Effects of Numerically Computed Next-to-Leading-Order Corrections on Light Tetraquark QCD Sum Rules

Abstract

Until the discovery of exotic hadrons containing more than three quarks in 2003, the experimental study of quarks was limited to the conventional three quark baryons and two quark mesons already studied extensively for most of the 20th century. Exotic hadrons provide new systems where the complexities of the strong interaction that governs the interaction of quarks and the gluons that they exchange can be studied. Of particular interest are tetraquarks consisting of four quarks/antiquarks. With the recent increase in experimental resources used for the detection of exotic hadrons, theoretical predictions must be as accurate as possible to compliment the experimental data. However, the extraction of physical predictions from quantum chromodynamics, the theory that describes the strong interaction, cannot be done exactly and often involves a series expansion which is typically only evaluated to leading-order. The effects of the higher order terms in the series (next-to-leading-order corrections) are unknown for most tetraquark states. Using the numerical integrator pySecDec, next-to-leading-order corrections are calculated for the light tetraquark with the exotic quantum numbers J^{PC}=0^{+-}. With applications to quantum chromodynamic sum rules (an established method for extracting particle masses and other properties from quantum chromodynamics), the size of the next-to-leading-order corrections are of the same order of magnitude as the leading-order results and are not small enough to be omitted. The size of the next-to-leading-order corrections will likely have a significant effect on a mass prediction obtained through quantum chromodynamic sum rules.