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

TL;DR

This paper calculates the masses of higher $D$ and $D_s$ meson excitations, showing string effects lower their masses and providing predictions for undiscovered states, with results aligning well with existing experimental data.

Contribution

It introduces a model accounting for string contributions to meson masses and predicts masses of unobserved higher excitations, improving agreement with experimental findings.

Findings

String contributions lower meson masses by up to 65 MeV.

Predicted masses for undiscovered states: D(2 3P2)=2965 MeV, D(2 3P0)=2880 MeV.

States with different j_q are nearly unmixed, with specific mixing angles.

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 $D_s(1\,{}^3D_3)$ 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 $D(2\,{}^1S_0)$, $D(2\,{}^3S_1)$, $D(1\,{}^3D_3)$, and $D(1D_2)$ are in agreement with the new BaBar data. For the yet undiscovered resonances we predict the masses $M(D(2\,{}^3P_2))=2965$ MeV, $M(D(2\,{}^3P_0))=2880$ MeV, $M(D(1\,{}^3F_4))=3030$ MeV, and $M(D_s(1\,{}^3F_2))=3090$ 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 ($\phi\simeq -1^\circ$), 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.