Higher excitations of the $D$ and $D_s$ mesons

Abstract

The masses of higher $D(nL)$ and $D_s(nL)$ excitations are shown to decrease due to the string contribution, originating from the rotation of the QCD string itself: it lowers the masses by 45 MeV for $L=2(n=1)$ and by 65 MeV for $L=3(n=1)$. An additional decrease $\sim 100$ MeV takes place if the current mass of the light (strange) quark is used in a relativistic model. For $D_s(1{}^3{D}_3)$ and $D_s(2P_1^H)$ the calculated masses agree with the experimental values for $D_s(2860)$ and $D_s(3040)$, and the masses of $D(2{}^1{S}_0)$, $D(2{}^3{S}_1)$, $D(1{}^3{D}_3)$, and $D(1D_2)$ are in agreement with the new BaBar data. For the yet undiscovered resonances we predict the masses $M(D(2{}^3{P}_2))=2965$ MeV, $M(D(2{}^3{P}_0))=2880$ MeV, $M(D(1{}^3{F}_4))=3030$ MeV, and $M(D_s(1{}^3{F}_2))=3090$ MeV. We show that for $L=2,3$ the states with $j_q=l+1/2$ and $j_q=l-1/2$ ($J=l$) are almost completely unmixed ($\varphi \simeq -1^{\circ }$), which implies that the mixing angles $\theta$ between the states with S=1 and S=0 ($J=L$) are $\theta \approx 40^{\circ }$ for L=2 and $\approx 42^{\circ }$ for L=3.

Comments: 22 pages, no figures, 4 tables Two references and corresponding discussion added