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

Natsumi Ikeno,Melahat Bayar,Eulogio Oset

doi:10.1140/epjc/s10052-021-09174-w

Natsumi Ikeno, Melahat Bayar + Show 1 more

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https://doi.org/10.1140/epjc/s10052-021-09174-w

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Abstract

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

Highlights

∗(890), among other resonances that only have a minor effect in the mass distributions [20]
It is interesting to look for reactions which show only effects of a single resonance. This was the case of the Ds+ → π +π 0η reaction measured at BESIII [22], which was shown to be dominated by the a0(980), seen in the π +η and π 0η mass distribution [23]
The final state in the D+ → π +π 0η reaction is the same as in Ds+ → π +π 0η measured in Ref. [22], the reaction mechanism is different here since it allows contributions from external emission and internal emission [25], while in the Ds+ → π +π 0η external emission did not occur and the process proceeded via internal emission [23]

Summary

Introduction

∗(890), among other resonances that only have a minor effect in the mass distributions [20]. It is interesting to look for reactions which show only effects of a single resonance This was the case of the Ds+ → π +π 0η reaction measured at BESIII [22], which was shown to be dominated by the a0(980), seen in the π +η and π 0η mass distribution [23]. In this reaction, the π +π 0 can come from the ρ+, but in the experiment [22] this contribution was eliminated with a simple cut, demanding that M(π +π 0) > 1 GeV. This information puts constraints on the free parameters of the theory and allows us to make predictions on mass distributions which can be tested in future runs of the reactions with more statistics

Formalism

Results

The results of d d Minv for

Conclusions