Open Access

$C P$ violation in two-body hadronic $Λ_{b}$ decays in the PQCD approach

Jia-Jie Han ¹, Ji-Xin Yu ^1,*, Ya Li ^2,†, Hsiang-nan Li ^3,‡, Jian-Peng Wang ^1,§, Zhen-Jun Xiao ^2,∥, and Fu-Sheng Yu^1,¶

¹Frontiers Science Center for Rare Isotopes, and School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, People’s Republic of China
²Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing 210023, People’s Republic of China
³Institute of Physics, Academia Sinica, Taipei, Taiwan 115, Republic of China

^*Contact author: yujx18@lzu.edu.cn
^†Contact author: liyakelly@163.com
^‡Contact author: hnli@phys.sinica.edu.tw
^§Contact author: wangjp20@lzu.edu.cn
^∥Contact author: xiaozhenjun@njnu.edu.cn
^¶Contact author: yufsh@lzu.edu.cn

PDF

Phys. Rev. D 112, 053007 – Published 29 September, 2025

DOI: https://doi.org/10.1103/lvsn-v3xj

Abstract

We systematically investigate the $C P$ -averaged branching ratios and $C P$ violations ( $C P V s$ ) for the two-body hadronic decays $Λ_{b} \to p h$ , where $h$ runs through the mesons $π^{-}$ , $ρ^{-}$ , $a_{1}^{-} (1260)$ , $K^{-}$ , $K^{* -}$ , $K_{1}^{-} (1270)$ , and $K_{1}^{-} (1400)$ , in the perturbative QCD approach to order $α_{s}^{2}$ in the strong coupling. Various topological amplitudes are obtained by incorporating subleading-twist hadron distribution amplitudes, which exhibit reasonable hierarchical patterns, sizable strong phases, and non-negligible higher-power corrections. The predicted direct $C P V s$ in $Λ_{b} \to p π^{-}, p K^{-}$ , different from those in similar $B$ meson decays, are as small as the current data. The low $C P V$ in $Λ_{b} \to p π^{-}$ results from the cancelation between the $S$ - and $P$ -wave $C P V s$ , while the one in $Λ_{b} \to p K^{-}$ is determined by the tiny $S$ -wave $C P V$ . However, individual partial-wave $C P V s$ can exceed 10%, consistent with direct $C P V s$ in $B$ meson decays. The $C P V s$ in the $Λ_{b} \to p K_{1}^{-} (1270), p K_{1}^{-} (1400)$ channels are relatively larger. In particular, $C P V s$ above 20% appear in the up-down asymmetries associated with the final-state angular distributions of $Λ_{b} \to p K_{1}^{-} (1270), p K_{1}^{-} (1400)$ , followed by the secondary $K_{1} \to K π π$ decays. These observables offer promising prospects for firmly establishing baryon $C P V s$ . The decay asymmetry parameters of $Λ_{b} \to p h$ are also predicted for future experimental confrontations.

Physics Subject Headings (PhySH)

Article Text

References (85)

