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High Energy Physics - Phenomenology · arXiv:2611.15273 v1 · submitted 11 Nov 2026 · 298 references

CP Violation in Beauty Baryon Decays

Jian-Peng Wang, Qin Qin, Stephane Monteil, Fu-Sheng Yu, Yan-Xi Zhang

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The paper says

“The 2025 discovery of CP violation in the baryon sector marks a tectonic shift in flavor physics, bridging a sixty-year gap since the initial discovery of CP asymmetry in mesons.”

more of the abstract

This review provides a comprehensive synthesis of the theoretical and experimental journey to this milestone. We integrate the development of dynamical calculation frameworks, such as perturbative QCD and the re-scattering mechanism, with the experimental breakthrough achieved through rate asymmetry measurements. Furthermore, we establish a roadmap for the future of the field by detailing the construction of multi-dimensional observables, which are instrumental in advancing the next era of precision physics and refining the search for new physics beyond the standard model.

from the abstract

Pith says

Machine review · deepseek-v4-flash · 13 Nov 2026 · what was read was not recorded · not checked by a person

It can be wrong. Challenge this review or reply to it.

Holds up. A thorough, honest review of the first CP violation in baryons—useful as a reference, but it's a synthesis, not a primary result. This line is wrong

5 minor

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5 minor objections

The paper says, at §1, Fig. 2

Pith says: minor objection 1 of 5

Figure 2 compares typical CP asymmetries in B-meson and Λ_b decays. The caption does not explain the source or methodology of the quoted numerical ranges. Adding a brief note that the Λ_b values are from the LHCb measurement or from PQCD predictions would help the reader assess the plot’s authority.

The paper says, at Table 1

Pith says: minor objection 2 of 5

Table 1 collects predicted and measured asymmetries from several frameworks. The column ordering (GF, QCDF(diquark), PQCD, FSIs, Experiment) could be clarified by a footnote that the GF and QCDF(diquark) entries are taken from Refs. [202,204,215] and that the PQCD and FSI entries are from Refs. [68,259] respectively. The experimental column should reference Ref. [205] and the LHCb papers for the two-body modes.

show 3 more

The paper says, at §6.3–6.4 (angular analysis discussion)

Pith says: minor objection 3 of 5

The discussion of spin-dependent observables and angular asymmetries is thorough, but the notation for the up–down asymmetry (Eq. 52–53) and its CP counterpart could be made more self-contained. Defining Γ(cosθ>0) explicitly as the rate where the proton direction is forward relative to the parent polarization axis in the Λ_b rest frame would improve readability for non-specialists.

The paper says, at §4.1.3

Pith says: minor objection 4 of 5

The description of the LHCb detector is detailed but includes some technical jargon (e.g., 'TISTOS method') without a full definition on first use. A brief parenthetical explanation or a cross-reference to the glossary of acronyms (mentioned in the supplementary material) would aid readers unfamiliar with LHCb terminology.

The paper says, at §7

Pith says: minor objection 5 of 5

The summary and prospects section is well-structured, but could be strengthened by a short table prioritising the most promising decay modes for next-generation measurements (e.g., those with predicted angular asymmetries >10%). This would make the roadmap more actionable.

What would settle it

Verify that the quoted value A_CP = (2.45 ± 0.46 ± 0.10)% and its significance of 5.2σ match the LHCb publication [1] and that the control channel subtraction procedure is correctly described in Section 5.1.

from the skeptic's reading

How the review went

4 readings by deepseek-v4-flash · 13 Nov 2026

  1. Reader holds up confidence high
  2. Skeptic agrees 14 s · 63,204 tokens read, 1,476 written
  3. Editor wrote the verdict above 12 s · 63,895 tokens read, 1,142 written
  4. Referee accept: 5 minor 14 s · 63,455 tokens read, 1,646 written

Not run on this paper: the simulated authors' defence.

Pith did not check this review's objections against the paper.

