Nucleon Structure, Duality and Elliptic Theta Functions

Nucleon structure functions are shown to have a qualitative (or ‘formal’) relation to the classical elliptic theta functions. In particular, θ 1/2 shows a clear resemblance to a non-singlet structure function like xF3. In the appropriate range, the Q2-dependence of the moments of θ 1/2 is in near-quantitative agreement with QCD, and at low-Q2 the moments converge to a common value, as observed empirically for xF3. At very high Q 2 (Q → MPL), θ 1/2 → η3(x) (where η(x) is the Dedekind eta function) while xF3 in the same limit appears closer to η 5(x). A comparison of the theta function identity θ4 2(0) = θ 4 3(0)− θ4 4(0) with the relation xF3 = Q(x) − Q̄(x) suggests that singlet structure functions have more in common with θ3 and θ4. The possibility of interesting large-x/small-x ‘duality’ relations for structure functions emerges naturally from the analysis. E-mail:[email protected]