J. H. Christenson, J. W. Cronin, V. L. Fitch, and R. Turlay, Evidence for the $2 π$ decay of the $K_{2}^{0}$ meson, Phys. Rev. Lett. 13, 138 (1964).
B. Aubert et al. (BABAR Collaboration), Measurement of $C P$ -violating asymmetries in $B^{0}$ decays to $C P$ eigenstates, Phys. Rev. Lett. 86, 2515 (2001).
K. Abe et al. (Belle Collaboration), Observation of large $C P$ violation in the neutral $B$ meson system, Phys. Rev. Lett. 87, 091802 (2001).
R. Aaij et al. (LHCb Collaboration), Observation of $C P$ violation in charm decays, Phys. Rev. Lett. 122, 211803 (2019).
BESIII Collaboration, Polarization and entanglement in baryon-antibaryon pair production in electron-positron annihilation, Nat. Phys. 15, 631 (2019).
M. Ablikim et al. (BESIII Collaboration), Probing $C P$ symmetry and weak phases with entangled double-strange baryons, Nature (London) 606, 64 (2022).
L. K. Li et al. (Belle Collaboration), Search for $C P$ violation and measurement of branching fractions and decay asymmetry parameters for $Λ_{c}^{+} \to Λ h^{+}$ and $Λ_{c}^{+} \to Σ^{0} h^{+}$ ( $h = K$ , $π$ ), Sci. Bull. 68, 583 (2023).
LHCb Collaboration, Measurement of matter-antimatter differences in beauty baryon decays, Nat. Phys. 13, 391 (2017).
R. Aaij et al. (LHCb Collaboration), A measurement of the $C P$ asymmetry difference in $Λ_{c}^{+} \to p K^{-} K^{+}$ and $p π^{-} π^{+}$ decays, J. High Energy Phys. 03 (2018) 182.
R. Aaij et al. (LHCb Collaboration), Search for $C P$ violation using triple product asymmetries in $Λ_{b}^{0} \to p K^{-} π^{+} π^{-}$ , $Λ_{b}^{0} \to p K^{-} K^{+} K^{-}$ and $Ξ_{b}^{0} \to p K^{-} K^{-} π^{+}$ decays, J. High Energy Phys. 08 (2018) 039.
R. Aaij et al. (LHCb Collaboration), Search for $C P$ violation in $Λ_{b}^{0} \to p K^{-}$ and $Λ_{b}^{0} \to p π^{-}$ decays, Phys. Lett. B 787, 124 (2018).
R. Aaij et al. (LHCb Collaboration), Measurements of $C P$ asymmetries in charmless four-body $Λ_{b}^{0}$ and $Ξ_{b}^{0}$ decays, Eur. Phys. J. C 79, 745 (2019).
R. Aaij et al. (LHCb Collaboration), Search for $C P$ violation and observation of $P$ violation in $Λ_{b}^{0} \to p π^{-} π^{+} π^{-}$ decays, Phys. Rev. D 102, 051101 (2020).
R. Aaij et al. (LHCb Collaboration), Measurement of $C P$ asymmetries in $Λ_{b}^{0} \to p h^{-}$ decays, Phys. Rev. D 111, 092004 (2025).
R. Aaij et al. (LHCb Collaboration), Study of $Λ_{b}^{0}$ and $Ξ_{b}^{0}$ decays to $Λ h^{+} h^{' -}$ and evidence for $C P$ violation in $Λ_{b}^{0} \to Λ K^{+} K^{-}$ decays, Phys. Rev. Lett. 134, 101802 (2025).
R. Aaij et al. (LHCb Collaboration), Observation of charge-parity symmetry breaking in baryon decays, Nature (London) 643, 1223 (2025).
F. S. Yu and C. D. Lü, New horizon in particle physics: First observation of $C P$ violation in baryon decays, Sci. Bull. 70, 2035 (2025).
J. J. Han, J. X. Yu, Y. Li, H. n. Li, J. P. Wang, Z. J. Xiao, and F. S. Yu, Establishing $C P$ violation in b-baryon decays, Phys. Rev. Lett. 134, 221801 (2025).
J. P. Wang, Q. Qin, and F. S. Yu, $C P$ violation observables in baryon decays, arXiv:2411.18323.
J. G. Korner and M. Kramer, Exclusive nonleptonic charm baryon decays, Z. Phys. C 55, 659 (1992).
