Solving QCD via multi-Regge theory. Page: 4 of 13
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1 Introduction
The QCD pomeron is usually discussed without much attention paid to the
scattering states. States containing only elementary constituents are normally
considered. As a matter of principle, a full solution of QCD at high-energy
requires that we find both the true hadronic states and the exchanged pomeron
giving scattering amplitudes. Unitarity must be satisfied in both the s-channel
and the t-channel.
Experimentally the pomeron appears, approximately, to be a Regge pole at
small Q2 and1 a single gluon at larger Q2. Neither property is present in QCD
perturbation theory. In the high-energy, transverse momentum cut-off, "solu-
tion" of QCD that I outline in this talk the experimental "non-perturbative
properties" of the pomeron are directly related to the confinement and chiral
symmetry breaking properties of hadrons. That is, experimental properties of
the pomeron are directly related to special properties of the scattering states.
It is particularly interesting that our solution may only be applicable to QCD
with a very special quark content.1
Our arguments involve the techniques of multi-regge QCD calculations,
the dynamics of the massless quark U(1) anomaly, which will be the main
focus of this talk, and reggeon field theory phase-transition analysis, which we
will avoid almost completely. Our results show' how confinement and chiral
symmetry breaking, normally understood as consequences of the vacuum, can
instead be produced by a "wee-parton" distribution. This is a very non-trivial
property that provides, I hope, a deeper basis for the parton model (and even4
the constituent quark model) in QCD !
Multi-Regge Theory is an abstract formalism' that we developed a major
part of in the 70's. The formalism is based on the existence of asymptotic
analyticity domains for multiparticle amplitudes derived 5,6 via "Axiomatic
Field Theory" and "Axiomatic S-Matrix Theory". All the assumptions made
are expected to be valid in a completely massive spontaneously-broken gauge
theory. Since we begin with massive reggeizing gluons, this is effectively the
starting point for our analysis of QCD.
For our purposes, the most important component of multi-regge theory is
the reggeon unitarity equations ',. Using these equations, well-known Regge
limit QCD calculations 8,9,10 can be extended to obtain amplitudes, of the
form illustrated in Fig. 1, involving multiple exchanges of reggeized gluons and
quarks in a variety of channels. The central idea of our work is that we can,
tIn general our work leads us to doubt very strongly that "We now know that there are an
infinite number of consistent S-Matrices that satisfy all the sacred principles. ... any gauge
group, and many sets of ferrmions"21
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White, A. R. Solving QCD via multi-Regge theory., article, November 4, 1998; Illinois. (https://digital.library.unt.edu/ark:/67531/metadc621067/m1/4/: accessed April 20, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.