Open Access

$Ξ_{c} \to Ξ$ form factors from lattice QCD with domain-wall quarks: A new piece in the puzzle of $Ξ_{c}^{0}$ decay rates

Department of Physics, University of Arizona, Tucson, Arizona 85721, USA

Phys. Rev. D 111, 114521 – Published 27 June, 2025

DOI: https://doi.org/10.1103/35c9-kbvr

Abstract

We present a lattice quantum chromodynamics (QCD) determination of the vector and axial-vector form factors that describe the charm-baryon semileptonic decays $Ξ_{c} \to Ξ ℓ^{+} ν_{ℓ}$ . The calculation uses a domain-wall action for the up, down, and strange quarks, and an anisotropic clover action for the charm quark. We use four ensembles of gauge-field configurations generated by the RBC and UKQCD collaborations, with lattice spacings between 0.111 and 0.073 fm and pion masses ranging from 420 to 230 MeV. We present Standard Model predictions for the decay rates and branching fractions of $Ξ_{c}^{0} \to Ξ_{c}^{-} ℓ^{+} ν_{ℓ}$ and $Ξ_{c}^{+} \to Ξ_{c}^{0} ℓ^{+} ν_{ℓ}$ for $ℓ = e$ , $μ$ . In particular, we obtain $Γ (Ξ_{c}^{0} \to Ξ^{-} e^{+} ν_{e}) / | V_{c s} |^{2} = 0.2515 (73) {ps}^{- 1}$ and $B (Ξ_{c}^{0} \to Ξ^{-} e^{+} ν_{e}) = 3.58 (12) %$ . These values are higher than those predicted by a previous lattice calculation and substantially higher than the experimentally measured values, but consistent with expectations from approximate $S U (3)$ flavor symmetry.

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (70)

