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Generalized bootstrap equations and possible implications for the NLO odderon

  • Regular Article - Theoretical Physics
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Abstract

We formulate and discuss generalized bootstrap equations in nonabelian gauge theories. They are shown to hold in the leading logarithmic approximation. Since their validity is related to the self-consistency of the Steinmann relations for inelastic production amplitudes they can be expected to be valid also in NLO. Specializing to the N=4 SYM, we show that the validity in NLO of these generalized bootstrap equations allows to find the NLO odderon solution with intercept exactly at one, a result which is valid also for the planar limit of QCD.

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Notes

  1. We define \(\mathop {\mathit {disc}}\nolimits _{x} f(x) = \frac{1}{2i} (f(x+i\epsilon) - f(x-i\epsilon))\).

  2. The notion ‘amputated’ refers to the transverse momentum propagators of the reggeized gluons. Our function D 2(k 1,k 2,q;ω) includes, for the outgoing reggeons, a reggeon denominator 1/(ω−ω(k 1)−ω(k 2)).

  3. In all our figures, the kernels are acting on wave functions to the left (sign of arrows) whereas in our formulas operators are acting on wave functions on the right.

  4. From now on we will use superscripts (0) and (1) for distinguishing between LO and NLO quantities.

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Acknowledgements

One of us, J.B., gratefully acknowledges the hospitality of the INFN Section of Bologna where most of this work has been done.

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Authors and Affiliations

  1. II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761, Hamburg, Germany

    J. Bartels

  2. INFN Sezione di Bologna, via Irnerio 46, 40126, Bologna, Italy

    G. P. Vacca

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  1. J. Bartels
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  2. G. P. Vacca
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Correspondence to G. P. Vacca.

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Bartels, J., Vacca, G.P. Generalized bootstrap equations and possible implications for the NLO odderon. Eur. Phys. J. C 73, 2602 (2013). https://doi.org/10.1140/epjc/s10052-013-2602-8

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  • DOI: https://doi.org/10.1140/epjc/s10052-013-2602-8

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