Reggeon field theory and self duality: making ends meet
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Springer
Received: July Revised: September Accepted: September Published: October
27, 10, 24, 28,
2020 2020 2020 2020
Alex Kovner,a Eugene Levin,b,c Ming Lia and Michael Lublinskyd a
Physics Department, University of Connecticut, 2152 Hillside Road, Storrs, CT 06269, U.S.A. b Departemento de F´ısica, Universidad T´ecnica Federico Santa Mar´ıa, and Centro Cient´ıfico-Tecnol´ ogico de Valpara´ıso, Avda. Espana 1680, Casilla 110-V, Valpara´ıso, Chile c Department of Particle Physics, Tel Aviv University, Tel Aviv 69978, Israel d Physics Department, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: Motivated by the question of unitarity of Reggeon Field Theory, we use the effective field theory philosophy to find possible Reggeon Field Theory Hamiltonians HRF T . We require that HRF T is self dual, reproduce all known limits (dilute-dense and dilutedilute) and exhibits all the symmetries of the JIMWLK Hamiltonian. We find a family of Hamiltonians which satisfy all the above requirements. One of these is identical in form to the so called “diamond action” discussed in [67, 68]. However we show by explicit calculation that the so called “diamond condition” is not satisfied beyond leading perturbative order. Keywords: Perturbative QCD, Resummation, Effective Field Theories ArXiv ePrint: 2007.12132
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)185
JHEP10(2020)185
Reggeon field theory and self duality: making ends meet
Contents 1 Introduction
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2 The Reggeon Field Theory: scattering amplitudes and field algebra
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4 The dense-dilute limit
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5 Continuous symmetries 5.1 The vector SUV (N ) symmetry 5.2 Is SUL (N ) there?
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6 Is this the “Diamond action”?
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7 Discussion
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A Checking SUL (N ) A.1 [QaL , V¯L (x)] A.2 Checking [QaL , HRF T ] = 0
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1
Introduction
Reggeon Field Theory (RFT) of Quantum Chromodynamics (QCD) is a putative effective theory that is meant to describe scattering at asymptotically high energies. Development of this theory during the last three decades lead to understanding of many features of high energy scattering as well as phenomenological applications to HERA, RHIC and LHC data. Nevertheless, much work notwithstanding the theoretical framework of RFT is incomplete. The basic pre-QCD ideas of RFT go back to Gribov [1], who considered a very general picture and properties of high energy exchanges in a local field theory. These ideas have been adopted to QCD and furhter developed over the years in many works [2–39]. Direct derivation of some elements of RFT from QCD has been given. In particular the Hamiltonian of RFT that governs the evolution of physical scattering amplitudes with energy has been derived in two limits - the dilute-dilute limit, where both scattering objects (the projectile and the target) are considered to be small and perturbative (which we refer to
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