Minimal complete sets for two-pseudoscalar-meson photoproduction

Light Baryon Spectroscopy

“…For single-meson photoproduction, early results by Barker, Donnachie and Storrow [77] have been corrected in a seminal work by Chiang and Tabakin [69], while the latter work has been put on a rigorous mathematical basis recently by Nakayama [85]. Two-meson photoproduction has been analyzed in a first study by Arenhoevel and Fix [87], while a more recent study has first worked out the complete sets of minimal length [88]. For vector meson photoproduction, brief considerations can be found in the work by Pichkowsky, Savkli and Tabakin [89], but a more thorough treatment is to our knowledge lacking at the moment.…”

“…The remaining 27 observables correspond to genuine triple-polarization (BT R-) measurements and they are written as O B T R (Table 6). Equations relating the 64 observables to the transversity-(or helicity-) amplitudes are not given here due to their length, but can be found in references [68,88]. Here, we just mention the fact that the observables can be grouped into 8 'shape-classes' [88], containing 8 observables each, similarly to the single-meson photoproduction observables (cf.…”

“…The observable I 0 in the first row is the unpolarized differential cross section. We have adopted the original notation by Roberts and Oed [68], while this Table itself is taken over from reference [88].…”

“…they might still allows for discrete ambiguities). A more recent study [88] has proposed alternative methods for the derivation of complete sets with 16 observables that are completely free of ambiguities, locally as well as globally. These alternative methods consist of a very specific algebraic approach (based on earlier ideas by Nakayama [85]) to directly derive complete sets of minimal length 16, numerical tests for the completeness of any proposed set, as well as graphical methods originally proposed for the solution of a CEA with an arbitrary number N A of amplitudes [70].…”

“…These alternative methods consist of a very specific algebraic approach (based on earlier ideas by Nakayama [85]) to directly derive complete sets of minimal length 16, numerical tests for the completeness of any proposed set, as well as graphical methods originally proposed for the solution of a CEA with an arbitrary number N A of amplitudes [70]. For explicit listings of complete sets in the two-meson photoproduction CEA, we refer the reader to references [88,87].…”