Measurement of multivariate scaling and factorization in exclusive multiparticle production

Several new model-independent techniques for the analysis of multidimensional data are presented and applied to exclusive multiparticle production. For the reaction pp→ppπ⁺π⁺π^-π^- from 12 to 28 GeV/c, an algorithm that directly compares two multidimensional point distributions is used to show that the shape of d¹²σ/d(p⃗_⊥)¹² is energy-independent, while d⁶σ/dx⁶ (x=p_∥/p_max) varies dramatically with beam energy. A multidimensional test for independence is used to show that the multivariate differential cross section approximately factors into its cylindrical momentum components, d¹⁸σ/d(p⃗)¹⁸≃(d⁶σ/dp_∥⁶) [d⁶σ/d(p_⊥²)⁶]d⁶σ/dϕ⁶. The shape of d⁶σ/dϕ⁶ is also shown to be compatible with that predicted solely by kinematics.