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SU(3)-symmetry breaking effects and mass splitting in scalar and pseudoscalar $D^{+}$ mesons from QCD sum rules

Motivated by the similar mass splitting in light-light and heavy-light meson system in $J^{P}=0^{-}$ and $J^{P}=0^{+}$ channel, taking into account the operator mixing to obtain an infrared stable OPE as well as a complete both non-perturbative and perturbative $\mathcal {O}(m_{q})$ corrections to the correlation function, the SU(3)-symmetry breaking effects in mass splitting in $0^{-}$ and $0^{+}$ channel of $D$ meson are analyzed by QCD sum rule approach based on a $c\bar{q}$ underlying structure. Within the sum rule we get, taking same threshold and Borel window for same channel, we find a correct mass splitting tendency in both channel which agrees with observed spectrum. We find $m_{D_{s}}-m_{D_{d}}\sim35\rm{MeV}$ in $0^{-}$ channel and $m_{D_{d}}-m_{D_{s}}\sim12\rm{MeV}$ in $0^{+}$ channel at scale $μ=1\rm{GeV}$. These splitting can be accommodated with the different role of combination of mass effects and the parity-dependent "force" induced from non-perturbative QCD vacuum. When we scale up to $μ=1.3\rm{GeV}$, the splitting remains unchanged which demonstrates a correct scale invariance. Combined with HQET, generalization to other channel of charmed meson and $b$-system are discussed briefly also.