In this study, we investigate the isospin-violating decays of $ B_{c}(1P)^{+}\to B_{c}^{(*)+}\pi^{0} $ , which may provide additional information for the determination of the properties of $ B_{c}(1P)^{+} $ , the first orbital excitation states of the $B_c $ meson. By assuming a dual relation between the $\textit{U}$(1) anomaly soft-gluon coupling for $ B_{c}(1P)^{+}\to B_{c}^{(*)+}\pi^{0} $ and the intermediate meson loop transitions, we can quantify the isospin-violating decay effects for these four $\textit{P}$-wave states. We observe that the partial decay width of $ B_{c0}^{*+}\to B_{c}^{+}\pi^{0} $ is approximately three orders of magnitude larger than that for $ B_{c2}^{*+}\to B_{c}^{+}\pi^{0} $ . This indicates that $ B_{c0}^{*+} $ can be established in the $ B_{c}^{+}\pi^{0} $ decay channel as a single state. Meanwhile, the two axial-vector states $ B_{c1}^{+}/B_{c1}'^{+} $ can be possibly identified in $ B_{c1}^{+}/B_{c1}'^{+}\to B_{c}^{*+}\pi^{0} $ with comparable strengths. Although these isospin-violating decays are observed to be small, the theoretical predictions should be useful for guiding future experimental efforts.

China

Jun Wang

Qiang Zhao

Predictions for the isospin-violating decays of ${{\boldsymbol B}_{\boldsymbol c}({\boldsymbol{1P}})^{\bf +}{\bf\to}{\boldsymbol B}_{\boldsymbol c}^{({\bf *})+}\boldsymbol\pi^{\bf 0}}$ * Supported, in part, by the National Natural Science Foundation of China (12235018), DFG and NSFC funds to the Sino-German CRC 110 'Symmetries and the Emergence of Structure in QCD' (12070131001, DFG Project-ID 196253076), National Key Basic Research Program of China (2020YFA0406300) and Strategic Priority Research Program of Chinese Academy of Sciences (XDB34030302)

Based on $ (10087\pm 44)\times10^{6} $ $ J/\psi $ events collected with the BESIII detector, we search for the lepton number violating decay $ J/\psi \to K^+K^+e^-e^- + c.c. $ for the first time. The upper limit on the branching fraction of this decay is set to $ 2.1 \times 10^{-9} $ at the 90% confidence level with a frequentist method. This is the first search for $ J/\psi $ decays with a lepton number change by two, offering valuable insights into the underlying physical processes.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

Germany

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

O. Bakina

Y. Ban

H.R. Bao

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M.B. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

