$$f_0(500)$$ f 0 ( 500 ) , $$f_0(980)$$ f 0 ( 980 ) , and $$a_0(980)$$ a 0 ( 980 ) production in the $$\chi _{c1} \rightarrow \eta \pi ^+\pi ^-$$ χ c 1 → η π + π - reaction

The $$D_s^+ \rightarrow a_0(980) e^+ \nu _e$$ reaction and the $$a_0(980)-f_0(980)$$ mixing

“…We can see that for q max = 600 MeV we obtain values of the masses of the f 0 (500) and f 0 (980) in fair agreement with experiment. The a 0 (980) does not show up with this value of q max , but it shows up as a cusp at the K K threshold [69], which is in very good agreement with the high precision experiment on a 0 (980) production in Ref. [70].…”

The $$D_s^+ \rightarrow a_0(980) e^+ \nu _e$$ reaction and the $$a_0(980)-f_0(980)$$ mixing

“…We can see that for q max = 600 MeV we obtain values of the masses of the f 0 (500) and f 0 (980) in fair agreement with experiment. The a 0 (980) does not show up with this value of q max , but it shows up as a cusp at the K K threshold [69], which is in very good agreement with the high precision experiment on a 0 (980) production in Ref. [70].…”

The $D_s^+ \to a_0(980) e^+ ν_e$ reaction and the $a_0(980)-f_0(980)$ mixing

“…We can see that for q max = 600 MeV we obtain values of the masses of the f 0 (500) and f 0 (980) in fair agreement with experiment. The a 0 (980) does not show up with this value of q max , but it shows up as a cusp at the K K threshold [64], which is in very good agreement with the high precision experiment on a 0 (980) production in Ref. [65].…”

Theoretical study of the $$D^0 \rightarrow K^- \pi ^+ \eta $$ reaction

“…The scattering amplitudes π + η → π + η and K +K 0 → π + η in the chiral unitary approach contain the a 0 (980) resonance, which comes as a consequence of the interaction of the mesons and is also not introduced by hand in the approach. We should stress the cusp like shape of this resonance both in the theory and in the experiment, something already noted in the high statistics BESIII experiment on the χ c1 → ηπ + π − reaction [52] accurately described theoretically in [53] along similar lines as shown here. It is also interesting to see the curious effect that theK * 0 contribution has in the M πη and M K η distributions, giving rise to two broad peaks at lower and higher invariant masses.…”

The $$D_s^+ \rightarrow a_0(980) e^+ \nu _e$$ reaction and the $$a_0(980)-f_0(980)$$ mixing

“…We can see that for q max = 600 MeV we obtain values of the masses of the f 0 (500) and f 0 (980) in fair agreement with experiment. The a 0 (980) does not show up with this value of q max , but it shows up as a cusp at the K K threshold [69], which is in very good agreement with the high precision experiment on a 0 (980) production in Ref. [70].…”

The $D_s^+ \to a_0(980) e^+ ν_e$ reaction and the $a_0(980)-f_0(980)$ mixing

“…We can see that for q max = 600 MeV we obtain values of the masses of the f 0 (500) and f 0 (980) in fair agreement with experiment. The a 0 (980) does not show up with this value of q max , but it shows up as a cusp at the K K threshold [64], which is in very good agreement with the high precision experiment on a 0 (980) production in Ref. [65].…”

Theoretical study of the $$D^0 \rightarrow K^- \pi ^+ \eta $$ reaction

“…The scattering amplitudes π + η → π + η and K +K 0 → π + η in the chiral unitary approach contain the a 0 (980) resonance, which comes as a consequence of the interaction of the mesons and is also not introduced by hand in the approach. We should stress the cusp like shape of this resonance both in the theory and in the experiment, something already noted in the high statistics BESIII experiment on the χ c1 → ηπ + π − reaction [52] accurately described theoretically in [53] along similar lines as shown here. It is also interesting to see the curious effect that theK * 0 contribution has in the M πη and M K η distributions, giving rise to two broad peaks at lower and higher invariant masses.…”

The $$D_s^+ \rightarrow a_0(980) e^+ \nu _e$$ reaction and the $$a_0(980)-f_0(980)$$ mixing

“…We can see that for q max = 600 MeV we obtain values of the masses of the f 0 (500) and f 0 (980) in fair agreement with experiment. The a 0 (980) does not show up with this value of q max , but it shows up as a cusp at the K K threshold [69], which is in very good agreement with the high precision experiment on a 0 (980) production in Ref. [70].…”

The $D_s^+ \to a_0(980) e^+ ν_e$ reaction and the $a_0(980)-f_0(980)$ mixing

“…We can see that for q max = 600 MeV we obtain values of the masses of the f 0 (500) and f 0 (980) in fair agreement with experiment. The a 0 (980) does not show up with this value of q max , but it shows up as a cusp at the K K threshold [64], which is in very good agreement with the high precision experiment on a 0 (980) production in Ref. [65].…”

Theoretical study of the $$D^0 \rightarrow K^- \pi ^+ \eta $$ reaction

“…The scattering amplitudes π + η → π + η and K +K 0 → π + η in the chiral unitary approach contain the a 0 (980) resonance, which comes as a consequence of the interaction of the mesons and is also not introduced by hand in the approach. We should stress the cusp like shape of this resonance both in the theory and in the experiment, something already noted in the high statistics BESIII experiment on the χ c1 → ηπ + π − reaction [52] accurately described theoretically in [53] along similar lines as shown here. It is also interesting to see the curious effect that theK * 0 contribution has in the M πη and M K η distributions, giving rise to two broad peaks at lower and higher invariant masses.…”