Open Access

Role of $a_{0} (980)$ in the decays $D^{0} \to K^{+} K^{-} η$ and $π^{+} π^{-} η$

Sara Rahmani ¹, Wei Liang ^2,*, Yu-Wen Peng ², Yu Lu ², De-Liang Yao¹, and Chu-Wen Xiao ^3,4,2,†

¹School of Physics and Electronics, Hunan University, Changsha 410082, China
²School of Physics, Hunan Key Laboratory of Nanophotonics and Devices, Central South University, Changsha 410083, China
³Department of Physics, Guangxi Normal University, Guilin 541004, China
⁴Guangxi Key Laboratory of Nuclear Physics and Technology, Guangxi Normal University, Guilin 541004, China

^*Contact author: 212201014@csu.edu.cn
^†Contact author: xiaochw@gxnu.edu.cn

Phys. Rev. D 112, 036001 – Published 4 August, 2025

DOI: https://doi.org/10.1103/yhzk-p2yp

Abstract

In the present work, we study the reactions $D^{0} \to K^{+} K^{-} η$ and $D^{0} \to π^{+} π^{-} η$ , and find that the $a_{0} (980)$ state plays a dominant role. At the quark level, the external and internal $W$ -emission mechanisms are taken into account, which can hadronize into the final states, and then the $a_{0} (980)$ state is generated from the final state interaction. In addition, the contributions of other intermediate resonances, such as $ρ (770)$ and $ϕ (1020)$ , are also considered. We make a combined fit of the invariant mass spectra measured by the Belle and BESIII Collaborations, where the results are in good agreement with the experiments, and the signal of $a_{0} (980)$ shows great significance. Furthermore, the antisymmetry data for the production of $a_{0} (980)^{+}$ and $a_{0} (980)^{-}$ are described well in the combined fit.

Physics Subject Headings (PhySH)

Article Text

References (73)

