By Yuval Neeman
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Additional info for Algebraic Theory of Particle Physics: Hadron Dynamics in Terms of Unitary Spin Currents
6 Polarized partons and high-energy proton-proton collisions The parton model factorization arguments can be extended to include fragmentation processes, for example the production of a pion with large transverse momentum pt in high-energy proton-proton or lepton-proton collisions. 5in 48 bass THE SPIN STRUCTURE OF THE PROTON process of high pt pion production, pp → πX, shown in Fig. 4. One defines the fragmentation function Dfπ (z, µ2 ) as the probability density for a parton f to produce a pion in the final state with momentum fraction z of the parton f through hadronization.
Thus polarized proton-proton collisions with a centre of mass system (CMS) energy in the range of 50-500 GeV could be provided at RHIC, with an integrated luminosity of 320 pb−1 at 200 GeV and 800 pb−1 at 500 GeV. There are two major experiments pursuing this programme: PHENIX and STAR which measure both longitudinal and transverse spin asymmetries, and also two smaller spin experiments: BRAHMS which measures transverse spin asymmetries and pp2pp which measures spin dependence in small-angle elastic scattering.
19) Next, the fact that both α1 and α2 are analytic for |ω| ≤ 1 allows us to make the Taylor series expansions (about ω = 0) α1 (x, Q2 ) = α2 (x, Q2 ) = Q2 β1 (Q2 ) 2M 2 2 + x n=0,2,4,.. 1 x 1 xn 1 dy y n g1 (y, Q2 ) 0 2 Q 1 β2 (Q2 ) 2M 2 x 2 1 + 3 x n=0,2,4,.. 5in 36 bass THE SPIN STRUCTURE OF THE PROTON with x = ω1 . Note that the power series in ω = 1/x converges only for |ω| < 1. Since energy-momentum conservation fixes 0 ≤ x ≤ 1 (or ω ≥ 1) it follows that α1 (x) and α2 (x) are unphysical exactly where they converge.
Algebraic Theory of Particle Physics: Hadron Dynamics in Terms of Unitary Spin Currents by Yuval Neeman