Abstract
Recently, the short-distance asymptotics of the generating functional of n-point correlators of twist-2 operators in SU(N) Yang–Mills (YM) theory has been worked out in Bochicchio et al. (Phys Rev D 108:054023, 2023). The above computation relies on a basis change of renormalized twist-2 operators, where -γ(g)/β(g) reduces to γ0/(β0g) to all orders of perturbation theory, with γ0 diagonal, γ(g)=γ0g2+⋯ the anomalous-dimension matrix and β(g)=-β0g3+⋯ the beta function. The construction is based on a novel geometric interpretation of operator mixing (Bochicchio in Eur Phys J C 81:749, 2021), under the assumption that the eigenvalues of the matrix γ0/β0 satisfy the nonresonant condition λi-λj≠2k, with λi in nonincreasing order and k∈N+. The nonresonant condition has been numerically verified up to i,j=104 in Bochicchio et al. (Phys Rev D 108:054023, 2023). In the present paper we provide a number theoretic proof of the nonresonant condition for twist-2 operators essentially based on the classic result that Harmonic numbers are not integers. Our proof in YM theory can be extended with minor modifications to twist-2 operators in N=1 SUSY YM theory, large-N QCD with massless quarks and massless QCD-like theories.
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