A. Astier, L. Montanet, M. Baubillier, and J. Duboc, Phys. Lett. 25B, 294 (1967).
R. Ammar, R. Davis, W. Kropac, J. Mott, D. Slate, B. Werner, M. Derrick, T. Fields, and F. Schweingruber, Phys. Rev. Lett. 21, 1832 (1968).
C. Defoix, P. Rivet, J. Siaud, B. Conforto, M. Widgoff, and F. Shively, Phys. Lett. 28B, 353 (1968).
S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024).
S. Godfrey and N. Isgur, Phys. Rev. D 32, 189 (1985).
D. Morgan and M. R. Pennington, Phys. Rev. D 48, 1185 (1993).
N. A. Tornqvist and M. Roos, Phys. Rev. Lett. 76, 1575 (1996).
R. L. Jaffe, Phys. Rev. D 15, 267 (1977).
J. D. Weinstein and N. Isgur, Phys. Rev. Lett. 48, 659 (1982).
N. N. Achasov, Nucl. Phys. A728, 425 (2003).
B. S. Zou and D. V. Bugg, Phys. Rev. D 50, 591 (1994).
G. Janssen, B. C. Pearce, K. Holinde, and J. Speth, Phys. Rev. D 52, 2690 (1995).
J. A. Oller and E. Oset, Nucl. Phys. A620, 438 (1997); A652, 407(E) (1999).
M. P. Locher, V. E. Markushin, and H. Q. Zheng, Eur. Phys. J. C 4, 317 (1998).
J. A. Oller, E. Oset, and J. R. Pelaez, Phys. Rev. Lett. 80, 3452 (1998).
D. L. Yao, L. Y. Dai, H. Q. Zheng, and Z. Y. Zhou, Rep. Prog. Phys. 84, 076201 (2021).
V. Baru, J. Haidenbauer, C. Hanhart, Y. Kalashnikova, and A. E. Kudryavtsev, Phys. Lett. B 586, 53 (2004).
R. Albuquerque, S. Narison, and D. Rabetiarivony, Nucl. Phys. A1039, 122743 (2023).
R. R. Akhmetshin et al. (CMD-2 Collaboration), Phys. Lett. B 462, 371 (1999).
F. Ambrosino et al. (KLOE Collaboration), Eur. Phys. J. C 49, 473 (2007).
F. Ambrosino et al. (KLOE Collaboration), Phys. Lett. B 681, 5 (2009).
M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 92, 052003 (2015); 93, 039906(E) (2016).
M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 94, 072005 (2016).
A. V. Sarantsev, I. Denisenko, U. Thoma, and E. Klempt, Phys. Lett. B 816, 136227 (2021).
R. Aaij et al. (LHCb Collaboration), J. High Energy Phys. 04 (2019) 063.
M. Ablikim et al. (BESIII Collaboration), Phys. Rev. Lett. 124, 241803 (2020).
L. K. Li et al. (Belle Collaboration), J. High Energy Phys. 09 (2021) 075.
M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 101, 052009 (2020).
M. Artuso et al. (CLEO Collaboration), Phys. Rev. D 77, 092003 (2008).
M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 110, L111102 (2024).
B. El-Bennich, O. Leitner, J. P. Dedonder, and B. Loiseau, Phys. Rev. D 79, 076004 (2009).
L. Yang, Z. T. Zou, Y. Li, X. Liu, and C. H. Li, Phys. Rev. D 103, 113005 (2021).
R. T. Aoude, P. C. Magalhães, A. C. Dos Reis, and M. R. Robilotta, Phys. Rev. D 98, 056021 (2018).
L. Roca and E. Oset, Phys. Rev. D 103, 034020 (2021).
S. X. Nakamura, Phys. Rev. D 93, 014005 (2016).
F. Niecknig and B. Kubis, J. High Energy Phys. 10 (2015) 142.
F. Niecknig and B. Kubis, Phys. Lett. B 780, 471 (2018).
E. Oset and A. Ramos, Nucl. Phys. A635, 99 (1998).
N. Kaiser, Eur. Phys. J. A 3, 307 (1998).
J. A. Oller and U. G. Meissner, Phys. Lett. B 500, 263 (2001).
J. J. Xie, L. R. Dai, and E. Oset, Phys. Lett. B 742, 363 (2015).
Z. Y. Wang, H. A. Ahmed, and C. W. Xiao, Phys. Rev. D 105, 016030 (2022).
M. Ablikim et al. (BESIII Collaboration), Phys. Lett. B 781, 368 (2018).
G. Toledo, N. Ikeno, and E. Oset, Eur. Phys. J. C 81, 268 (2021).
Z. Y. Wang, J. Y. Yi, Z. F. Sun, and C. W. Xiao, Phys. Rev. D 105, 016025 (2022).
W. Liang, J. Y. Yi, C. W. Xiao, and S. Q. Zhou, Phys. Rev. D 108, 116001 (2023).
L. Wolfenstein, Phys. Rev. D 43, 151 (1991).
M. Suzuki and L. Wolfenstein, Phys. Rev. D 60, 074019 (1999).
H. Y. Cheng and C. W. Chiang, Phys. Rev. D 104, 073003 (2021).
C. P. Jia, H. Y. Jiang, J. P. Wang, and F. S. Yu, J. High Energy Phys. 11 (2024) 072.
Z. D. Duan, J. P. Wang, R. H. Li, C. D. Lv, and F. S. Yu, arXiv:2412.20458.
L. L. Chau, Phys. Rep. 95, 1 (1983).
L. L. Chau and H. Y. Cheng, Phys. Rev. D 36, 137 (1987).
R. J. Morrison and M. S. Witherell, Annu. Rev. Nucl. Part. Sci. 39, 183 (1989).
R. Molina, J. J. Xie, W. H. Liang, L. S. Geng, and E. Oset, Phys. Lett. B 803, 135279 (2020).
H. A. Ahmed, Z. Y. Wang, Z. F. Sun, and C. W. Xiao, Eur. Phys. J. C 81, 695 (2021).
Z. Wang, Y. Y. Wang, E. Wang, D. M. Li, and J. J. Xie, Eur. Phys. J. C 80, 842 (2020).
Y. W. Peng, W. Liang, X. Xiong, and C. W. Xiao, Phys. Rev. D 110, 036013 (2024).
H. Zhang, Y. H. Lyu, L. J. Liu, and E. Wang, Chin. Phys. C 47, 043101 (2023).
L. R. Dai, G. Y. Wang, X. Chen, E. Wang, E. Oset, and D. M. Li, Eur. Phys. J. A 55, 36 (2019).
G. Montaña, A. Ramos, L. Tolos, and J. M. Torres-Rincon, Phys. Rev. D 107, 054014 (2023).
L. Alvarez-Ruso, J. A. Oller, and J. M. Alarcon, Phys. Rev. D 82, 094028 (2010).
J. A. Oller and E. Oset, Phys. Rev. D 60, 074023 (1999).
D. Gamermann, E. Oset, D. Strottman, and M. J. Vicente Vacas, Phys. Rev. D 76, 074016 (2007).
Z. H. Guo, L. Liu, U. G. Meißner, J. A. Oller, and A. Rusetsky, Phys. Rev. D 95, 054004 (2017).
E. Oset, A. Ramos, and C. Bennhold, Phys. Lett. B 527, 99 (2002).
F. K. Guo, R. G. Ping, P. N. Shen, H. C. Chiang, and B. S. Zou, Nucl. Phys. A773, 78 (2006).
J. M. Dias, F. S. Navarra, M. Nielsen, and E. Oset, Phys. Rev. D 94, 096002 (2016).
W. H. Liang and E. Oset, Phys. Lett. B 737, 70 (2014).
H. A. Ahmed and C. W. Xiao, Eur. Phys. J. A 59, 245 (2023).
V. R. Debastiani, W. H. Liang, J. J. Xie, and E. Oset, Phys. Lett. B 766, 59 (2017).
Y. Ding, E. Wang, D. M. Li, L. S. Geng, and J. J. Xie, Phys. Rev. D 110, 014032 (2024).
X. H. Zhang, H. Zhang, B. C. Ke, L. J. Liu, D. M. Li, and E. Wang, Phys. Rev. D 110, 114050 (2024).

Phys. Rev. D 112, 036001– Published 4 August, 2025

Vol. 112, Iss. 3 — 1 August 2025

Received 10 March 2025
Accepted 8 July 2025

DOI: https://doi.org/10.1103/yhzk-p2yp

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physical Review D

Reuse & Permissions

Export citation

Export citation

Role of $a_{0} (980)$ in the decays $D^{0} \to K^{+} K^{-} η$ and $π^{+} π^{-} η$

Abstract

Physics Subject Headings (PhySH)

Article Text

References (73)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

Role of a0(980) in the decays D0→K+K−η and π+π−η

Abstract

Physics Subject Headings (PhySH)

Article Text

References (73)

Role of $a_{0} (980)$ in the decays $D^{0} \to K^{+} K^{-} η$ and $π^{+} π^{-} η$