Combined theoretical study of the $$D^+ \rightarrow \pi ^+ \eta \eta $$ and $$D^+ \rightarrow \pi ^+ \pi ^0 \eta $$ reactions

Abstract We study the $$D^+ \rightarrow \pi ^+ \eta $$ D+→π+ηη and ^0 xmlns:mml="http://www.w3.org/1998/Math/MathML">D+→π+π0η reactions, which are single Cabibbo suppressed can proceed both through internal external emission. The primary mechanisms at quark level considered, followed by hadronization to produce three mesons in $$D^+$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">D+ decay, after that final state interaction of these leads production $$a_0(980)$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">a0(980) resonance, seen $$\pi xmlns:mml="http://www.w3.org/1998/Math/MathML">π+η , xmlns:mml="http://www.w3.org/1998/Math/MathML">π0η mass distributions. theory has unknown parameters determine shape distributions ratio between rates. This restricts much sets but there is still freedom leading different shapes call for a measurement will settle reaction mechanism, while same time provide relevant information on way resonance produced reactions.