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The main predictions include: (i) in the $\\Xi_{cc}$ and $\\Omega_{cc}$ family, the $1P~\\rho$ mode excitations with $J^P=1/2^-$ and $3/2^-$ should be the fairly narrow states. (ii) For the $1P~\\lambda$ mode excitations, $|^2P_{\\lambda}\\frac{3}{2}^-\\rangle$ and $|^4P_{\\lambda}\\frac{3}{2}^-\\rangle$ have a width of $\\Gamma\\sim150$ MeV, and mainly decay into the $J^P=3/2^+$ ground state. 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The main predictions include: (i) in the $\\Xi_{cc}$ and $\\Omega_{cc}$ family, the $1P~\\rho$ mode excitations with $J^P=1/2^-$ and $3/2^-$ should be the fairly narrow states. (ii) For the $1P~\\lambda$ mode excitations, $|^2P_{\\lambda}\\frac{3}{2}^-\\rangle$ and $|^4P_{\\lambda}\\frac{3}{2}^-\\rangle$ have a width of $\\Gamma\\sim150$ MeV, and mainly decay into the $J^P=3/2^+$ ground state. 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