United States

R.A. Briere

A. Brueggemann

H. Cai

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

Türkiye

S.A. Cetin

X.Y. Chai

J.F. Chang

T.T. Chang

G.R. Che

Y.Z. Che

C.H. Chen

Chao Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.L. Chen

S.M. Chen

T. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z. Chen

Z.K. Chen

J.C. Cheng

L.N. Cheng

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

United Kingdom

J. Cottee-Meldrum

H.L. Dai

J.P. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denisenko

M. Destefanis

F. De Mori

B. Ding

X.X. Ding

Y. Ding

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. Du

X.L. Du

Y.Y. Duan

Z.H. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

R. Farinelli

L. Fava

F. Feldbauer

G. Felici

C.Q. Feng

J.H. Feng

Search for the lepton number violating process ${{\boldsymbol J}/{\boldsymbol\psi }{\bf\to}{\boldsymbol K}^{\bf +}{\boldsymbol K}^{\bf +}{\boldsymbol e}^{\bf -}{\boldsymbol e}^{\bf -}{\bf +}{\boldsymbol {c.c.}}}$ * This work is supported in part by National Key R&D Program of China under Contracts Nos. 2023YFA1606000, 2023YFA1606704; National Natural Science Foundation of China (NSFC) under Contracts Nos. 12035009, 11635010, 11935015, 11935016, 11935018, 12025502, 12035013, 12061131003, 12192260, 12192261, 12192262, 12192263, 12192264, 12192265, 12221005, 12225509, 12235017, 12361141819; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; CAS under Contract No. YSBR-101; 100 Talents Program of CAS; The Institute of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology; German Research Foundation DFG under Contract No. FOR5327; Istituto Nazionale di Fisica Nucleare, Italy; Knut and Alice Wallenberg Foundation under Contracts Nos. 2021.0174, 2021.0299; Ministry of Development of Turkey under Contract No. DPT2006K-120470; National Research Foundation of Korea under Contract No. NRF-2022R1A2C1092335; National Science and Technology fund of Mongolia; National Science Research and Innovation Fund (NSRF) via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation of Thailand under Contract No. B50G670107; Polish National Science Centre under Contract No. 2024/53/B/ST2/00975; Swedish Research Council under Contract No. 2019.04595; U. S. Department of Energy under Contract No. DE-FG02-05ER41374

Based on a sample of $2.7\times10^{9}$ $\psi(3686)$ events collected by the BESIII detector operating at the BEPCII collider, the decay $\psi(3686)\to\gamma\chi_{cJ}, \chi_{cJ}\to\eta\eta\eta^{\prime}$ is analyzed. The decay modes $\chi_{c1}$ and $\chi_{c2}\to\eta\eta\eta^{\prime}$ are observed for the first time, and their corresponding branching fractions are determined to be ${\cal{B}}(\chi_{c1}\to\eta\eta\eta^{\prime}) = $ $ (1.40\, \pm 0.13\, (\text{stat.}) \pm 0.09\, (\text{sys.})) \times 10^{-4}$ and ${\cal{B}}(\chi_{c2}\to\eta\eta\eta^{\prime}) = (4.18\, \pm 0.84\, (\text{stat.}) \pm 0.48\, (\text{sys.})) \times 10^{-5}$ . An upper limit on the branching fraction of $\chi_{c0}\to\eta\eta\eta^{\prime}$ is set as $2.59 \times 10^{-5}$ at a 90% confidence level (CL). A partial wave analysis (PWA) of the decay $\chi_{c1}\to\eta\eta\eta^{\prime}$ is performed to search for the $1^{-+}$ exotic state $\eta_1(1855)$ . The PWA result indicates that the structure in the $\eta\eta^{\prime}$ mass spectrum is attributed to $f_0(1500)$ , while in the $\eta\eta$ mass spectrum, it is attributed to the $0^{++}$ phase space. The upper limit of ${\cal{B}}(\chi_{c1}\to\eta_{1}(1855)\eta) \cdot {\cal{B}}(\eta_{1}(1855)\to\eta\eta^{\prime}) \lt $ $ 9.79 \times 10^{-5}$ is set based on the PWA at 90% CL.

M. Bertani

Z.J. Chen

J.J. Cui

I. Denysenko

L. Feng

Q.X. Feng

Search for $\textit{η}$ $_{1}$(1855) in $\textit{χ}$ $\textit{cJ}$ → $\textit{ηηη}$′ decays * Supported in part by National Key R&D Program of China (2023YFA1606000, 2023YFA1606704); National Natural Science Foundation of China (NSFC) (11635010, 11935015, 11935016, 11935018, 12025502, 12035009, 12035013, 12061131003, 12192260, 12192261, 12192262, 12192263, 12192264, 12192265, 12221005, 12225509, 12235017, 12361141819); the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; CAS (YSBR-101); 100 Talents Program of CAS; The Institute of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology; Agencia Nacional de Investigación y Desarrollo de Chile (ANID), Chile (ANID PIA/APOYO AFB230003); German Research Foundation DFG (FOR5327); Istituto Nazionale di Fisica Nucleare, Italy; Knut and Alice Wallenberg Foundation (2021.0174, 2021.0299); Ministry of Development of Turkey (DPT2006K-120470); National Research Foundation of Korea ( NRF-2022R1A2C1092335); National Science and Technology fund of Mongolia; National Science Research and Innovation Fund (NSRF) via the Program Management Unit for Human Resources Institutional Development, Research and Innovation of Thailand ( B50G670107); Polish National Science Centre (2024/53/B/ST2/00975); Swedish Research Council (2019.04595); U. S. Department of Energy (DE-FG02-05ER41374)

Lepton number violation decay $ \omega \to \pi^+ \pi^+ e^-e^- +c.c. $ is searched for via $ J/\psi \to \omega\eta $ using a data sample of $ (1.0087 \pm 0.0044) \times 10^{10} $ $ J/\psi $ events collected via the BESIII detector at the BEPCII collider. No significant signal is observed, and the upper limit on the branching fraction of $ \omega \to \pi^+ \pi^+ e^-e^- +c.c. $ at the 90% confidence level is determined for the first time to be $ 2.8 \times 10^{-6} $ .

