Electromagnetic Properties of Diquarks

Abstract

Abstract. Diquark correlations play an important role in hadron physics. The properties of diquarks can be obtained from the corresponding bound state equation. Using a model for the effective quark-quark interaction that has proved successful in the light meson sector, we solve the scalar diquark Bethe-Salpeter equations and use the obtained Bethe-Salpeter amplitudes to compute the diquarks' electromagnetic form factors. The scalar ud diquark charge radius is about 8% larger than the pion charge radius, indicating that these diquarks are somewhat larger in size than the corresponding mesons. We also provide analytic fits for the form factor over a moderate range in Q 2 , which may be useful, for example, in building quark-diquark models of nucleons. DiquarksDiquarks are coloured states of two quarks. Due to their colour charge, they are expected to be confined, and cannot be observed directly. Despite being confined, they can play a role in the dynamics of baryons: two quarks in a colour anti-triplet configuration can couple with a third quark to form a colour singlet baryon. Indeed quark-diquark models have been used quite successfully in various models for baryons [1,2,3]. More recently, they also have been suggested as the constituents of pentaquarks: one could imagine a pentaquark as a bound state of two diquarks and an antiquark [4], or as a bound state of a diquark and a triquark [5].For calculations of the baryon spectrum within a quark-diquark model, the most important property of the diquarks is their mass. There are a number of different calculations of these masses available, both from lattice QCD [6] and using the set of Dyson-Schwinger equations [DSEs] [7,8,9]. These calculations seem to agree with each other to within about 20%. For calculations of electromagnetic properties of nucleons (and other baryons), one also needs to know how photons couple to diquarks. Since they are not observable, we cannot obtain *

Nucleon and pion distribution functions in the valence region

“…This approach capitalizes on the importance of scalar and axial-vector diquark correlations within the nucleon. In QCD these correlations are essentially nonpointlike (Alexandrou et al, 2006;Maris, 2004). While no DSE computations of the pointwise behavior of the nucleon structure functions are yet available, based on the diquark-correlation probabilities presented in Table 2 of the DSE study of nucleon electromagnetic form factors described in ) and the fact that the ratio is a fixed-point under evolution, one can estimate …”

On Nucleon Electromagnetic Form Factors

“…Reference [52] also evaluates charge radii for the scalar diquarks: r (ud) 0 + ≈ 1.1 r π ; r (ds) 0 + ≈ r K + ; and r (us) 0 + ≈ 1.3 -1.4 r K + . The Bethe-Salpeter amplitude is canonically normalised via:…”

“…[52] is a first step toward calculating this vertex. However, in providing only an on-shell component, it is insufficient for our requirements.…”

πandρmesons, and their diquark partners, from a contact interaction

“…and of interactions in Refs. [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. There is nevertheless a need to return to this theme; namely, a programme aimed at charting the interaction between lightquarks by explicating the impact of differing assumptions about the behaviour of the Bethe-Salpeter kernel on hadron elastic and transition form factors [48].…”

“…At leading-order in a global-symmetry preserving truncation of the DSEs [15,17], simple changes in the equations describing π-and ρ mesons yield expressions that provide detailed information about the scalar and axial-vector diquarks; e.g., their masses [9,10,18,23,50,51], and electromagnetic elastic [41] and transition form factors, which are critical elements in the computation of a baryon's kindred properties. It is therefore natural to elucidate concurrently the properties of π-and ρ-mesons and those of the scalar and axial-vector diquark correlations because it opens the way to a unified, symmetry-preserving explanation of meson and baryon properties as they are predicted by a single interaction.…”