@MISC{Wilczek_diquarksas, author = {Frank Wilczek}, title = {Diquarks as Inspiration and as Objects}, year = {} }

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Abstract

Attraction between quarks is a fundamental aspect of QCD. It is plausible that several of the most profound aspects of low-energy QCD dynamics are connected to diquark correlations, including: paucity of exotics (which is the foundation of the quark model and of traditional nuclear physics), similarity of mesons and baryons, color superconductivity at high density, hyperfine splittings, ∆I = 1/2 rule, and some striking features of structure and fragmentation functions. After a brief overview of these issues, I discuss how diquarks can be studied in isolation, both phenomenologically and numerically, and present approximate mass differences for diquarks with different quantum numbers. The mass-loaded generalization of the Chew-Frautschi formula provides an essential tool. 1 Diquarks as Inspiration 1.1 Diquarks in Microscopic QCD In electrodynamics the basic interaction between like-charged particles is repulsive. In QCD, however, the primary interaction between two quarks can be attractive. At the most heuristic level, this comes about as follows. Each quark is in the 3 representation, so that the two-quark color state 3 ⊗3 can be either the symmetric 6 or the antisymmetric ¯3. Antisymmetry, of course, is not possible with just 1 color! Two widely separated quarks each generate the color flux associated with the fundamental representation; if they are brought together in the ¯3, they will generate the flux associated with a single anti-fundamental, which is just half as much. Thus by bringing the quarks together we lower the gluon field energy: there is attraction in the ¯3 channel. We might expect this attraction to be roughly half as powerful as the quark-antiquark 3 ⊗¯3 → 1. Since quark-antiquark attraction drives the energy in the attractive channel below zero, triggering condensation 〈¯qq 〉 = 0 of q¯q pairs and chiral symmetry breaking, an attraction even half as powerful would appear to be potentially quite important for understanding low-energy QCD dynamics. Solicited contribution to the Ian Kogan memorial volume, ed. M. Shifman. 1 One can calculate the quark-quark interaction due to single gluon exchange, and of course one does find that the color ¯3 channel for quarks is attractive. Going a step further, one can consider magnetic forces, and distinguish the favored spin configuration. One finds