Search for the lepton number violation decay $\textit{ω}$→$\textit{π}$ $^{+}$ $\textit{π}$ $^{+}$ $\textit{e}$ $^{−}$ $\textit{e}$ $^{−}$+$\textit{c}$.$\textit{c}$. * Supported in part by National Key R&D Program of China (2023YFA1606000, 2023YFA1606704); National Natural Science Foundation of China (NSFC) (12035009, 11875170, 11635010, 11935015, 11935016, 11935018, 12025502, 12035013, 12061131003, 12192260, 12192261, 12192262, 12192263, 12192264, 12192265, 12221005, 12225509, 12235017, 12361141819); the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; CAS (YSBR-101); 100 Talents Program of CAS; The Institute of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology; Agencia Nacional de Investigación y Desarrollo de Chile (ANID), Chile (ANID PIA/APOYO AFB230003); ERC (758462); German Research Foundation DFG (FOR5327); Istituto Nazionale di Fisica Nucleare, Italy; Knut and Alice Wallenberg Foundation (2021.0174, 2021.0299); Ministry of Development of Turkey (DPT2006K-120470); National Research Foundation of Korea (NRF-2022R1A2C1092335); National Science and Technology fund of Mongolia; Polish National Science Centre (2024/53/B/ST2/00975); STFC (United Kingdom); Swedish Research Council (2019.04595); U. S. Department of Energy (DE-FG02-05ER41374)

By analyzing a $\psi(3686)$ data sample containing $(107.7\pm0.6)\times10^{6}$ events taken with the BESIII detector at the BEPCII storage ring in 2009, the $\chi_{c0}$ resonance parameters are precisely measured using $\chi_{c0,c2} \to \pi^+\pi^-/K^+K^-$ events. The mass of $\chi_{c0}$ is determined to be $M(\chi_{c0})=(3415.63\pm0.07\pm0.07\pm0.07$ ) MeV/ $c^2$ , and its full width is $\Gamma(\chi_{c0})=(12.52\pm0.12\pm0.13)~{\rm{MeV}}$ , where the first uncertainty is statistical, the second systematic, and the third for mass comes from $\chi_{c2}$ mass uncertainty. These measurements improve the precision of $\chi_{c0}$ mass by a factor of four and width by one order of magnitude over the previous individual measurements, and significantly boost our knowledge about the charmonium spectrum. Together with additional $(345.4\pm2.6)\times10^{6}$ $\psi(3686)$ data events taken in 2012, the decay branching fractions of $\chi_{c0,c2}\to\pi^+\pi^-/K^+K^-$ are measured as well, with precision improved by a factor of three compared to previous measurements. These $\chi_{c0}$ decay branching fractions provide important inputs for the study of glueballs.

