Role of scalar $$a_0(980)$$ a 0 ( 980 ) in the single Cabibbo suppressed process $$D^+ \rightarrow \pi ^{+} \pi ^{0} \eta $$ D + → π + π 0 η

Abstract

Abstract Taking into account that the scalar $$a_0(980)$$ a 0 ( 980 ) can be dynamically generated from the pseudoscalar-pseudoscalar interaction within the chiral unitary approach, we have studied the single Cabibbo suppressed process $$D^+\rightarrow \pi ^+\pi ^0\eta $$ D + → π + π 0 η . We find clear peaks of $$a_0(980)^+$$ a 0 ( 980 ) + and $$a_0(980)^0$$ a 0 ( 980 ) 0 in the $$\pi ^+\eta $$ π + η and $$\pi ^0\eta $$ π 0 η invariant mass distributions, respectively. The predicted Dalitz plots of $$D^+\rightarrow \pi ^+\pi ^0\eta $$ D + → π + π 0 η also manifest the significant signals for $$a_0(980)^+$$ a 0 ( 980 ) + and $$a_0(980)^0$$ a 0 ( 980 ) 0 states. The uncertainties of the results due to the free parameters are also discussed. Our study shows that the process $$D^+\rightarrow \pi ^+\pi ^0\eta $$ D + → π + π 0 η can be used to explore the nature of the scalar $$a_0(980)$$ a 0 ( 980 ) , thus we encourage the experimental physicists to measure this reaction with more precision.