mainly spin triplet has $j_q=l-{1\over 2}$ and is labelled with a prime [@Cahn:2003cw]. For $L=2$ the HQL gives rise to two doublets, $j_q=3/2$ and $j_q=5/2$ with $\theta_{D}=-\tan^{-1}(\sqrt{2/3})=-39.2^\circ$ where the minus sign arises from our $c\bar{s}$ convention [@Cahn:2003cw; @Zhang:2009nu; @DiPierro:2001uu; @Colangelo:2006rq; @Colangelo:2007ds; @Chen:2009zt; @Chen:2011rr]. In some approaches it is more natural to use the $j-j$ basis but because we solve our Hamiltonian equations assuming $L-S$ eigenstates and then include the $LS$ mixing we use the notation of eqn. \[eqn:mixing\]. It is straightforward to transform between the $L-S$ basis and the $j-j$ basis [@Cahn:2003cw]. We also note that the definition of the mixing angles is frought with ambiguities and one should be extremely careful comparing predictions from different publications [@barnes].

Strong Decays
-------------

We calculate decay widths using the pseudoscalar emission model (see Ref. [@godfrey85xj] and references therein). There are a number of predictions for $D_s$ decay widths in the literature using the $^3P_0$ model [@Close:2005se; @Close:2006gr; @Zhang:2006yj; @Li:2009qu; @Li:2010vx; @Yuan:2012ej] and other models [@Colangelo:2006rq; @Colangelo:2007ds; @Zhong:2009sk; @DiPierro:2001uu; @Chen:2011rr]. A weakness of the pseudoscalar emission model is that it can only calculate partial widths that include light (non-charm) pseudoscalar mesons in the final state. For a few states that we consider, decays 