The review in full

The review in brief, machine-written

This is a solid review of the 2025 LHCb discovery of CP violation in Λb0 → p K^- π^+ π^- decays. It accurately describes the experimental measurement (5.2σ, robust) and surveys the theoretical landscape—PQCD, FSI, Nπ rescattering—without overselling any framework. The paper is well-organized, candid about theoretical limitations, and will probably become a go-to reference for people entering this subfield.

The main strength is the honest treatment of theory. The authors repeatedly flag that factorization-based methods for baryons are less mature than for mesons, that power counting doesn't guarantee numerical hierarchy, and that model calculations have large uncertainties. The discussion of partial-wave cancellations in two-body modes and the Nπ rescattering picture for multibody decays are genuinely instructive.

Soft spots: The paper is a review, so its novelty is in the assembly, not in new equations or data. The theoretical predictions quoted in Table 1 span a wide range (e.g., Λb→pK^- asymmetries from −6% to +10%), and no framework is decisively validated or ruled out. The paper maps the landscape but doesn't resolve it. This is fine for a review, but readers looking for a crisp takeaway will find ambiguity.

The authors themselves acknowledge the key issues: generalized factorization is not self-consistent, PQCD uncertainties are large, FSI models depend on cutoffs and channel truncation. They don't hide these facts.

Overall: this is a well-crafted synthesis that serves its purpose. It deserves peer review as a review article. I would bring it to a reading group focused on heavy-flavor physics. I might cite it for context, but not for quantitative predictions.

Recommendation: publish as a review after minor editorial checks (the paper is long but clean). No major revisions needed.

The strongest objection

The paper is a review that accurately summarizes the LHCb discovery of CP violation in baryon decays and the current theoretical landscape. The experimental result (A_CP = (2.45 ± 0.46 ± 0.10)%, 5.2σ) is robustly established by LHCb and independently published. The review honestly acknowledges the limitations of the theoretical frameworks (PQCD, FSI, hadronic-loop) and does not claim a definitive theoretical explanation. The central claim—that CP violation has been observed in a baryon decay—rests on the experimental measurement, not on the theoretical models. No internal inconsistency, factual error, or missing support that would undermine this claim has been identified. The paper fulfills its purpose as a synthesis and roadmap.

The reader's verdict ACCEPT with high confidence is appropriate. The paper is a comprehensive review of the 2025 discovery of CP violation in beauty baryon decays. The experimental result is the central claim, and it is correctly presented and well-documented. The theoretical interpretation sections honestly describe the limitations, as the reader noted. No additional load-bearing concern has been found that would change the verdict. The paper is factual, well-organized, and fulfills its stated purpose.

The referee's report

The paper fills an important gap by providing a unified overview of the first observation of CP violation in baryons, a milestone that bridges a sixty-year gap after the discovery in mesons. Its significance lies in three aspects: (i) it accurately and comprehensively summarises the experimental result, which is robust and independently published; (ii) it honestly catalogues the theoretical frameworks used to interpret baryonic CP violation, including their acknowledged shortcomings (e.g., uncontrolled power corrections in QCDF, model dependence in hadronic-loop and PQCD calculations, and the lack of a rigorous factorization theorem for charmless baryon decays); (iii) it outlines a clear set of future directions—multi-dimensional angular observables, improved hadronic inputs, and next-generation experimental facilities—that will guide the field. The review does not overclaim: the central claim (that CP violation has been observed in baryon decays) rests on the LHCb measurement, not on the theoretical models. As a reference work, it will be valuable to both theorists and experimentalists working in flavour physics.

