English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We complete and improve the fits to experimental $\pi\pi$ scatteringamplitudes, both at low and high energies, that we performed in the previouspapers of this series. We then verify that the corresponding amplitudes satisfyanalyticity requirements, in the form of partial wave analyticity at lowenergies, forward dispersion relations (FDR) at all energies, and Roy equationsbelow$\bar{K}K$ threshold; the first by construction, the last two, insideexperimental errors. Then we repeat the fits including as constraints FDR andRoy equations. The ensuing central values of the various scattering amplitudesverify very accurately FDR and, especially, Roy equations, and change verylittle from what we found by just fitting data, with the exception of the D2wave phase shift, for which one parameter moves by $1.5 \sigma$. These improvedparametrizations therefore provide a reliable representation of pion-pionamplitudes with which one can test various physical relations. We also presenta list of low energy parameters and other observables. In particular, we find$a_0^{(0)}=0.223\pm0.009 M^{-1}_\pi$, $a_0^{(2)}=-0.0444\pm0.0045 M^{-1}_\pi$and $\delta_0^{(0)}(m^2_K)-\delta_0^{(2)}(m^2_K)=50.9\pm1.2^{\rm o}$.

The pion-pion scattering amplitude. III: Improving the analysis with forward dispersion relations and Roy equations