Partial-wave bases for mixed-symmetry little-group representations

Construct the partial-wave basis for all irreducible representations of the massive little group SO(d−1) that can propagate in half-ladder diagrams, including mixed-symmetry representations labeled by two quantum numbers [σ,τ], and determine the corresponding special functions and coefficient matrices beyond the symmetric-traceless tensor case.

Background

The paper constructs and proves an all-multiplicity, all-dimension partial-wave expansion for half-ladder diagrams under the restriction that every internal particle transforms in a symmetric-traceless tensor representation of the massive little group SO(d−1). The construction relies on special functions, particularly the T-functions, whose explicit closed forms are obtained for these representations.

Starting at six points, the authors note that internal particles can instead transform in mixed-symmetry representations, such as the antisymmetric rank-two tensor corresponding to [σ,τ]=[1,1]. Extending the basis to these representations would require determining how the T-functions and potentially the coefficient matrices Y are modified; the paper leaves this unresolved.