Pith's reading of the paper (a machine's summary, not the authors')

In 2025, the LHCb collaboration measured a 2.45% difference between the decay rates of $Λ_b^{0}$ → p K^- π^+ π^- and its CP conjugate, with a significance of 5.2 standard deviations, establishing CP violation in a baryon for the first time. This review synthesizes the theoretical and experimental developments that led to this milestone, bridging a sixty-year gap since CP violation was first seen in mesons. The paper argues that the effect is real, driven by interference between tree and penguin amplitudes with different strong phases provided by the rich resonance structure of the four-body final state. It also outlines a roadmap for future precision studies using multidimensional angular observables to probe new physics beyond the Standard Model.

What carries the argument. The experimental analysis uses the control channel $Λ_b^{0}$ → Λ_c^+ (→ p K^- π^+) π^- to cancel production, detection, and trigger asymmetries. Theoretically, the CP asymmetry arises from interference between tree (V_ub V*_us) and penguin (V_tb V*_ts) amplitudes; the required strong phases are generated by hadronic final-state interactions described by perturbative QCD (PQCD) or hadronic rescattering models (e.g., Nπ rescattering or triangle-loop diagrams). The rich resonance structure of the four-body final state provides the necessary strong-phase differences.

Core claim. The paper establishes that the 5.2σ asymmetry in $Λ_b^{0}$ → p K^- π^+ π^- is the first confirmed CP violation in a baryon decay. The phase-space-integrated CP asymmetry is A_CP = (2.45 ± 0.46 ± 0.10)%, and local asymmetries reach 5.4% with 6σ significance in the low-mass pπ^+π^- region. This result extends experimentally established CP violation from mesons to baryons, providing a new laboratory to test the CKM mechanism and search for additional CP-violating dynamics.

The premise it rests on. The theoretical interpretation of the observed CP asymmetries relies on phenomenological models (perturbative QCD, hadronic rescattering) whose key inputs—such as baryon light-cone distribution amplitudes, transition form factors, and the truncation of intermediate hadronic states—are poorly constrained and may introduce uncertainties large enough to accommodate or challenge the Standard Model explanation.

If the paper is right (Pith's inferences, not the authors')

Beauty baryon decays now constitute a new sector for precision CP-violation studies, complementary to meson systems.

Future measurements with larger data sets (LHCb Run III) will test whether the observed asymmetries are consistent with the CKM mechanism or reveal new physics.

Multidimensional angular observables, such as the CP asymmetry of the Lee-Yang decay parameter, can isolate partial-wave CP asymmetries that cancel in integrated rates, increasing sensitivity.

Similar searches in other beauty baryon modes (e.g., Ξ_b, Ω_b) will probe universality of CP violation across different baryon species.

Improved theoretical calculations of baryon light-cone distribution amplitudes and higher-order QCD corrections are needed to reduce the current large uncertainties.

The cancellation between S-wave and P-wave CP asymmetries predicted by PQCD for Λ_b^0 → p π^- and p K^- suggests that integrated rate asymmetries alone may miss large CP-violating effects; angular analysis of subsequent decays (e.g., via up-down asymmetry) is essential.

If the observed CP asymmetry originates entirely from Standard Model CKM physics, it places no direct constraint on baryogenesis models; if new physics contributes, deviations in other rare beauty baryon decays or electric dipole moments may provide further evidence.

The theoretical description of multibody baryon decays remains highly model-dependent—addressing this through data-driven approaches (e.g., using Nπ scattering amplitudes) could become a standard method for future precision.

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The paper

Abstract

The 2025 discovery of CP violation in the baryon sector marks a tectonic shift in flavor physics, bridging a sixty-year gap since the initial discovery of CP asymmetry in mesons. This review provides a comprehensive synthesis of the theoretical and experimental journey to this milestone. We integrate the development of dynamical calculation frameworks, such as perturbative QCD and the re-scattering mechanism, with the experimental breakthrough achieved through rate asymmetry measurements. Furthermore, we establish a roadmap for the future of the field by detailing the construction of multi-dimensional observables, which are instrumental in advancing the next era of precision physics and refining the search for new physics beyond the standard model.

