PerturbativeO(αs)corrections to the correlation functions of light tetraquark currents

Abstract

We calculate the next-to-leading-order QCD corrections to the perturbative term in the operator product expansion of the spectral functions of light tetraquark currents. By using also configuration-space methods we keep the momentum-space four-loop calculation to a manageable level. We find that the next-to-leading-order corrections to the perturbative term are large and can amount to O(100%). The corrections to the corresponding Borel sum rules, however, are small since the nonperturbative condensate contributions dominate the Borel sum rules.

Analysis of the scalar nonet mesons with QCD sum rules

“…QCD sum rules provides a powerful theoretical tool in studying the hadronic properties, and has been applied extensively to study the masses, decay constants, hadronic form-factors, coupling constants, etc [12,13]. There have been several works on the light tetraquark states using the QCD sum rules [14,15,16,17,18,19,20,21,22]. In Refs.…”

“…We take the truncations n ≤ 10 and k ≤ 1, the operators of the orders O(α k s ) with k > 1 are discarded. Furthermore, we take into account the O(α s ) corrections to the perturbative terms, which were calculated recently [40]. As there are normalization factors qq 2 in the correlation functions 22 S ( p) , we count those perturbative terms as of the order qq 2 , and we truncate the operator product expansion to the order qq 2 q q , where q, q = u, d, s.…”

“…[19][20][21]. There have been several works on the light tetraquark states using the QCD sum rules [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. In Refs.…”

Next-to-Leading Order (NLO) Perturbative Effects in QCD Sum-Rule Analyses of Light Tetraquark Systems: A Case Study in the Scalar-Isoscalar Channel

“…[23] and the NLO contributions were calculated in the chiral limit for the MS scheme with renormalization scale µ in Ref. [22]. 1 The NLO perturbative contributions in (15) imply that ρ(s) satisfies an inhomogeneous renormalizationgroup (RG) equation containing an anomalous-dimension term γ ρ…”

“…[21] for discussion of the non-factorizable contributions). However, in lightquark systems exact calculations of NLO perturbative effects have been performed for scalar-isoscalar σ currents with tetraquark (i.e., diquark-antidiquark) composition [22]. For the optimized σ currents identified in the comprehensive LO sum-rule analysis [23], the NLO effects are surprisingly large [22] indicating slow perturbative convergence of the QCD correlation function, motivating a detailed study comparing the LO and NLO QCD sum-rule analyses and mass estimates for these systems.…”