The Light-Cone Fock State Expansion and QCD Phenomenology

Abstract

The concept of the “number of constituents” of a relativistic bound state, such as a hadron in quantum chromodynamics, is not only frame-dependent, but its value can fluctuate to an arbitrary number of quanta. Thus when a laser beam crosses a proton at fixed “light-cone” time τ = 3Dt + z/c = 3Dx ⁰ + x ^z, an interacting photon can encounter a state with any given number of quarks, anti-quarks, and gluons in flight (as long as n _q - n _q̄ = 3D3). The probability amplitude for each such n-particle state of on-mass shell quarks and gluons in a hadron is given by a light-cone Fock state wavefunction ${\Psi _{n/H}}({x_i}{\overrightarrow {,k} _{ \bot \iota }},\lambda )$ , where the constituents have longitudinal light-cone momentum fractions

$${x_i} = 3D\frac{{k_i^ + }}{{{p^ + }}} = 3D\frac{{{k^0} + k_i^x}}{{{p^0} + {p^z}}},\sum\limits_{i = 3D1}^n {{x_i} = 3D1} $$

((1))

relative transverse momentum

$${\overrightarrow k _{ \bot \iota }},\sum\limits_{i = 3D1}^n {{{\overrightarrow k }_{ \bot \iota }}} = 3D{\overrightarrow 0 _ \bot }$$

((2))

and helicities λ _i . The ensemble {ψ _n/H } of such hght-cone Fock wavefunctions is a key concept for hadronic physics, providing a conceptual basis for representing physical hadrons (and also nuclei) in terms of their fundamental quark and gluon degrees of freedom.[1]

Work supported by the Department of Energy, contract DE-AC03-76SF00515.