Determining the dominant partial wave contributions from angular distributions of single- and double-polarization observables in pseudoscalar meson photoproduction

Abstract

This work presents a simple method to determine the significant partial wave contributions to experimentally determined observables in pseudoscalar meson photoproduction. First, fits to angular distributions are presented and the maximum orbital angular momentum Lmax needed to achieve a good fit is determined. Then, recent polarization measurements for γp → π 0 p from ELSA, GRAAL, JLab and MAMI are investigated according to the proposed method. This method allows us to project high-spin partial wave contributions to any observable as long as the measurement has the necessary statistical accuracy. We show, that high precision and large angular coverage in the polarization data are needed in order to be sensitive to high-spin resonance-states and thereby also for the finding of small resonance contributions. This task can be achieved via interference of these resonances with the well-known states. For the channel γp → π 0 p, those are the N (1680) + , contributing to the F -waves.

Determining dominant partial waves in photoproduction

“…The multipoles present in a certain truncation are sorted in the vector Table 1 lists a consistent set of parameters defining the photoproduction moment expansion. They are consistent with reference [7], where also the Legendre parametrizations (2) and (3) were published. Tiator [8] showed similarly formalized expansions in the context of a cos(θ )-series.…”

“…Figure 1 and Table 3 show results for moment-analyses for a measurement of the beam-asymmetry Σ measured by the GRAAL-collaboration [13]. These illustrative results were discussed during the talk and are also a part of reference [7], where also a lot more details, as well as results for more observables, can be found. obtained from a fit to theΣ-data by the GRAAL-collaboration [13] (black points).…”

“…The question whether or not they allow for a unique amplitude extraction in so-called complete experiments has received recent attention [11,12]. In reference [7], we chose to represent these matrices in a color-scheme ('chessboard-plots'), which is exemplified in Table 2. Table 2: The Matrix CΣ 2 which defines the coefficient (a 2 )Σ 2 for an expansion ofΣ up to max = 2 is shown.…”

“….). These figure have originally been published in exactly this form in reference [7]. We refer the reader to this paper for more details.…”

Spectroscopy of baryon resonances

“…The ansatz described here is capable of giving a good estimate of the maximal angular momentum content L max needed to describe a given data set in any kind of partial wave analysis. More details on the method, as well as its application to a wide array of polarization data, will be published in a forthcoming paper [105].…”