Y. J. Zhao, Z. H. Zhang, and X. H. Guo, Decay-angular-distribution correlated $C P$ violation in heavy hadron cascade decays, Phys. Rev. D 110, 013007 (2024).
C. Q. Geng and C. W. Liu, Time-reversal asymmetries and angular distributions in $Λ_{b} \to Λ V$ , J. High Energy Phys. 11 (2021) 104.
W. Wang, Factorization of heavy-to-light baryonic transitions in SCET, Phys. Lett. B 708, 119 (2012).
J. J. Han, Y. Li, H. n. Li, Y. L. Shen, Z. J. Xiao, and F. S. Yu, $Λ_{b} \to p$ transition form factors in perturbative QCD, Eur. Phys. J. C 82, 686 (2022).
M. Beneke, G. Buchalla, M. Neubert, and C. T. Sachrajda, QCD factorization for $B \to π π$ decays: Strong phases and $C P$ violation in the heavy quark limit, Phys. Rev. Lett. 83, 1914 (1999).
M. Beneke, G. Buchalla, M. Neubert, and C. T. Sachrajda, QCD factorization for exclusive, nonleptonic B meson decays: General arguments and the case of heavy light final states, Nucl. Phys. B 591, 313 (2000).
C. W. Bauer, S. Fleming, D. Pirjol, and I. W. Stewart, An effective field theory for collinear and soft gluons: Heavy to light decays, Phys. Rev. D 63, 114020 (2001).
C. W. Bauer, D. Pirjol, and I. W. Stewart, Soft collinear factorization in effective field theory, Phys. Rev. D 65, 054022 (2002).
C. W. Bauer, S. Fleming, D. Pirjol, I. Z. Rothstein, and I. W. Stewart, Hard scattering factorization from effective field theory, Phys. Rev. D 66, 014017 (2002).
Y. Y. Keum, H. N. Li, and A. I. Sanda, Penguin enhancement and $B \to K π$ decays in perturbative QCD, Phys. Rev. D 63, 054008 (2001).
C. D. Lu, K. Ukai, and M. Z. Yang, Branching ratio and $C P$ violation of $B \to π π$ decays in perturbative QCD approach, Phys. Rev. D 63, 074009 (2001).
Y. Y. Keum, H. n. Li, and A. I. Sanda, Fat penguins and imaginary penguins in perturbative QCD, Phys. Lett. B 504, 6–14 (2001).
Y. K. Hsiao and C. Q. Geng, Direct $C P$ violation in $Λ_{b}$ decays, Phys. Rev. D 91, 116007 (2015).
Y. K. Hsiao, Y. Yao, and C. Q. Geng, Charmless two-body anti-triplet $b$ -baryon decays, Phys. Rev. D 95, 093001 (2017).
C. Q. Geng, C. W. Liu, and T. H. Tsai, Non-leptonic two-body decays of $Λ_{b}^{0}$ in light-front quark model, Phys. Lett. B 815, 136125 (2021).
J. P. Wang and F. S. Yu, $C P$ violation of baryon decays with N $π$ rescatterings*, Chin. Phys. C 48, 101002 (2024).
Z. D. Duan, J. P. Wang, R. H. Li, C. D. Lv, and F. S. Yu, Final-state rescattering mechanism of bottom-baryon decays, arXiv:2412.20458.
J. Zhu, H. W. Ke, and Z. T. Wei, The decay of $Λ_{b} \to p K^{-}$ in QCD factorization approach, Eur. Phys. J. C 76, 284 (2016).
J. Zhu, Z. T. Wei, and H. W. Ke, Semileptonic and nonleptonic weak decays of $Λ_{b}^{0}$ , Phys. Rev. D 99, 054020 (2019).
C. D. Lu, Y. M. Wang, H. Zou, A. Ali, and G. Kramer, Anatomy of the perturbative QCD approach to the baryonic decays $Λ_{b} \to p π, p K$ , Phys. Rev. D 80, 034011 (2009).
C. Q. Zhang, J. M. Li, M. K. Jia, and Z. Rui, Nonleptonic two-body decays of $Λ_{b} \to Λ_{c} π, Λ_{c} K$ in the perturbative QCD approach, Phys. Rev. D 105, 073005 (2022).
Z. Rui, C. Q. Zhang, J. M. Li, and M. K. Jia, Investigating the color-suppressed decays $Λ_{b} \to Λ ψ$ in the perturbative QCD approach, Phys. Rev. D 106, 053005 (2022).
