On the renormalization of operator products: the scalar gluonic case

We verify, both perturbatively and nonperturbatively asymptotically in the ultraviolet (UV), a special case of a low-energy theorem of the NSVZ type in QCD-like theories, recently derived in Phys. Rev. D 95 (2017) 054010, that relates the logarithmic derivative with respect to the gauge coupling, or the logarithmic derivative with respect to the renormalization-group (RG) invariant scale, of an npoint correlator of local operators in one side to an n + 1-point correlator with the insertion of Tr F 2 at zero momentum in the other side. Our computation involves the operator product expansion (OPE) of the scalar glueball operator, Tr F 2 , in massless QCD, worked out perturbatively in JHEP 1212 (2012) 119 -and in its RG-improved form in the present paper -by means of which we extract both the perturbative divergences and the nonperturbative UV asymptotics in both sides. We also discuss the role of the contact terms in the OPE, both finite and divergent, discovered some years ago in JHEP 1212 (2012) 119, in relation to the low-energy theorem. Besides, working the other way around by assuming the low-energy theorem for any 2-point correlator of a multiplicatively renormalizable gauge-invariant operator, we compute in a massless QCD-like theory the corresponding perturbative OPE to the order of g 2 and nonperturbative asymptotics. The low-energy theorem has a number of applications: to the renormalization in asymptotically free QCD-like theories, both perturbatively and nonperturbatively in the large-N 't Hooft and Veneziano expansions, and to the way the open/closed string duality may or may not be realized in the would-be solution by canonical string theories for QCD-like theories, both perturbatively and in the 't Hooft large-N expansion. Our computations will also enter further developments based on the low-energy theorem. (S) 1 (Eq. (3.6)) [11], which arises from performing the OPE in Eq. (1.3), that has been skipped in [3].Moreover, we extend the perturbative computation in [3] to the order of g 4 in Subsec. 4.2, including as well the divergent contact term to the order of g 4 in 1 We define in App. A what we mean by the universal UV asymptotics.-4 -

Section: Perturbative Ope Formentioning

confidence: 56%

Section: Plan Of the Papermentioning

confidence: 98%

Section: Plan Of the Papermentioning

confidence: 99%

“…The asymptotic equalities in the second lines of Eqs. that, according to [13], should be renormalized to zero.…”

Section: Order Of Gmentioning

confidence: 99%

Section: Low-energy Theorem and Perturbation Theorymentioning

confidence: 99%

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