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. No sentence in this record was written by a model.

abstract compiled · 2026-11-13

The authors' main claim, as the classifier picked it out 0.90

“The 2025 discovery of CP violation in the baryon sector marks a tectonic shift in flavor physics, bridging a sixty-year gap since the initial discovery of CP asymmetry in mesons.”

How the main claim is stated: asserted 1.00

What the abstract itself states, as probabilities: claims first 0.15 · states limitation 0.04 · human participants 0.02 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.13 · compares with prior results 0.44 · mentions code or data availability 0.02

The abstract, sentence by sentence

This table labels the abstract only (arXiv listing abstract v1). The number is the probability the classifier gave the label.

SentenceRoleThe authors' own workStates the main conclusionStrength
The 2025 discovery of CP violation in the baryon sector marks a tectonic shift in flavor physics, bridging a sixty-year gap since the initial discovery of CP asymmetry in mesons. background 0.69 0.10 0.55 asserted 1.00
This review provides a comprehensive synthesis of the theoretical and experimental journey to this milestone. contribution 0.98 0.60 0.06 asserted 0.98
We integrate the development of dynamical calculation frameworks, such as perturbative QCD and the re-scattering mechanism, with the experimental breakthrough achieved through rate asymmetry measurements. contribution 0.79 0.61 0.13 asserted 1.00
Furthermore, we establish a roadmap for the future of the field by detailing the construction of multi-dimensional observables, which are instrumental in advancing the next era of precision physics and refining the search for new physics beyond the standard model. future work 0.96 0.64 0.26 asserted 0.99

What kind of paper the classifier reports this is: review 1.00 · evidence from literature 0.97

What was examined, and what was not

Sources read

  • arXiv listing abstract v1

Not examined

  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers

Levels run

  • P abstract

Not run

  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

How the labels were made

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-11-13: 1 request, 3,665 input tokens.

