Fitting and selecting Scattering Data

Abstract

The main purpose of scattering experiments is to unveil the underlying structure of the colliding particles and their interaction. Typically one measures scattering observables (cross sections and polarizations) at discrete angles and energies and mutually consistent data may validate or falsify proposed theories or models. However, the accumulation of data from different laboratories while potentially improves the statistical significance it may sometimes generate mutually inconsistent data as a side-effect. Thus, some decision has to be made on what are the maximal amount of data which are mutually compatible. We show elastic πN and NN scattering as prominent examples where this selection is called for. We discuss how it can be done in a self-consistent manner invoking a principle of maximal consensus of the database and with the help of a sufficiently flexible model involving a minimal number of theoretical assumptions. In the NN case this has become possible with a combination of long distance field theoretical constraints at the hadronic level such as pion exchanges and electromagnetic effects and a coarse graining of the unknown interaction over the shortest de Broglie wavelength being probed in the scattering process.

Coarse graining hadronic scattering

“…While the abundance of data is usually perceived as an increase on the statistics, and hence an improvement on the precision, it often has the side effect that many more inconsistences may also arise and a data selection process becomes mandatory. Fortunately, the large number of experiments suggests that this selection may be implemented by a majority vote type of argument [3].…”

“…4 we show the dependence of the impact parameter on the CM momentum for the lowest partial waves with angular momentum L = 0, 1, 2, 3 assuming for simplicity r c = 1.5 fm. For instance, if we have p CM ≤ 300 MeV only S-and P-waves probe the interaction region 3 . For a given partial wave the idea of coarse graining is illustrated in Fig.…”

“…5 for a maximal CM momentum of p max = 400 MeV. = pr c (5.6) 3 We are assuming a sharp boundary for the potential at r = r c . If the potential U(r)is known above r c , the argument applies equally, since roughly speaking peripheral waves with J > J max are essentially determined from U(r).…”

Baryonic susceptibilities, quark-diquark models, and quark-hadron duality at finite temperature

“…Since a hadronic model is not expected to reproduce the QCD crossover we fit the data corresponding to the lower temperatures in lattice measurements. Statistical considerations [48] indicate that those data points should be included for which where ν is the number of degrees of freedom. This condition fixes our choice of j max .…”

Coarse graining $$\pi \pi $$ π π scattering

“…Our present investigation within ππ is in a sense of exploratory character and it pretends also to provide some training playground with an eye put on the more compelling π N case, where the selection of the currently existing database is largely needed (see for e.g. [36][37][38] and references therein).…”