O. Afedulidis

I. Balossino

G. Chelkov

C. Chen

Z.Y. Chen

Y. Fang

Y.T. Feng

M. Fritsch

C.D. Fu

J.L. Fu

Y.W. Fu

H. Gao

X.B. Gao

Precise measurement of the $\textit{χ}$ $\textit{c}$0 resonance parameters and branching fractions of $\textit{χ}$ $\textit{c}$0,$\textit{c}$2 → $\textit{π}$ $^{+}$ $\textit{π}$ $^{−}$/$\textit{K}$ $^{+}$ $\textit{K}$ $^{−}$ * Supported in part by National Key R&D Program of China (2020YFA0406300, 2020YFA0406400, 2023YFA1606000); National Natural Science Foundation of China (NSFC) (11635010, 11735014, 11935015, 11935016, 11935018, 12025502, 12035009, 12035013, 12061131003, 12192260, 12192261, 12192262, 12192263, 12192264, 12192265, 12221005, 12225509, 12235017, 12361141819); the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; the CAS Center for Excellence in Particle Physics (CCEPP); Joint Large-Scale Scientific Facility Funds of the NSFC and CAS (U1832207); 100 Talents Program of CAS; (ZR2022JQ02, ZR2024QA151) supported by Shandong Provincial Natural Science Foundation; supported by the China Postdoctoral Science Foundation (2023M742100); The Institute of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology; German Research Foundation DFG (FOR5327, GRK 2149); Istituto Nazionale di Fisica Nucleare, Italy; Knut and Alice Wallenberg Foundation (2021.0174, 2021.0299); Ministry of Development of Turkey (DPT2006K-120470); National Research Foundation of Korea (NRF-2022R1A2C1092335); National Science and Technology fund of Mongolia; National Science Research and Innovation Fund (NSRF) via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation of Thailand (B16F640076, B50G670107); Polish National Science Centre (2019/35/O/ST2/02907); Swedish Research Council (2019.04595); The Swedish Foundation for International Cooperation in Research and Higher Education (CH2018-7756); U. S. Department of Energy (DE-FG02-05ER41374)

Using 20.3 fb$^{–1}$ of $e^+e^-$ annihilation data collected at a center-of-mass energy of 3.773 GeV with the BESIII detector, we report on an improved search for the radiative leptonic decay $D^+\to\gamma e^+\nu_e$ . An upper limit on its partial branching fraction for photon energies $E_\gamma \gt 10 $ MeV was determined to be $1.2\times10^{-5}$ at a 90% confidence level; this excludes most current theoretical predictions. A sophisticated deep learning approach, which includes thorough validation and is based on the Transformer architecture, was implemented to efficiently distinguish the signal from massive backgrounds.

Search for radiative leptonic decay $\textit{D}$ $^{+}$→$\textit{γe}$ $^{+}$ ν$_{e}$ using deep learning * This work is supported in part by National Key R&D Program of China (2020YFA0406400, 2023YFA1606000, 2020YFA0406300); National Natural Science Foundation of China (NSFC) (11635010, 11735014, 11935015, 11935016, 11935018, 12025502, 12035009, 12035013, 12061131003, 12192260, 12192261, 12192262, 12192263, 12192264, 12192265, 12221005, 12225509, 12235017, 12361141819); the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; the CAS Center for Excellence in Particle Physics (CCEPP); Joint Large-Scale Scientific Facility Funds of the NSFC and CAS (U1832207); CAS (YSBR-101); 100 Talents Program of CAS; CAS Project for Young Scientists in Basic Research (YSBR-117); The Institute of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology; Agencia Nacional de Investigación y Desarrollo de Chile (ANID), Chile (ANID PIA/APOYO AFB230003); German Research Foundation DFG (FOR5327); Istituto Nazionale di Fisica Nucleare, Italy; Knut and Alice Wallenberg Foundation (2021.0174, 2021.0299); Ministry of Development of Turkey (DPT2006K-120470); National Research Foundation of Korea (NRF-2022R1A2C1092335); National Science and Technology fund of Mongolia; National Science Research and Innovation Fund (NSRF) via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation of Thailand (B50G670107); Polish National Science Centre (2019/35/O/ST2/02907); Swedish Research Council (2019.04595); The Swedish Foundation for International Cooperation in Research and Higher Education (CH2018-7756); U. S. Department of Energy (DE-FG02-05ER41374)

Utilizing 4.5 $ \text{fb}^{-1} $ of $ e^+e^- $ annihilation data collected at center-of-mass energies ranging from 4599.53 MeV to 4698.82 MeV by the BESIII detector at the BEPCII collider, we searched for singly Cabibbo-suppressed hadronic decays $ \Lambda_{c}^{+}\to\Sigma^{0} K^{+}\pi^{0} $ and $ \Lambda_{c}^{+}\to\Sigma^{0}K^{+} \pi^+ \pi^- $ with a single-tag method. No significant signals were observed for both decays. The upper limits on the branching fractions at the 90% confidence level were determined to be $ 5.0\times 10^{-4} $ for $ \Lambda_{c}^{+}\to\Sigma^{0} K^{+}\pi^{0} $ and $ 6.5\times 10^{-4} $ for $ \Lambda_c^{+}\to\Sigma^0K^{+}\pi^{+}\pi^{-} $ .