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON

Figures (26)
Figure 1 of the paper
Figure 1. History and milestones of 𝐶𝑃 violation. i.e., the antiparticles [30]. The existence of such antiparticles was spectacularly confirmed by Anderson’s cloud￾chamber observation of the positron in 1932 [31]. Thus, the operation of charge conjugation (𝐶), which interchanges particles and antiparticles, became a physically meaningful symmetry to investigate. Parity and charge-conjugation invariance were subsequently assumed to hold in all fundamental interactions. The first challenge to this assumption came in 1956. Prompted by the 𝜏–𝜃 puzzle posed by two apparently identical particles…
Figure 2 of the paper
Figure 2. Comparison of 𝐶𝑃 violation in 𝐵-meson and Λ 0 𝑏 decays. Typical 𝐶𝑃 asymmetries are at the (10%) level in 𝐵 mesons, but only at the (1%) level in Λ 0 𝑏 baryons . Indeed, the discovery of baryonic 𝐶𝑃 violation in [1] is dominated by one of the four examined phase-space regions, specifically the low-𝑝𝜋+𝜋 −-mass region. Here, the 𝐶𝑃 asymmetry is measured to be 𝐴𝐶𝑃 ( Λ 0 𝑏 → 𝑅(𝑝𝜋+𝜋 − )𝐾 − ) 𝑚𝑝𝜋+𝜋−<2.7 GeV = (5.4 ± 0.9 ± 0.1)%, (2) which reaches a significance of 6𝜎. Nevertheless, many-body decays introduce the theoretical challenge of describing multibody hadronic dynamics a
Figure 3 of the paper
Figure 3. (a) Decay of a polarized spin-1∕2 baryon, where 𝜃 is the angle between the parent-baryon polarization and the proton momentum; (b) For a fully polarized parent baryon and 𝜃 = 0, only the positive-helicity amplitude ℎ+ contributes, which can be expressed in terms of the partial-wave amplitudes as ℎ+ = (𝑆 +𝑃 )∕√ 2; (c) For a fully polarized parent baryon and 𝜃 = 𝜋, only the positive-helicity amplitude ℎ− contributes, which can be expressed as ℎ− = (𝑆 − 𝑃 )∕√ 2. Each partial-wave amplitude receives both tree and penguin contributions, 𝑆 = 𝜆 |𝑆 |𝑒 𝑖𝛿𝑆  + 𝜆|𝑆|𝑒 𝑖𝛿𝑆  , 𝑃 = 𝜆
Figure 4 of the paper
Figure 4. Schematic illustration of the interference mechanisms contributing to different 𝐶𝑃 -violating observables in Λ 0 𝑏 → 𝑝ℎ− decays. Curves of the same color denote the two interfering amplitudes. (a) The direct 𝐶𝑃 asymmetry 𝐴 dir 𝐶𝑃 arises from the interference between tree and penguin amplitudes within the same partial wave (i.e., 𝑆-wave tree with 𝑆-wave penguin, and 𝑃 -wave tree with 𝑃 -wave penguin). (b) The 𝐶𝑃 violation in angular distribution observables originates from the interference between tree and penguin amplitudes belonging to different partial waves (i.e., 𝑆-wave tree with
Figure 5 of the paper
Figure 5. Topological diagrams for two-body non-leptonic decays of the Λ 0 𝑏 baryon. The first two rows correspond to tree topologies, while the third row represents penguin topologies. elements of effective operators in non-leptonic 𝐵-meson decays, including naive factorization [157, 158], generalized factorization [159–161], QCD factorization (QCDF) [162–165], perturbative QCD (PQCD) [166–168], soft-collinear effective theory (SCET) [169, 170], 𝑆𝑈(3) flavor symmetry [171, 172], and hadronic rescattering methods [173, 174]. However, the extension of these methods to exclusive non-leptonic…
Figure 6 of the paper
Figure 6. The QCD penguin operators 5 and 6 contributions to the Λ 0 𝑏 → 𝑝𝜋− (upper panel) and Λ 0 𝑏 → 𝑝𝐾− (lower panel) decay amplitudes, shown in the complex plane. The red (blue) vectors represent the 𝑆-wave (𝑃 -wave) penguin amplitudes. For Λ 0 𝑏 → 𝑝𝜋− , the combined 𝑃 𝐶2 and 𝑃 𝐸1 contributions dominate the strong phases and lead to opposite sign 𝑆- and 𝑃 -wave 𝐶𝑃 asymmetries that partially cancel each other in the total 𝐶𝑃 asymmetry. For Λ 0 𝑏 → 𝑝𝐾− , the strong phases generated by 𝑃 𝐶1 and 𝑃 𝐸1 contributions from 5 and 6 are opposite in sign, while that is not true after combining…