M. Ablikim et al. (BESIII Collaboration), Measurement of the absolute branching fraction for $Λ_{c}^{+} \to Λ e^{+} ν_{e}$ , Phys. Rev. Lett. 115, 221805 (2015).
M. Ablikim et al. (BESIII Collaboration), Measurement of the absolute branching fraction for $Λ_{c}^{+} \to Λ μ^{+} ν_{μ}$ , Phys. Lett. B 767, 42 (2017).
M. Ablikim et al. (BESIII Collaboration), Study of the semileptonic decay $Λ_{c}^{+} \to Λ e^{+} ν_{e}$ , Phys. Rev. Lett. 129, 231803 (2022).
M. Ablikim et al. (BESIII Collaboration), Study of $Λ_{c}^{+} \to Λ μ^{+} ν_{μ}$ and test of lepton flavor universality with $Λ_{c}^{+} \to Λ ℓ^{+} ν_{ℓ}$ decays, Phys. Rev. D 108, L031105 (2023).
S. Meinel, $Λ_{c} \to Λ l^{+} ν_{l}$ form factors and decay rates from lattice QCD with physical quark masses, Phys. Rev. Lett. 118, 082001 (2017).
M. Ablikim et al. (BESIII Collaboration), Measurement of the absolute branching fraction of the inclusive semileptonic $Λ_{c}^{+}$ decay, Phys. Rev. Lett. 121, 251801 (2018).
M. Ablikim et al. (BESIII Collaboration), First observation of the semileptonic decay $Λ_{c}^{+} \to p K^{-} e^{+} ν_{e}$ , Phys. Rev. D 106, 112010 (2022).
M. Ablikim et al. (BESIII Collaboration), Observation of a rare beta decay of the charmed baryon with a graph neural network, Nat. Commun. 16, 681 (2025).
S. Meinel, $Λ_{c} \to N$ form factors from lattice QCD and phenomenology of $Λ_{c} \to n ℓ^{+} ν_{ℓ}$ and $Λ_{c} \to p μ^{+} μ^{-}$ decays, Phys. Rev. D 97, 034511 (2018).
S. Meinel and G. Rendon, $Λ_{c} \to Λ^{*} (1520)$ form factors from lattice QCD and improved analysis of the $Λ_{b} \to Λ^{*} (1520)$ and $Λ_{b} \to Λ_{c}^{*} (2595, 2625)$ form factors, Phys. Rev. D 105, 054511 (2022).
S. Meinel and G. Rendon, Charm-baryon semileptonic decays and the strange $Λ^{*}$ resonances: New insights from lattice QCD, Phys. Rev. D 105, L051505 (2022).
H. Albrecht et al. (ARGUS Collaboration), Observation of $Ξ_{c}^{0}$ semileptonic decay, Phys. Lett. B 303, 368 (1993).
J. P. Alexander et al. (CLEO Collaboration), First observation of $Ξ_{c}^{+} \to Ξ^{0} e^{+} ν_{e}$ and a measurement of the $Ξ_{c}^{+} / Ξ_{c}^{0}$ lifetime ratio, Phys. Rev. Lett. 74, 3113 (1995); 75, 4155(E) (1995).
Y. B. Li et al. (Belle Collaboration), Measurements of the branching fractions of the semileptonic decays $Ξ_{c}^{0} \to Ξ^{-} ℓ^{+} ν_{ℓ}$ and the asymmetry parameter of $Ξ_{c}^{0} \to Ξ^{-} π^{+}$ , Phys. Rev. Lett. 127, 121803 (2021).
S. Acharya et al. (ALICE Collaboration), Measurement of the cross sections of $Ξ_{c}^{0}$ and $Ξ_{c}^{+}$ baryons and of the branching-fraction ratio $BR (Ξ_{c}^{0} \to Ξ^{-} e^{+} ν_{e}) / BR (Ξ_{c}^{0} \to Ξ^{-} π^{+})$ in $p p$ collisions at 13 TeV, Phys. Rev. Lett. 127, 272001 (2021).
Y. B. Li et al. (Belle Collaboration), First measurements of absolute branching fractions of the $Ξ_{c}^{0}$ baryon at Belle, Phys. Rev. Lett. 122, 082001 (2019).
S. Navas et al. (Particle Data Group Collaboration), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
Q.-A. Zhang, J. Hua, F. Huang, R. Li, Y. Li, C. Lü, P. Sun, W. Sun, W. Wang, and Y. Yang, First lattice QCD calculation of semileptonic decays of charmed-strange baryons $Ξ_{c}$ , Chin. Phys. C 46, 011002 (2022).
X.-G. He, F. Huang, W. Wang, and Z.-P. Xing, SU(3) symmetry and its breaking effects in semileptonic heavy baryon decays, Phys. Lett. B 823, 136765 (2021).
C.-Q. Geng, X.-N. Jin, and C.-W. Liu, Resolving puzzle in $Ξ_{c}^{0} \to Ξ^{-} e^{+} ν_{e}$ with $Ξ_{c} - Ξ_{c}^{'}$ mixing spectrum within the quark model, Phys. Lett. B 838, 137736 (2023).
M. Bona et al. (UTfit Collaboration), New UTfit analysis of the unitarity triangle in the Cabibbo-Kobayashi-Maskawa scheme, Rend. Lincei Sci. Fis. Nat. 34, 37 (2023).
Z. S. Brown, W. Detmold, S. Meinel, and K. Orginos, Charmed bottom baryon spectroscopy from lattice QCD, Phys. Rev. D 90, 094507 (2014).
H. Liu, L. Liu, P. Sun, W. Sun, J.-X. Tan, W. Wang, Y.-B. Yang, and Q.-A. Zhang, $Ξ_{c} - Ξ_{c}^{'}$ mixing from lattice QCD, Phys. Lett. B 841, 137941 (2023).
H. Liu, W. Wang, and Q.-A. Zhang, An improved method to determine the $Ξ_{c} - Ξ_{c}^{'}$ mixing, Phys. Rev. D 109, 036037 (2024).
