other calcuations where the widths shown here used the observed $D_{s1}^*$ and $D_{sJ}^*$ masses. For the $D$-wave states we find that there are two narrow and two broad states corresponding to the $j=5/2$ and $3/2$ doublets of the $m_Q\to \infty$ limit which are composed of the $(3^-, 2^-)$ and $(2^-, 1^-)$ states respectively. The $j=5/2$ states are narrower due to the higher angular momentum barrier. This pattern is similar to what is expected and observed for the $P$-waves states [@Rosner:1985dx; @Godfrey:1986wj; @Godfrey:2005ww]. This may be an important piece of the puzzle which we will return to in the next section.

  ----------------------- ------------------------------ ----------------------------------------------------------------------- ---------- -------
  State                   Decay                          Amplitude                                                                 Width     Width
                                                                                                                                   (MeV)     (MeV)
  $D_s^*(2^3S_1)(2732)$   $D_s^*(2^3S_1)\to DK$          $-i \sqrt{2\over{81}} \; \widetilde{P}_{c\bar{s}} $                         13       12
                          $D_s^*(2^3S_1)\to D^*K$        $ -i \sqrt{4\over{81}} \; \widetilde{P}_{c\bar{s}} $                        13       12
                          $D_s^*(2^3S_1)\to D_s\eta$     $ +i \sqrt{1\over{162}} \; \widetilde{P}_{c\bar{s}} $                      1.7       1.4
                          $D_s^*(2^3S_1)\to D_s^*\eta$   $+i \sqrt{1\over{81}} \; \widetilde{P}_{c\bar{s}} $                        0.7       0.4
  $D_s(2^1S_0)(2673)$     $D_s(2^1S_0)\to D^*K$          $ +i \sqrt{2\over{27}} \; \widetilde{P}_{c\bar{s}}$                         13     
                          $D_s(2^1S_0)\to D_s^*\eta$     $ -i \sqrt{1\over{54}} \; \widetilde{P}_{c\bar{s}} $                       0.1     
  $D_s^*(1^3D_3)(2917)$   $D_s^*(1^3D_3)\to DK$          $+i \sqrt{1\over{35}} \; \widetilde{A}_{c\bar{s}} $                         27       19
                          $D_s^*(1^3D_3)\to D^*K$        $+i \sqrt{4\over{105}} \; \widetilde{A}_{c\bar{s}} $                        13        8
                          $D_s^*(1^3D_3)\to D_s\eta$     $-i \sqrt{1\over{140}} \; \widetilde{A}_{c\bar{s}} $                       2.7       1.6
                          $D_s^*(1^3D_3)\to D_s^*\eta$   $-i 