Abstract
We consider the short-distance expansion of the product of two gluon field strength tensors connected by a straight-line-ordered Wilson line. The vacuum expectation value of this nonlocal operator is a common object in studies of the QCD vacuum structure, whereas its nucleon expectation value is known as the gluon quasi-parton distribution and is receiving a lot of attention as a tool to extract gluon distribution functions from lattice calculations. Extending our previous study [1], we calculate the three-loop coefficient functions of the scalar operators in the operator product expansion up to dimension four. As a by-product, the three-loop anomalous dimension of the nonlocal two-gluon operator is obtained as well.
Highlights
PreliminariesThe renormalization of Π⊥⊥(z) and Π ⊥(z) is determined by their respective anomalous dimension (AD), γ⊥⊥ and γ ⊥, which are currently known to two-loop accuracy [1, 23, 24]
JHEP05(2021)231 of heavy-quarkonium production [10] and decay [11]
The vacuum expectation value of this nonlocal operator is a common object in studies of the QCD vacuum structure, whereas its nucleon expectation value is known as the gluon quasi-parton distribution and is receiving a lot of attention as a tool to extract gluon distribution functions from lattice calculations
Summary
The renormalization of Π⊥⊥(z) and Π ⊥(z) is determined by their respective ADs, γ⊥⊥ and γ ⊥, which are currently known to two-loop accuracy [1, 23, 24]. We do not consider operators of mass dimension higher than four.1 Where Πm⊥⊥4 (z) and Πm⊥4(z) stand for the purely perturbative contributions expanded in the quark masses through order m4q. Where C⊥0 ⊥(z) and C0⊥(z) correspond to massless, purely perturbative contributions, which are known to two- and three-loop accuracy from refs. The new contribution of this work is the calculation of the CFs Cm⊥⊥2 , Cm⊥⊥4,di, Cm⊥⊥4,nd, C2⊥⊥, C1⊥⊥, Cm⊥2 , Cm⊥4,di, Cm⊥4,nd, C2⊥, C1⊥, and the ADs γ⊥⊥, γ ⊥ to three-loop accuracy
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