Z. Rui and Z. T. Zou, Charmonium decays of beauty baryons in the perturbative QCD approach, Phys. Rev. D 109, 033013 (2024).
G. Buchalla, A. J. Buras, and M. E. Lautenbacher, Weak decays beyond leading logarithms, Rev. Mod. Phys. 68, 1125 (1996).
L. L. Chau, H. Y. Cheng, and B. Tseng, Analysis of two-body decays of charmed baryons using the quark diagram scheme, Phys. Rev. D 54, 2132 (1996).
F. S. Yu, H. Y. Jiang, R. H. Li, C. D. Lü, W. Wang, and Z. X. Zhao, Discovery potentials of doubly charmed baryons, Chin. Phys. C 42, 051001 (2018).
C. P. Jia, H. Y. Jiang, J. P. Wang, and F. S. Yu, Final-state rescattering mechanism of charmed baryon decays, J. High Energy Phys. 11 (2024) 072.
A. K. Leibovich, Z. Ligeti, I. W. Stewart, and M. B. Wise, Predictions for nonleptonic $Λ_{b}$ and $Θ_{b}$ decays, Phys. Lett. B 586, 337 (2004).
P. Ball, V. M. Braun, and E. Gardi, Distribution amplitudes of the $Λ_{b}$ baryon in QCD, Phys. Lett. B 665, 197 (2008).
G. Bell, T. Feldmann, Y. M. Wang, and M. W. Y. Yip, Light-cone distribution amplitudes for heavy-quark hadrons, J. High Energy Phys. 11 (2013) 191.
Y. M. Wang and Y. L. Shen, Perturbative corrections to $Λ_{b} \to Λ$ form factors from QCD light-cone sum rules, J. High Energy Phys. 02 (2016) 179.
A. Ali, C. Hambrock, and A. Y. Parkhomenko, Light-cone wave functions of heavy baryons, Theor. Math. Phys. 170, 2 (2012).
S. Groote, J. G. Korner, and O. I. Yakovlev, An analysis of diagonal and nondiagonal QCD sum rules for heavy baryons at next-to-leading order in alpha-s, Phys. Rev. D 56, 3943 (1997).
K. S. Huang, W. Liu, Y. L. Shen, and F. S. Yu, $Λ_{b} \to p, N^{*} (1535)$ form factors from QCD light-cone sum rules, Eur. Phys. J. C 83, 272 (2023).
V. Braun, R. J. Fries, N. Mahnke, and E. Stein, Higher twist distribution amplitudes of the nucleon in QCD, Nucl. Phys. B589, 381 (2000); B607, 433(E) (2001).
V. M. Braun, A. Lenz, and M. Wittmann, Nucleon form factors in QCD, Phys. Rev. D 73, 094019 (2006).
G. S. Bali et al. (RQCD Collaboration), Light-cone distribution amplitudes of octet baryons from lattice QCD, Eur. Phys. J. A 55, 116 (2019).
V. L. Chernyak and A. R. Zhitnitsky, Asymptotic behavior of exclusive processes in QCD, Phys. Rep. 112, 173 (1984).
V. M. Braun and I. E. Filyanov, QCD sum rules in exclusive kinematics and pion wave function, Z. Phys. C 44, 157 (1989).
V. M. Braun and I. E. Filyanov, Conformal invariance and pion wave functions of nonleading twist, Z. Phys. C 48, 239 (1990).
T. Kurimoto, H. n. Li, and A. I. Sanda, Leading power contributions to $B \to π, ρ$ transition form-factors, Phys. Rev. D 65, 014007 (2002).
P. Ball and R. Zwicky, New results on $B \to π, K, η$ decay formfactors from light-cone sum rules, Phys. Rev. D 71, 014015 (2005).
P. Ball, V. M. Braun, and A. Lenz, Higher-twist distribution amplitudes of the K meson in QCD, J. High Energy Phys. 05 (2006) 004.
R. H. Li, C. D. Lu, and W. Wang, Transition form factors of B decays into p-wave axial-vector mesons in the perturbative QCD approach, Phys. Rev. D 79, 034014 (2009).
A. Ali, G. Kramer, Y. Li, C. D. Lu, Y. L. Shen, W. Wang, and Y. M. Wang, Charmless non-leptonic $B_{s}$ decays to $P P$ , $P V$ and $V V$ final states in the pQCD approach, Phys. Rev. D 76, 074018 (2007).
