}\otimes\mathbf{3}_{\bar{c}\bar{s}} color configurations using QCD sum rule method. construct diquark-antidiquark type interpolating currents various excitation structures $(L_\lambda,L_\rho\{l_{\rho_1},l_{\rho_2}\})=(2,0\{0,0\}),\,(1,1\{1,0\}),\,(1,1\{0,1\}),\,(0,2\{1,1\}),\,(0,2\{2,0\}),\,(0,2\{0,2\})$?> . Our results support interpretation recently observed X(4685) resonance as a state (2,0\{0,0\}) or (0,2\{2,0\}) mode, although some other possible cannot be excluded exhaustively within theoretical errors. Moreover, our provide relations 6_{\rho\rho}<3_{\lambda\lambda}<3_{\lambda\rho}<3_{\rho\rho} 6_{\rho\rho}<3_{\lambda\lambda}<6_{\lambda\lambda}< 3_{\rho\rho} for positive negative \mathbb{C} -parity tetraquarks, respectively. suggest searching these tetraquarks hidden-charm channels J/\psi\phi \eta_c\phi , well open-charm such D_s\bar{D}_s^* D_{s}\bar{D}_{s1}^*