Search for Cabibbo-suppressed decays ${\boldsymbol\Lambda_{\boldsymbol c}^{\bf +} }$ → Σ$^{0}$ $\textit{K}$ $^{+}$ $\textit{π}$ $^{0}$ and $ {\boldsymbol\Lambda_{\boldsymbol c}^{\bf +} }$ → Σ$^{0}$ $\textit{K}$ $^{+}$ $\textit{π}$ $^{+}$ $\textit{π}$ $^{−}$ * This study has been supported in part by National Key R&D Program of China (2020YFA0406300, 2020YFA0406400, 2023YFA1606000); National Natural Science Foundation of China (NSFC) (12205141, 11635010, 11735014, 11935015, 11935016, 11935018, 12025502, 12035009, 12035013, 12061131003, 12192260, 12192261, 12192262, 12192263, 12192264, 12192265, 12221005, 12225509, 12235017, 12361141819); Natural Science Foundation of Hunan Province (2024JJ2044); the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; the CAS Center for Excellence in Particle Physics (CCEPP); Joint Large-Scale Scientific Facility Funds of the NSFC and CAS (U1832207); 100 Talents Program of CAS; The Institute of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology; German Research Foundation DFG (FOR5327); Istituto Nazionale di Fisica Nucleare, Italy; Knut and Alice Wallenberg Foundation (2021.0174, 2021.0299); Ministry of Development of Turkey (DPT2006K-120470); National Research Foundation of Korea (NRF-2022R1A2C1092335); National Science and Technology fund of Mongolia; National Science Research and Innovation Fund (NSRF) via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation of Thailand (B16F640076, B50G670107); Polish National Science Centre (2019/35/O/ST2/02907); Swedish Research Council (2019.04595); The Swedish Foundation for International Cooperation in Research and Higher Education (CH2018-7756); and U. S. Department of Energy (DE-FG02-05ER41374)

We search for the leptonic decay $ D^+\to e^+\nu_{e} $ using an $ e^+e^- $ collision data sample with an integrated luminosity of 20.3 fb $ ^{-1} $ collected with the BESIII detector at a center-of-mass energy of 3.773 GeV. Significant signal is not observed, and an upper limit on the branching fraction of $ D^+\to e^+\nu_{e} $ is set as $ 9.7 \times 10^{-7} $ , at a confidence level of 90%. Our upper limit is an order of magnitude smaller than the previous limit for this decay mode.

Search for the leptonic decay ${\boldsymbol D^{\bf +}{\bf\to}{\boldsymbol e}^{\bf +}\boldsymbol\nu_{\boldsymbol e}}$ * Supported in part by the National Key R&D Program of China (2023YFA1606000, 2020YFA0406400, 2020YFA0406300), the National Natural Science Foundation of China(NSFC) (11635010, 11735014, 11935015, 11935016, 11875054, 11935018, 12025502, 12035009, 12035013, 12061131003, 12192260, 12192261, 12192262, 12192263, 12192264, 12192265, 12221005, 12225509, 12235017, 12361141819), the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program, the CAS Center for Excellence in Particle Physics (CCEPP), the Joint Large-Scale Scientific Facility Funds of the NSFC and CAS (U2032104, U1832207), the 100 Talents Program of CAS, the Excellent Youth Foundation of Henan Scientific Commitee (242300421044), the Institute of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology, the German Research Foundation DFG (FOR5327), the Istituto Nazionale di Fisica Nucleare, Italy, the Knut and Alice Wallenberg Foundation (2021.0174, 2021.0299), the Ministry of Development of Turkey (DPT2006K-120470), the National Research Foundation of Korea (NRF-2022R1A2C1092335), the National Science and Technology Fund of Mongolia, the National Science Research and Innovation Fund (NSRF) via the Program Management Unit for Human Resources & Institutional Development, Research, and Innovation of Thailand (B16F640076, B50G670107), the Polish National Science Center (2019/35/O/ST2/02907), the Swedish Research Council (2019.04595), the Swedish Foundation for International Cooperation in Research and Higher Education (CH2018-7756), and the US Department of Energy (DE-FG02-05ER41374).