M. Tanabashi et al. (Particle Data Group Collaboration), Review of particle physics, Phys. Rev. D 98, 030001 (2018).
R. Aaij et al. (LHCb Collaboration), Precision measurement of the $Λ_{c}^{+}$ , $Ξ_{c}^{+}$ and $Ξ_{c}^{0}$ baryon lifetimes, Phys. Rev. D 100, 032001 (2019).
LHCb Collaboration, Measurement of the lifetimes of promptly produced $Ω_{c}^{0}$ and $Ξ_{c}^{0}$ baryons, Sci. Bull. 67, 479 (2022).
Z.-X. Zhao, X.-Y. Sun, F.-W. Zhang, Y.-P. Xing, and Y.-T. Yang, Semileptonic form factors of $Ξ_{c} \to Ξ$ in QCD sum rules, Phys. Rev. D 108, 116008 (2023).
C. Q. Geng, C.-W. Liu, and T.-H. Tsai, Semileptonic weak decays of antitriplet charmed baryons in the light-front formalism, Phys. Rev. D 103, 054018 (2021).
R. N. Faustov and V. O. Galkin, Semileptonic $Ξ_{c}$ baryon decays in the relativistic quark model, Eur. Phys. J. C 79, 695 (2019).
C.-Q. Geng, C.-W. Liu, T.-H. Tsai, and S.-W. Yeh, Semileptonic decays of anti-triplet charmed baryons, Phys. Lett. B 792, 214 (2019).
Z.-X. Zhao, Weak decays of heavy baryons in the light-front approach, Chin. Phys. C 42, 093101 (2018).
C. Q. Geng, Y. K. Hsiao, C.-W. Liu, and T.-H. Tsai, Antitriplet charmed baryon decays with SU(3) flavor symmetry, Phys. Rev. D 97, 073006 (2018).
C. Q. Geng, Y. K. Hsiao, C.-W. Liu, and T.-H. Tsai, Charmed baryon weak decays with SU(3) flavor symmetry, J. High Energy Phys. 11 (2017) 147.
K. Azizi, Y. Sarac, and H. Sundu, Light cone QCD sum rules study of the semileptonic heavy $Ξ_{Q}$ and $Ξ_{Q}^{'}$ transitions to $Ξ$ and $Σ$ baryons, Eur. Phys. J. A 48, 2 (2012).
Y.-L. Liu and M.-Q. Huang, A light-cone QCD sum rule approach for the $Ξ$ baryon electromagnetic form factors and the semileptonic decay $Ξ_{c} \to Ξ e^{+} ν_{e}$ , J. Phys. G 37, 115010 (2010).
C. Farrell and S. Meinel, Form factors for the charm-baryon semileptonic decay $Ξ_{c} \to Ξ ℓ ν$ from domain-wall lattice QCD, Proc. Sci. LATTICE2023 (2024) 210 [arXiv:2309.08107].
T. Feldmann and M. W. Y. Yip, Form factors for $Λ_{b} \to Λ$ transitions in the soft-collinear effective theory, Phys. Rev. D 85, 014035 (2012); 86, 079901(E) (2012).
W. Detmold, C. Lehner, and S. Meinel, $Λ_{b} \to p ℓ^{-} {\bar{ν}}_{ℓ}$ and $Λ_{b} \to Λ_{c} ℓ^{-} {\bar{ν}}_{ℓ}$ form factors from lattice QCD with relativistic heavy quarks, Phys. Rev. D 92, 034503 (2015).
W. Detmold and S. Meinel, $Λ_{b} \to Λ ℓ^{+} ℓ^{-}$ form factors, differential branching fraction, and angular observables from lattice QCD with relativistic $b$ quarks, Phys. Rev. D 93, 074501 (2016).
Y. Aoki et al. (RBC, UKQCD Collaborations), Continuum limit physics from $2 + 1$ flavor domain wall QCD, Phys. Rev. D 83, 074508 (2011).
T. Blum et al. (RBC, UKQCD Collaborations), Domain wall QCD with physical quark masses, Phys. Rev. D 93, 074505 (2016).
P. A. Boyle, L. Del Debbio, N. Garron, A. Juttner, A. Soni, J. T. Tsang, and O. Witzel (RBC/UKQCD Collaboration), SU(3)-breaking ratios for $D_{(s)}$ and $B_{(s)}$ mesons, arXiv:1812.08791.
S. Meinel, Status of next-generation $Λ_{b} \to p, Λ, Λ_{c}$ form-factor calculations, Proc. Sci. LATTICE2023 (2024) 275 [arXiv:2309.01821].
T. Blum, T. Izubuchi, and E. Shintani, New class of variance-reduction techniques using lattice symmetries, Phys. Rev. D 88, 094503 (2013).
E. Shintani, R. Arthur, T. Blum, T. Izubuchi, C. Jung, and C. Lehner, Covariant approximation averaging, Phys. Rev. D 91, 114511 (2015).
Y. Aoki, N. H. Christ, J. M. Flynn, T. Izubuchi, C. Lehner, M. Li, H. Peng, A. Soni, R. S. Van de Water, and O. Witzel (RBC, UKQCD Collaborations), Nonperturbative tuning of an improved relativistic heavy-quark action with application to bottom spectroscopy, Phys. Rev. D 86, 116003 (2012).
S. Hashimoto, A. X. El-Khadra, A. S. Kronfeld, P. B. Mackenzie, S. M. Ryan, and J. N. Simone, Lattice QCD calculation of $\bar{B} \to D ℓ \bar{ν}$ decay form-factors at zero recoil, Phys. Rev. D 61, 014502 (1999).
A. X. El-Khadra, A. S. Kronfeld, P. B. Mackenzie, S. M. Ryan, and J. N. Simone, The semileptonic decays $B \to π ℓ ν$ and $D \to π ℓ ν$ from lattice QCD, Phys. Rev. D 64, 014502 (2001).