Figure 7 of the paper
Figure 7. Representative hadronic triangle-loop contribution to the decay Λ 0 𝑏 (𝑝𝑖 ) → 𝑝(𝑝3 )𝑀(𝑝4 ) via single-meson exchange. The arrows indicate the momentum-flow convention. 3.7.1. Hadronic loop mechanism Hadronic rescattering via triangle loops was developed as a means of studying long-distance effects in 𝐵-meson decays. These analyses showed that soft hadronic rescattering could have a non-negligible impact on decay amplitudes and 𝐶𝑃 -violating observables [173]. This motivates its use as a phenomenological tool for investigating the possible impact of final-state rescattering in heavy…
Figure 8 of the paper
Figure 8. Schematic illustration of the mechanism for 𝐶𝑃 violation induced by hadronic rescattering. The figures are taken from Ref. [69]. The decay is modeled as a two-step process: short-distance weak production of an 𝑁𝜋 subsystem together with a bachelor meson ℎ − , followed by long-distance rescattering within the subsystem. Interfering tree and penguin contributions carry different CKM weak phases, while the relevant scattering partial waves provide strong phases; the 𝑁𝜋 amplitudes are constrained by experimental data, including the SAID analysis. scattering partial wave amplitudes are…
Figure 9 of the paper
Figure 9. The Large Hadron Collider CERN accelerator complex.
Figure 10 of the paper
Figure 10. (Left) Polar angle distribution of PYTHIA simulated
Figure 11 of the paper
Figure 11. Side view of the LHCb detector design
Figure 12 of the paper
Figure 12. Photograph of one half of the VELO detector. Each half is composed of 21 modules placed perpendicular to the beam direction. Each module is equipped with two sensors mounted back-to-back: a sensor made of concentric silicon strip provides a measurement of the radial coordinate from the beam axis and the oppositely-mounted sensor measures the azimuthal angle of the hit. The last coordinate is given by the position of the station on the beamline. The amount of data collected by the LHCb experiment is reported in
Figure 13 of the paper
Figure 13. Total integrated luminosity recorded by the LHCb experiment during proton-proton data taking periods [293]. from these improvements. The data samples discussed in this review are multiplied by about a factor of 6 in the current data on tape! 4.2. Review of Baryonic 𝐶𝑃 Violation Searches before First Observation Various experimental techniques and observables have been mobilised to search for 𝐶𝑃 -symmetry breaking in baryon decays: • measurement of decay width asymmetries (𝐴𝐶𝑃 ), evaluating directly the decay rate difference between a baryon 𝑋𝑏 decay (𝑋𝑏 → 𝑓) and its 𝐶𝑃 -conjugate…
Figure 14 of the paper
Figure 14. Invariant-mass distributions: (top left) 𝑚𝑝𝐾− , (top right) 𝑚𝑝𝐾+ , (bottom left) 𝑚𝑝𝜋− and (bottom right) 𝑚𝑝𝜋+ for candidates passing the selections. The results of the fits are superimposed. samples yielded the most precise determination of these 𝐶𝑃 asymmetries to date, indicating no further evidence of 𝐶𝑃 violation, 𝐴𝐶𝑃 (𝑝𝐾− ) = −0.011 ± 0.007 ± 0.004, 𝐴𝐶𝑃 (𝑝𝜋− ) = −0.002 ± 0.008 ± 0.004. (67) 4.2.2. Search for 𝐶𝑃 violation in three-body decays Charmless three-body 𝑏-baryon decays offer a rich phenomenology to search for 𝐶𝑃 violation. Fully charged modes Ξ − 𝑏 → 𝑝𝐾−𝐾− is explored…
