Light scalar quarkonia from QCD Laplace sum rule at higher order

Abstract: We review our estimations on the light scalar $\bar{q}q$, $(\bar{q}q')(\bar{q'}q)$ and $\overline{qq'}qq'$ ($q,q'\equiv u,d,s$) states from relativistic Laplace sum rule (LSR) within stability criteria and including higher order perturbative (PT) corrections up to the (estimated) N5LO. We evaluate the QCD spectral functions at Lowest Order (LO) of PT QCD and up to the $D=6$ dimension of quark and gluon condensates. Using stability criteria and the constraint: Pole contribution is larger than the QCD continuum one ($R_{P/C}\geqslant 1$) our results exclude an on-shell mass around $(500-600)$ MeV obtained for values of the QCD continuum threshold $t_c \leqslant(1\sim 1.5)$ GeV$^2$. The complete results for the different scalar states are given in Tables 1 to 3. We conclude from the complete analysis that the assignement of the nature of the scalar mesons is not crystal clear and needs further studies.