Gauge theory high-energy behavior from j-plane unitarity

Corianò, Claudio; White, Alan R.

doi:10.1016/0550-3213(95)00129-8

Cited by 7 publications

(3 citation statements)

References 35 publications

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“…All these aspects show that also the next less singular terms need to be calculated, despite the enormous work that has been carried out so far to derive the resummed anomalous dimensions and coefficient functions [4,[8][9][10]48,49], before firm conclusions on the small-x evolution of singlet structure functions can be drawn. Since contributions which are even less singular than these ones may, even then cause relevant corrections, it appears indispensable to compare the corresponding results to those of future complete fixed-order calculations.…”

Section: Discussionmentioning

confidence: 99%

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The evolution of unpolarized singlet structure functions at smallx

Blümlein¹,

1998

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A systematic study is performed of the impact of the various resummed small-x contributions to the anomalous dimensions and coefficient functions on the evolution of unpolarized structure functions in deep-inelastic scattering. The proton structure functions F p 2 and F p L as well as the photon structure function F γ 2 are considered together with the corresponding parton densities. The general analytic solution of the evolution equations in Mellin-N space is derived, and different approximate solutions are compared. Potential effects of less singular small-x terms in the anomalous dimension and coefficient functions are discussed.

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Section: Discussionmentioning

confidence: 99%

“…The contributions ∝ N f [9,[46][47][48] and the energy-scale independent terms ∝ C A [10,47] of γ gg,NL (N, α s ), cf. also [49], have been calculated recently. As shown in ref.…”

Section: Next-order Correctionsmentioning

confidence: 99%

The evolution of unpolarized singlet structure functions at smallx

Blümlein¹,

1998

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“…We conjecture that this pattern may extend to even higher point functions when the external mass invariants are separated from the remaining invariants scalar products of 2 different momenta. It seems clear that such factorized ansätze capture the essential behaviour of these correlators in some special kinematical limits, as it has been long known in the case of the Regge limit even at next-to-leading order in the gauge coupling, using conformal methods of t-channel unitarity [34,35,36,37]. In all these cases the CFT constraints provide rather simple predictions compared to the explicit NLO computations performed in QCD, with new partial waves appearing at NLO in the conformal reconstruction of the evolution (BFKL) kernel at the same order.…”

Section: Approximate Conformal Solutions Of Primary Operators and The...mentioning

confidence: 99%

On some hypergeometric solutions of the conformal Ward identities of scalar 4-point functions in momentum space

Corianò

Maglio

2019

J. High Energ. Phys.

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We discuss specific hypergeometric solutions of the conformal Ward identities (CWI's) of scalar 4-point functions of primary fields in momentum space, in d spacetime dimensions. We determine such solutions using various dual conformal ansätze (DCA's). We start from a generic dual conformal correlator, and require it to be conformally covariant in coordinate space. The two requirements constrain such solutions to take a unique hypergeometric form. They describe correlators which are at the same time conformal and dual conformal in any dimension. These specific ansätze also show the existence of a link between 3-and 4-point functions of a CFT for such class of exact solutions, similarly to what found for planar ladder diagrams. We show that in d = 4 only the box diagram and its melonic variants, in free field theory, satisfies such conditions, the remaining solutions being nonperturbative. We then turn to the analysis of some approximate high energy fixed angle solutions of the CWI's which also in this case take the form of generalized hypergeometric functions. We show that they describe the behaviour of the 4-point functions at large energy and momentum transfers, with a fixed −t/s. The equations, in this case, are solved by linear combinations of Lauricella functions of 3 variables and can be rewritten as generalized 4K integrals. In both cases the CWI's alone are sufficient to identify such solutions and their special connection with generalized hypergeometric systems of equations.Using the definitons above, each equation can be characterized in terms of the set of operators

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Scale-invariant O(g4) Lipatov kernels at non-zero momentum transfer

1996

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We summarize recent work on the evaluation of the scale invariant next-toleading order Lipatov kernel, constructed via transverse momentum diagrams. At zero momentum transfer the square of the leading-order kernel appears together with an additional component, now identified as a new partial-wave amplitude, having a separate, holomorphically factorizable, spectrum. We present a simplified expression for the full kernel at non-zero momentum transfer and give a complete analysis of its infrared properties. We also construct a nonforward extension of the new amplitude which is infra-red finite and satifies Ward identity constraints. We conjecture that this new kernel has the conformal invariance properties corresponding to the holomorphic factorization of the forward spectrum. * Work supported by the U.S. Department of Energy, Division of High Energy Physics, † coriano@phys.ufl.edu + parwani@iopb.ernet.in # arw@hep.anl.gov A BRIEF OVERVIEWThe Regge limit of QCD has recently undergone a considerable revival of interest. The small-x behaviour of the parton distributions observed at HERA, characterized by a strong rise of the gluon density, and the detection of diffractive hard scattering events in DIS, both provide motivation for developing a better understanding of the Regge regime of QCD. Because of the overlap of the small-x and Regge limits, it is natural to expect that the theoretical tools developed in the past in the analysis of Regge theory are useful also at small-x. Properties of the "exchanged reggeon singularities" can be constructed from perturbation theory, by resumming the leading log 1/x and/or logQ 2 behaviour. Resummation is achieved in various possible ways, but it is widely anticipated that the BFKL evolution equation [1], first derived more than 20 years ago, plays a crucial role in describing the physical properties of the leading "Pomeron" singularity.The crucial ingredient in the "construction" of the BFKL Pomeron is the kernel of the evolution equation, its spectrum and its leading eigenvalue. Both forward (q = 0) and non-forward (q = 0) versions of the lowest order (O(g 2 )) kernel are known. Conformal partial waves diagonalize the O(g 2 ) equation at non zero q, since the equation is invariant under special conformal transformations, and in the limit of q → 0 reproduce the well known eigenfunctions, and eigenvalues of the BFKL parton (or forward) kernel. A necessary condition for the conformal invariance of the equation is the property of holomorphic factorization of the eigenvalues of the parton kernel.Most analyses of the BFKL equation involve only the O(g 2 ) kernel and its related properties of conformal invariance. It is, of course, important to see how radiative corrections affect the leading order evolution. It is expected that renormalization effects will introduce a running of the coupling and will spoil conformal invariance. The direct evaluation of next-to-leading-order(NLO) contributions to this equation requires both a calculation of the correction to the Regge traject...

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Gauge theory high-energy behavior from j-plane unitarity

Cited by 7 publications

References 35 publications

The evolution of unpolarized singlet structure functions at smallx

The evolution of unpolarized singlet structure functions at smallx

On some hypergeometric solutions of the conformal Ward identities of scalar 4-point functions in momentum space

Scale-invariant O(g4) Lipatov kernels at non-zero momentum transfer

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