Figure 15 of the paper
Figure 15. Invariant-mass distributions: (left) the smallest invariant mass 𝑚𝑝𝐾− among the two possible combinations of negatively charged kaons, (right) 𝑚𝑝𝐾+ . A good description of the Dalitz plot is obtained. 5400 5600 5800 6000 ]2 ) [MeV/c − K + m(ΛK 0 20 40 60 80 100 120 140 160 ) 2 c Candidates / (20 MeV/ −1 LHCb 9 fb )> 2.2 GeV − K + m(K )< 2.9 GeV + m(ΛK Total fit − K + → ΛK 0 Λb − K + → ΛK 0 Ξ b (mis) + π − → ΛK 0 Λb Comb. bkg. γ − K + → ΛK 0 Λb 0 π − K + → ΛK 0 Λb 5400 5600 5800 6000 ]2 ) [MeV/c − K + m(ΛK 0 20 40 60 80 100 120 140 160 ) 2 c Candidates / (20 MeV/ −1 LHCb 9 fb )> 2.2…
Figure 16 of the paper
Figure 16. Invariant-mass distributions of (left) Λ 0 𝑏 → Λ𝐾+𝐾− and (right) Λ 0 𝑏 → Λ𝐾+𝐾− in 𝑁∗+ resonance-dominated regions. Fit results are shown as well and superimposed. for Λ 0 𝑏 → Λ𝐾+𝐾− (Λ 0 𝑏 → Λ𝐾+𝜋 −). The decay mode Λ 0 𝑏 → 𝑝𝐾0 S 𝜋 − was initially studied on a fraction of the Run I data and a yield of about 100 events were observed as well. Though measurements of 𝐶𝑃 asymmetries were performed, the statistics at hand was too scarce to be conclusive. Analyses including the data collected during the Run II are gathering larger yields [67] and allows for a scrutiny a Dalitz plot of these…
Figure 17 of the paper
Figure 17. (top left) Invariant mass distribution of Λ 0 𝑏 → 𝑝𝜋−𝜋 +𝜋 − and (top right) Λ 0 𝑏 → 𝑝 − 𝜋 +𝜋 +𝜋 − decays, with fit projections superimposed. The control channels Λ 0 𝑏 → Λ− 𝑐 𝜋 + (bottom left) and (bottom right) Λ 0 𝑏 → Λ+ 𝑐 𝜋 − . Reproduced from [251]. 4.2.3. Search for 𝐶𝑃 violation in multi-body decays of 𝑏-flavored baryons The dataset collected during the LHC Run I for four-body fully charged decays of Λ 0 𝑏 and Ξ 0 𝑏 baryons is comprehensively analysed by means of Δ𝐴𝐶𝑃 technique featuring tree-level-dominated control modes with the same final state particles to cancel out the…
Figure 18 of the paper
Figure 18. Leading diagrams contributing to the Λ 0 𝑏 → 𝑝𝐾−𝜋 +𝜋 − decay. The light quarks from the 𝑏-quark decay and the spectator quarks hadronize into the final-state hadrons 𝑝𝐾−𝜋 +𝜋 − , with or without intermediate resonances. The left (right) diagram corresponds to the tree (loop) contribution. decay, with a 𝜋 + misidentified as a 𝑝, can pollute the signal sample and may carry a large 𝐶𝑃 asymmetry. Peaking backgrounds also arise from partially reconstructed decays, such as Λ 0 𝑏 → 𝑝𝐾−𝜋 +𝜋 −𝜋 0 with the 𝜋 0 not reconstructed. In addition, there is combinatorial background from random…
Figure 19 of the paper
Figure 19. Total interaction cross section of charged hadrons impacting on a deuterium target. Reproduced from [4]. ideal control channel for the 𝐶𝑃 measurement of the Λ 0 𝑏 → 𝑝𝐾−𝜋 +𝜋 − decay. This decay is dominated by the CKM￾favored 𝑏 → 𝑐 tree transition and is expected to have negligible 𝐶𝑃 violation at the current level of precision (0.1%). Thus, its raw asymmetry, defined as the relative difference between the yields of Λ 0 𝑏 and Λ 0 𝑏 decays, is dominated by asymmetries in production, detection, and selection. Moreover, the control channel has the same initial state and the same fin
Figure 20 of the paper
Figure 20. Invariant mass distribution of Λ 0 𝑏 → 𝑝𝐾−𝜋 +𝜋 − (left) and Λ 0 𝑏 → 𝑝𝐾+𝜋 +𝜋 − (right) decays, together with fit projections. Run I and Run II data samples are merged. Reproduced from [1] the Gaussian width, and the average Crystal Ball width are allowed to float, while the other parameters are fixed to the values obtained from simulation. The simulated signal yield is about twenty times larger than that in data. The background components are modeled as follows. The partially reconstructed background from Λ 0 𝑏 → 𝑝𝐾−𝜋 +𝜋 −𝜋 0 with a missing 𝜋 0 is described by an ARGUS function…
