Connections between deep-inelastic and annihilation processes at next-to-next-to-leading order and beyond

We have discovered 7 intimate connections between the published results for the radiative corrections, CK, to the Gross–Llewellyn Smith (GLS) sum rule, in deepinelastic lepton scattering, and the radiative corrections, CR, to the Adler function of the flavour-singlet vector current, in ee annihilation. These include a surprising relation between the scheme-independent single-electron-loop contributions to the 4-loop QED β-function and the zero-fermion-loop abelian terms in the 3-loop GLS sum rule. The combined effect of all 7 relations is to give the factorization of the 2-loop β-function in ∆S ≡ CKCR − 1 = β(as) as { S1CFas + [S2TFNF + SACA + SFCF]CFa 2 s } +O(as) , where as = αs(μ 2 = Q)/4π is the MS coupling of an arbitrary colour gauge theory, and S1 = − 21 2 + 12ζ3 ; S2 = 326 3 − 304 3 ζ3 ; SA = − 629 2 + 884 3 ζ3 ; SF = 397 6 + 136ζ3 − 240ζ5 specify the sole content of CK that is not already encoded in CR and β(as) = Q das/dQ 2 at O(as ). The same result is obtained by combining the radiative corrections to Bjorken’s polarized sum rule with those for the Adler function of the non-singlet axial current. We suggest possible origins of β in the ‘Crewther discrepancy’, ∆S, and determine ∆S/(β(as)/as), to all orders in NFas, in the large-NF limit, obtaining the entire series of coefficients of which S1 and S2 are merely the first two members. INR-820/93 OUT–4102–45 ) In memoriam Sergei Grigorievich Gorishny, 1958–1988 ) [email protected] ) [email protected]