V. M. Braun and A. Lenz, On the SU(3) symmetry-breaking corrections to meson distribution amplitudes, Phys. Rev. D 70, 074020 (2004).
P. Ball and R. Zwicky, SU(3) breaking of leading-twist K and K* distribution amplitudes: A reprise, Phys. Lett. B 633, 289 (2006).
P. Ball and R. Zwicky, $| V_{t d} / V_{t s} |$ from $B \to V γ$ , J. High Energy Phys. 04 (2006) 046.
P. Ball and G. W. Jones, Twist-3 distribution amplitudes of K* and phi mesons, J. High Energy Phys. 03 (2007) 069.
H. Y. Cheng, Mixing angle of $K_{1}$ axial vector mesons, Proc. Sci. Hadron2013 (2013) 090.
H. Hatanaka and K. C. Yang, $B \to K_{1} γ$ decays in the light-cone QCD sum rules, Phys. Rev. D 77, 094023 (2008); 78, 059902(E) (2008).
H. Y. Cheng, Revisiting axial-vector meson mixing, Phys. Lett. B 707, 116 (2012).
Y. J. Shi, J. Zeng, and Z. F. Deng, Revisiting $K_{1} (1270) - K_{1} (1400)$ mixing with QCD sum rules, Phys. Rev. D 109, 016027 (2024).
G. P. Lepage, A new algorithm for adaptive multidimensional integration, J. Comput. Phys. 27, 192 (1978).
G. P. Lepage, Adaptive multidimensional integration: vegas enhanced, J. Comput. Phys. 439, 110386 (2021).
Y. Y. Keum and H. n. Li, Nonleptonic charmless B decays: Factorization versus perturbative QCD, Phys. Rev. D 63, 074006 (2001).
H. Y. Cheng, Nonleptonic weak decays of bottom baryons, Phys. Rev. D 56, 2799 (1997); 99, 079901(E) (2019).
H. Y. Cheng and S. Oh, Flavor SU(3) symmetry and QCD factorization in $B \to P P$ and $P V$ decays, J. High Energy Phys. 09 (2011) 024.
C. Q. Geng, C. W. Liu, and T. H. Tsai, Nonleptonic two-body weak decays of $Λ_{b}$ in modified MIT bag model, Phys. Rev. D 102, 034033 (2020).
T. D. Lee and C. N. Yang, General partial wave analysis of the decay of a hyperon of spin $1 / 2$ , Phys. Rev. 108, 1645 (1957).
S. M. Berman and M. Jacob, Systematics of angular and polarization distributions in three-body decays, Phys. Rev. 139, B1023 (1965).
R. Aaij et al. (LHCb Collaboration), Measurement of the $b$ -quark production cross-section in 7 and 13 TeV $p p$ collisions, Phys. Rev. Lett. 118, 052002 (2017); 119, 169901(E) (2017).
S. Chen, Y. Li, W. Qian, Z. Shen, Y. Xie, Z. Yang, L. Zhang, and Y. Zhang, Heavy flavour physics and $C P$ violation at LHCb: A ten-year review, Front. Phys. 18, 44601 (2023).
See https://lbfence.cern.ch/alcm/public/figure/details/3837.
S. Pakvasa, S. P. Rosen, and S. F. Tuan, Parity violation and flavor selection rules in charmed baryon decays, Phys. Rev. D 42, 3746 (1990).

Phys. Rev. D 112, 053007– Published 29 September, 2025

Vol. 112, Iss. 5 — 1 September 2025

Received 10 June 2025
Accepted 11 September 2025

DOI: https://doi.org/10.1103/lvsn-v3xj

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

$C P$ violation in two-body hadronic $Λ_{b}$ decays in the PQCD approach

Abstract

Physics Subject Headings (PhySH)

Article Text

References (85)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

CP violation in two-body hadronic Λb decays in the PQCD approach

Abstract

Physics Subject Headings (PhySH)

Article Text

References (85)

$C P$ violation in two-body hadronic $Λ_{b}$ decays in the PQCD approach