Conformal Symmetry as a Template: Commensurate Scale Relations and Physics Renormalization Schemes

Commensurate scale relations are perturbative QCD predictions which relate observable to observable at fixed relative scale, such as the "generalized Crewther relation", which connects the Bjorken and Gross-Llewellyn Smith deep inelastic scattering sum rules to measurements of the e+ e- annihilation cross section. We show how conformal symmetry provides a template for such QCD predictions, providing relations between observables which are present even in theories which are not scale invariant. All non-conformal effects are absorbed by fixing the ratio of the respective momentum transfer and energy scales. In the case of fixed-point theories, commensurate scale relations relate both the ratio of couplings and the ratio of scales as the fixed point is approached. In the case of the $\alpha_V$ scheme defined from heavy quark interactions, virtual corrections due to fermion pairs are analytically incorporated into the Gell-Mann Low function, thus avoiding the problem of explicitly computing and resumming quark mass corrections related to the running of the coupling. Applications to the decay width of the Z boson, the BFKL pomeron, and virtual photon scattering are discussed.Comment: 27 pages, Talk presented at the Les Rencontres de Physique de la Vallee d'Aoste, La Thuile, Italy, February 28-March 6, 199

Rapidity Gaps in DIS through Soft Colour Interactions

We present a new mechanism for the creation of large rapidity gaps in DIS events at HERA. Soft colour interactions between perturbatively produced partons and colour-charges in the proton remnant, modifies the colour structure for hadronization giving colour singlet systems that are well separated in rapidity. An explicit model is presented that, although the detailed results depend on the initial state parton emission, can describe both the observed rapidity gaps and, in addition, the forward energy flow in an inclusive event sample.Comment: 4 pages Latex, 4 encapsulated Postscript figures, uses qcdparis.sty, tar-compressed and uuencoded with uufiles, Presented by GI at workshop `DIS and QCD', Paris, April 1995, minor Postscript problem fixe

Odderon-Pomeron Interference

We show that the asymmetry in the fractional energy of charm versus anticharm jets produced in high energy diffractive photoproduction is sensitive to the interference of the Odderon $(C = -)$ and Pomeron $(C = +)$ exchange amplitudes in QCD. We predict the dynamical shape of the asymmetry in a simple model and estimate its magnitude to be of the order 15% using an Odderon coupling to the proton which saturates constraints from proton-proton vs. proton-antiproton elastic scattering. Measurements of this asymmetry at HERA could provide firm experimental evidence for the presence of Odderon exchange in the high energy limit of strong interactions.Comment: 12 pages, 4 figures, Minor corrections, Main results unchanged, Contribution from photon exchange added, Numerical estimates updated and uncertainties clarified. To appear in Physics Letters

Disentangling running coupling and conformal effects in QCD

We investigate the relation between a postulated skeleton expansion and the conformal limit of QCD. We begin by developing some consequences of an Abelian-like skeleton expansion, which allows one to disentangle running-coupling effects from the remaining skeleton coefficients. The latter are by construction renormalon-free, and hence hopefully better behaved. We consider a simple ansatz for the expansion, where an observable is written as a sum of integrals over the running-coupling. We show that in this framework one can set a unique Brodsky-Lepage-Mackenzie (BLM) scale-setting procedure as an approximation to the running-coupling integrals, where the BLM coefficients coincide with the skeleton ones. Alternatively, the running-coupling integrals can be approximated using the effective charge method. We discuss the limitations in disentangling running coupling effects in the absence of a diagrammatic construction of the skeleton expansion. Independently of the assumed skeleton structure we show that BLM coefficients coincide with the conformal coefficients defined in the small $\beta_0$ (Banks-Zaks) limit where a perturbative infrared fixed-point is present. This interpretation of the BLM coefficients should explain their previously observed simplicity and smallness. Numerical examples are critically discussed.Comment: 38 pages; Revised version (to appear in PRD); includes modifications of section 3 and an added section 4. Sections 6 and 7 of the original version have been extracted and will be published separatel

Scheme-Independent Predictions in QCD: Commensurate Scale Relations and Physical Renormalization Schemes

Commensurate scale relations are perturbative QCD predictions which relate observable to observable at fixed relative scale, such as the ``generalized Crewther relation", which connects the Bjorken and Gross-Llewellyn Smith deep inelastic scattering sum rules to measurements of the $e^+ e^-$ annihilation cross section. All non-conformal effects are absorbed by fixing the ratio of the respective momentum transfer and energy scales. In the case of fixed-point theories, commensurate scale relations relate both the ratio of couplings and the ratio of scales as the fixed point is approached. The relations between the observables are independent of the choice of intermediate renormalization scheme or other theoretical conventions. Commensurate scale relations also provide an extension of the standard minimal subtraction scheme, which is analytic in the quark masses, has non-ambiguous scale-setting properties, and inherits the physical properties of the effective charge $\alpha_V(Q^2)$ defined from the heavy quark potential. The application of the analytic scheme to the calculation of quark-mass-dependent QCD corrections to the $Z$ width is also reviewed.Comment: LaTex, 21 page

Rapidity Gaps from Colour String Topologies

Diffractive deep inelastic scattering at HERA and diffractive W and jet production at the Tevatron are well described by soft colour exchange models. Their essence is the variation of colour string-field topologies giving both gap and no-gap events, with a smooth transition and thereby a unified description of all final states.Comment: 3 pages, 6 eps figures, contribution to the DIS 99 workshop proceedings, uses npb.st

Soft Colour Interactions in Non-perturbative QCD

Improved understanding of non-perturbative QCD dynamics can be obtained in terms of soft colour exchange models. Their essence is the variation of colour string-field topologies giving a unified description of final states in high energy interactions. In particular, both events with and without large rapidity gaps are obtained in agreement with data from ep at HERA and ppbar at the Tevatron, where also the surprisingly large production rate of high-p_T charmonium and bottomonium is reproduced.Comment: 4 pages, contribution to PANIC 99 conference proceedings, to appear in Nucl. Phys. A. Uses espcrc1.st