The scalar f_0(500), f_0(980), and a_0(980) resonances and vector mesons in the single Cabibbo-suppressed decays Lambda _c rightarrow p K^+K^- and ppi ^+pi ^-

Zhe Wang,En Wang,De-Min Li,Ju-Jun Xie,Yan-Yan Wang

doi:10.1140/epjc/s10052-020-8347-2

Abstract

In the chiral unitary approach, we have studied the single Cabibbo-suppressed decays Lambda _crightarrow pK^+K^- and Lambda _c rightarrow p pi ^+pi ^- by taking into account the s-wave meson–meson interaction as well as the contributions from the intermediate vectors phi and rho ^0. Our theoretical results for the ratios of the branching fractions of Lambda _crightarrow p {bar{K}}^{*0} and Lambda _crightarrow p omega with respect to the one of Lambda _crightarrow p phi are in agreement with the experimental data. Within the picture that the scalar resonances f_0(500), f_0(980), and a_0(980) are dynamically generated from the pseudoscalar-pseudoscalar interactions in s-wave, we have calculated the K^+K^- and pi ^+pi ^- invariant mass distributions respectively for the decays Lambda _crightarrow pK^+K^- and Lambda _crightarrow ppi ^+pi ^-. One can find a broad bump structure for the f_0(500) and a narrow peak for the f_0(980) in the pi ^+pi ^- invariant mass distribution of the decay Lambda _crightarrow ppi ^+pi ^-. For the K^+K^- invariant mass distribution, in addition to the narrow peak for the phi meson, there is an enhancement structure near the K^+K^- threshold mainly due to the contribution from the f_0(980). Both the pi ^+pi ^- and K^+K^- invariant mass distributions are compatible with the BESIII measurement. We encourage our experimental colleagues to measure these two decays, which would be helpful to understand the nature of the f_0(500), f_0(980), and a_0(980).

Highlights

The BESIII Collaboration has reported the branching fractions of the c → pK + K −, pπ +π −, B( B( c c → pφ) → pK−π+) = (1.81 ± 0.33 ± 0.13)%, (1)B( c → p K + K −)non−φ B( c → pK −π+)= (9.36 ± 2.22 ± 0.71)%, (2) B( B(
M 2φ π ( Mi2nvφc→pφ − m2φ)2 + m2φ where we have considered that the K + K − decay accounts for 1/2 of the K Kdecay width of the φ meson
For the π +π − invariant mass distribution of the decay c → pπ +π − as shown in Fig. 10, one can see a clear peak around 770 MeV, corresponding to the vector meson ρ0, and a broad peak around 500 MeV, which can be associated to the scalar meson f0(500), dynamically generated from the meson-meson interactions in s-wave

Summary

Introduction

The BESIII Collaboration has reported the branching fractions of the c → pK + K −, pπ +π −, B( B( c c → pφ) → pK−π+). Before the BESIII and LHCb results, the above two decay modes have been observed by the NA32 [19], E687 [20], CLEO [21], and Belle Collaborations [7]. The productions of f0(500), f0(980), and a0(980) have been recently studied with the chiral unitary approach and the final state interactions in the decays of the D0 [28], Ds+ [29], Band Bs [30,31,32,33], χc1 [34,35], τ − [36], and J/ψ [37]. Numerical results for the K + K − and π +π − invariant mass distributions and discussions are given in Sect. 3, followed by a short summary in the last section

Formalism

Results and discussion

BESIII

Conclusions