Derivation of Hadron Structure Functions from Quantum ChromoDynamics

Abstract

We solve a long-standing problem in particle physics: that of deriving the Deep Inelastic structure functions of the proton from the fundamental theory of strong interactions, Quantum ChromoDynamics (QCD). In the Bjorken limit, the momenta of the constituents of the proton (the partons) can be assumed to be in a two-dimensional plane in Minkowski space: a dimensional reduction of QCD to two space-time dimensions. Two dimensional QCD is then shown to be equivalent for all energies and values of number of colors \m{N} to a new theory of hadrons, Quantum HadronDynamics (QHD). The phase space of QHD is the Grassmannian (set of subspaces) of the complex Hilbert space L^2(R). The natural symplectic form along with a hamiltonian define a classical dynamical system, which is equivalent to the large N limit of QCD. 't Hooft's planar limit is the linear approximation to our theory: we recover his integral equation for the meson spectrum but also all the interactions of the mesons. The Grassmannian is a union of connected components labelled by an integer (the renormalized dimension of the subspace) which has the physical meaning of baryon number. The proton is the topological soliton: the minimum of the energy in the sector with baryon number one gives the structure functions of the proton. We solve the resulting integral equations numerically; the agreement with experimental data is quite good for values of the Bjorken variable x>0.2.