X(3872) in lattice QCD with exact chiral symmetry

Abstract

We investigate the mass spectrum of $1^{++}$ exotic mesons with quark content $(\stackrel{¸}{\text{q}}\text{cbar}\text{qbar})$, using molecular and diquark-antidiquark operators, in quenched lattice QCD with exact chiral symmetry. For the molecular operator $\{(\text{qbar}{\gamma }_i\stackrel{¸}{)}(\text{cbar}{\gamma }_5\text{q})-(\text{cbar}{\gamma }_i\text{q})(\text{qbar}{\gamma }_5\stackrel{¸}{)}\}$ and the diquark-antidiquark operator $\{({\text{q}}^{T}C\text{gi}\stackrel{¸}{)}(\text{qbar}C{\gamma }_5{\text{cbar}}^T)-(\text{qbar}C{\text{gi}}^T{\text{cbar}}^T)({\text{q}}^{T}C{\gamma }_5\stackrel{¸}{)}\}$, both detect a resonance with mass around $3890\pm 30$ MeV in the limit $m_q\to m_u$, which is naturally identified with $X(3872)$. Further, heavier exotic meson resonance with $J^{PC}=1^{++}$ is also detected, with quark content $(\stackrel{¸}{\text{s}}\text{cbar}\text{sbar})$ around $4100\pm 50$ MeV.

Comments: 11 pages, 6 figures, v2: eq.(6) has been corrected, 4-charm operators are omitted, and references are updated