C. Lehner, Automated lattice perturbation theory and relativistic heavy quarks in the Columbia formulation, Proc. Sci. LATTICE2012 (2012) 126 [arXiv:1211.4013].
J. M. Flynn, R. C. Hill, A. Jüttner, A. Soni, J. T. Tsang, and O. Witzel (RBC/UKQCD Collaborations), Exclusive semileptonic $B_{s} \to K ℓ ν$ decays on the lattice, Phys. Rev. D 107, 114512 (2023).
M. Marshall, Lattice determination of semi-leptonic, heavy-light meson decay form factors, Ph.D. thesis, Edinburgh University, 2024.
S. Meinel and G. Rendon, $Λ_{b} \to Λ^{*} (1520) ℓ^{+} ℓ^{-}$ form factors from lattice QCD, Phys. Rev. D 103, 074505 (2021).
L. Leskovec, S. Meinel, M. Pflaumer, and M. Wagner, Lattice QCD investigation of a doubly-bottom $\bar{b} \bar{b} u d$ tetraquark with quantum numbers $I (J^{P}) = 0 (1^{+})$ , Phys. Rev. D 100, 014503 (2019).
F. D. R. Bonnet, P. Fitzhenry, D. B. Leinweber, M. R. Stanford, and A. G. Williams, Calibration of smearing and cooling algorithms in SU(3): Color gauge theory, Phys. Rev. D 62, 094509 (2000).
C. Morningstar and M. J. Peardon, Analytic smearing of SU(3) link variables in lattice QCD, Phys. Rev. D 69, 054501 (2004).
W. I. Jay and E. T. Neil, Bayesian model averaging for analysis of lattice field theory results, Phys. Rev. D 103, 114502 (2021).
E. T. Neil and J. W. Sitison, Model averaging approaches to data subset selection, Phys. Rev. E 108, 045308 (2023).
C. Bourrely, I. Caprini, and L. Lellouch, Model-independent description of $B \to π ℓ ν$ decays and a determination of $| V_{u b} |$ , Phys. Rev. D 79, 013008 (2009); 82, 099902(E) (2010).
See Supplemental Material at http://link.aps.org/supplemental/10.1103/35c9-kbvr for files containing the form-factor parameter values and covariance matrices.
A. X. El-Khadra, A. S. Kronfeld, and P. B. Mackenzie, Massive fermions in lattice gauge theory, Phys. Rev. D 55, 3933 (1997).
C.-Q. Geng, X.-G. He, X.-N. Jin, C.-W. Liu, and C. Yang, Complete determination of $S U (3)_{F}$ amplitudes and strong phase in $Λ_{c}^{+} \to Ξ^{0} K^{+}$ , Phys. Rev. D 109, L071302 (2024).
Z.-P. Xing, Y.-J. Shi, J. Sun, and Y. Xing, $S U (3)$ symmetry analysis in charmed baryon two body decays with penguin diagram contribution, Eur. Phys. J. C 84, 1014 (2024).
J. Towns, T. Cockerill, M. Dahan, I. Foster, K. Gaither, A. Grimshaw, V. Hazlewood, S. Lathrop, D. Lifka, G. D. Peterson, R. Roskies, J. R. Scott, and N. Wilkins-Diehr, XSEDE: Accelerating scientific discovery, Comput. Sci. Eng. 16, 62 (2014).
T. J. Boerner, S. Deems, T. R. Furlani, S. L. Knuth, and J. Towns, ACCESS: Advancing innovation: NSF’s Advanced cyberinfrastructure coordination ecosystem: Services & support, in Practice and Experience in Advanced Research Computing 2023: Computing for the Common Good, PEARC ’23 (Association for Computing Machinery, New York, NY, USA, 2023), pp. 173–176.
R. G. Edwards and B. Joo (SciDAC, LHPC, UKQCD Collaborations), The chroma software system for lattice QCD, Nucl. Phys. B, Proc. Suppl. 140, 832 (2005).
R. G. Edwards, B. Joó et al., chroma, https://github.com/JeffersonLab/chroma.
A. Pochinsky, S. Syritsyn et al., qlua, https://usqcd.lns.mit.edu/w/index.php/QLUA.
A. Pochinsky, S. Syritsyn et al., Möbius Domain Wall inverter, https://github.com/usqcd-software/mdwf.
USQCD Collaboration, usqcd Software, http://usqcd-software.github.io.

Phys. Rev. D 111, 114521– Published 27 June, 2025

Vol. 111, Iss. 11 — 1 June 2025

Received 22 April 2025
Accepted 10 June 2025

DOI: https://doi.org/10.1103/35c9-kbvr

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

$Ξ_{c} \to Ξ$ form factors from lattice QCD with domain-wall quarks: A new piece in the puzzle of $Ξ_{c}^{0}$ decay rates

Abstract

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (70)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

Ξc→Ξ form factors from lattice QCD with domain-wall quarks: A new piece in the puzzle of Ξc0 decay rates

Abstract

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (70)

$Ξ_{c} \to Ξ$ form factors from lattice QCD with domain-wall quarks: A new piece in the puzzle of $Ξ_{c}^{0}$ decay rates