Figure 21 of the paper
Figure 21. Invariant mass distribution of Λ 0 𝑏 → Λ+ 𝑐 (𝑝𝐾−𝜋 + )𝜋 − (left) and Λ 0 𝑏 → Λ − 𝑐 (𝑝𝐾+𝜋 − )𝜋 + decays, together with fit projections. Run I and Run II data samples are merged. Reproduced from [1]. and control channels; therefore, to properly cancel the production asymmetry, the 𝑝T–𝑦 distribution in the control channel is weighted to match that in the signal decay. The reweighting is performed in two-dimensional bins of 𝑝T and 𝑦, in the range 2 < 𝑝T < 30 GeV∕𝑐 and 2.1 < 𝑦 < 4.5. After reweighting, the raw asymmetry of the control channel changes only slightly, from 𝐴raw =
Figure 22 of the paper
Figure 22. The log-likelihood as a function of the difference in 𝐶𝑃 asymmetries between the signal and control channels, shifted by the log-likelihood of the nominal result. for Run II, where the uncertainties are propagated using pseudoexperiments. The larger uncertainty for the Run I measurement is due to the limited statistics of the calibration samples. The trigger asymmetry is dominated by the hardware trigger, while the software-trigger asymmetry is measured to be 0.01–0.02% for Run I and 0.00–0.01% for Run II and is therefore neglected. The hardware-trigger asymmetry is split into TOS…
Figure 23 of the paper
Figure 23. Invariant-mass distributions of two-body and three-body final-state particles:
Figure 24 of the paper
Figure 24. The left panel shows the kinematic configuration of the three-body decay Λ 0 𝑏 → 𝑝𝑉 → 𝑝ℎ1ℎ2 , where 𝜃 is the angle between the momentum of ℎ1 in the 𝑉 rest frame and the direction of motion of 𝑉 in the Λ 0 𝑏 rest frame. The right panel shows the corresponding configuration for the four-body decay Λ 0 𝑏 → 𝑝𝐴 → 𝑝ℎ1ℎ2ℎ3 , where 𝜃 is the angle between the normal to the 𝐴 → ℎ1ℎ2ℎ3 decay plane and the direction of motion of 𝐴 in the Λ 0 𝑏 rest frame. A fixed ordering of the daughter momenta is used to define the orientation of the normal vector. Because the helicity angle is const
Figure 25 of the paper
Figure 25. Coordinate systems and helicity angles for the production of a Λ+ 𝑐 Λ̄ − 𝑐 pair and the cascade decay Λ+ 𝑐 → Λ𝜋 + → (𝑝𝜋− )𝜋 + . In the 𝑒 + 𝑒 − center-of-mass frame, 𝑧 denotes the beam direction and 𝑧𝑐 is chosen along the Λ+ 𝑐 momentum. The remaining axes are defined by 𝑦𝑐 ∝ 𝑧 × 𝑧𝑐 and 𝑥𝑐 = 𝑦𝑐 × 𝑧𝑐 . The direction of the Λ momentum in the Λ+ 𝑐 rest frame is specified by (𝜃0 , 𝜙0 ). In the Λ rest frame, 𝑧Λ is chosen along the Λ momentum in the Λ+ 𝑐 frame, while 𝑦Λ ∝ 𝑧𝑐 × 𝑧Λ and 𝑥Λ = 𝑦Λ × 𝑧Λ . The proton direction in this frame is specified by (𝜃, 𝜙). The same construction applies to…
Figure 26 of the paper
Figure 26. Angles for the cascade decay Λ 0 𝑏 → Λ𝜙 → (𝑝𝜋− )(𝐾+𝐾− ). The angles 𝜃𝑎 and 𝜃𝑏 are the helicity angles of the proton and 𝐾+ in the Λ and 𝜙 rest frames, respectively, while 𝜙 is the relative azimuthal angle between the two decay planes. their charge-conjugate counterparts to be determined simultaneously [63]. The parameter 𝛽 is particularly interesting because 𝐶𝑃 -odd observables constructed from it probe the imaginary part of the interference between the 𝑆- and 𝑃 -wave amplitudes. Decomposing both partial-wave amplitudes into contributions with different weak phases, as in Eqs. (2

Figures are the authors', reproduced from the paper.

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