Using an electron-positron collision data sample corresponding to $ (1.0087\pm0.0044)\times10^{10} $ $ J/\psi $ events collected using the BESIII detector at the BEPCII collider, we firstly search for the lepton number violation decay $ \phi \to \pi^+ \pi^+ e^- e^- $ via $ J/\psi\to \phi\eta $ . No obviously signals are found. The upper limit on the branching fraction of $ \phi \to \pi^+ \pi^+ e^- e^- $ is set to be $ 1.3\times10^{-5} $ at the 90% confidence level.

M.R. An

S.C. Coen

K. Fischer

Y.N. Gao

Yang Gao

S. Garbolino

I. Garzia

Search for the lepton number violation decay $\textit{ϕ}$ → $\textit{π}$ $^{+}$ $\textit{π}$ $^{+}$ $\textit{e}$ $^{−}$ $\textit{e}$ $^{−}$ via $\textit{J}$/$\textit{ψ}$ → $\textit{ϕη}$ * The BESIII Collaboration appreciates the staff of BEPCII and the IHEP Computing Center for their strong support. This work is supported in part by the National Key R&D Program of China (2020YFA0406300, 2020YFA0406400); National Natural Science Foundation of China (NSFC) (12035009, 11635010, 11735014, 11835012, 11935015, 11935016, 11935018, 11961141012, 12025502, 12035013, 12061131003, 12192260, 12192261, 12192262, 12192263, 12192264, 12192265, 12221005, 12225509, 12235017); the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; the CAS Center for Excellence in Particle Physics (CCEPP); Joint Large-Scale Scientific Facility Funds of the NSFC and CAS (U1832207); CAS Key Research Program of Frontier Sciences (QYZDJ-SSW-SLH003, QYZDJ-SSW-SLH040); 100 Talents Program of CAS; the Institute of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology; the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement (894790); the German Research Foundation DFG (455635585), the Collaborative Research Center CRC 1044, FOR5327, GRK 2149; Istituto Nazionale di Fisica Nucleare, Italy; Knut and Alice Wallenberg Foundation (2021.0174, 2021.0299); Ministry of Development of Turkey (DPT2006K-120470); National Research Foundation of Korea (NRF-2022R1A2C1092335); National Science and Technology Fund of Mongolia; National Science Research and Innovation Fund (NSRF) via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation of Thailand (B16F640076); Polish National Science Centre (2019/35/O/ST2/02907); Swedish Research Council (2019.04595); the Swedish Foundation for International Cooperation in Research and Higher Education (CH2018-7756); and the U. S. Department of Energy (DE-FG02-05ER41374).

Based on the generalized quantum electrodynamics expression for the Podolsky propagator, which preserves gauge invariance for massive photons, we propose a model for the massive gluon propagator that reproduces well-known features of established strong-interaction models in the framework of the Dyson-Schwinger equation. By adjusting the Podolsky mass and the coupling strength we thus construct a model with simple analytical properties known from perturbative theory, yet well suited to describe a confining interaction. We obtain solutions of the Dyson-Schwinger equation for the quark at spacelike momenta on the real axis as well as on the complex plane and solving the bound-state problem with the Bethe-Salpeter equation yields masses and weak decay constants of the <math><mrow><mi>π</mi></mrow></math>, <math><mrow><mi>K</mi></mrow></math> and <math><msub><mi>η</mi><mi>c</mi></msub></math> in excellent agreement with experimental values, while the <math><mi>D</mi></math> and <math><msub><mi>D</mi><mi>s</mi></msub></math> are reasonably well described. The analytical simplicity of this effective interaction has the potential to be useful for phenomenological applications and may facilitate calculations in Minkowski space.