Decays of B mesons to three-body charmless final states offer a good environment to study CP violation phenomena. They also provide important insight into the dynamics of hadronic B decays.

The LHCb Bu→hhh Rio Group has been studying charmless three-body B decays since the beginning of LHCb data taking in 2009. The first analysis was a measurement of the relative branching fractions of B^±→K^±K^±K^- and B^±→ppK^± decays with respect to the reference mode B^±→K^±π^±π^-. The analysis was performed using 34 pb^-1 of 2010 data, and was reported in the public note LHCb-CONF-2011-059. The branching ratios relative to B^±→K^±π^±π^- are found to be

• ^{ℬℛ(B±→K±K±K-)}⁄_{ℬℛ(B^±→K^±π^±π^-)}= 0.52 ± 0.003(stat) ± 0.01(syst)
• ^{ℬℛ(B±→ppK±)}⁄_{ℬℛ(B^±→K^±π^±π^-)} = 0.19 ± 0.02(stat) ± 0.02(syst)

With the larger dataset of 3 fb^-1 of data collected by LHCb in 2011 and 2012, we measured the direct CP asymmetries of four charmless decay modes. We found for the the first evidences of CP violation in these modes, as well as localised asymmetries much larger than the integrated ones in some regions of phase space. The results are listed below in the LHCb Collaboration Results. The inclusive CP asymmetries (A_CP) of these modes are measured to be

• A_CP(B^±→K^±π^±π^-) = +0.025 ± 0.004 ± 0.004 ± 0.007
• A_CP(B^±→K^±K^±K^-) = -0.036 ± 0.004 ± 0.002 ± 0.007
• A_CP(B^±→π^±π^±π^-) = +0.058 ± 0.008 ± 0.009 ± 0.007
• A_CP(B^±→K^±K^±π^-) = -0.123 ± 0.017 ± 0.012 ± 0.007

In addition, a measurement of the forward-backward asymmetry (A_FB) of the light meson in the pp rest frame are measured to be

• A_FB(ppK⁺, m_pp < 2.85 GeV/c²) = 0.495 ± 0.012(stat) ± 0.007(syst)
• A_FB(ppπ⁺, m_pp < 2.85 GeV/c²) = -0.409 ± 0.033(stat) ± 0.006(syst)

and the branching fraction of the decay B⁺→Λ(1520)p is measured to be

• ℬℛ (B⁺→Λ(1520)p) = (3.15 ± 0.48(stat) ± 0.07(syst) ± 0.26(BF))×10^-7

where BF denotes the uncertainty on secondary branching fractions.

The phase space of three-body decays is the Dalitz plot, and its complete understanding is achieved by a complex amplitude analysis. However, such an amplitude analysis is model dependent. The CBPF group proposed in 2009 a model-independent method for a CP anisotropy measurement in the Dalitz plot. This “Mirandizing” method performs a direct measurement of the diference between particles and antiparticles in the Dalitz plot. Although qualitative, the method can be used as a guide to locate the decay channels and the Dalitz plot regions with large asymmetry, thus aiding the choice of a future amplitude analysis model.

In addition to the Mirandizing analysis, we are now working on a full Dalitz plot amplitude analysis within the framework of existing theoretical models.

Irina Nasteva and Fernando Rodrigues
Last update: August 11, 2017

• (Video) Observation of 𝐶𝑃 violation in charmless three-body B meson decays at LHCb (LHC Seminar [D. Torres Machado] – WebCast – Mar 15, 2022)
• LHCb workshop on multi-body decays of B and D mesons (Event – Jul 27, 2015)
• XXXV ENFPC [J. Otalora] (Slides – Sep 17, 2014)
• 3rd Implications of LHCb [I. Nasteva] (Slides – Oct 16, 2013)
• WIN 2013 [A. Hicheur] (Slides – Sep 17, 2013)
• FPCP 2013 [J. H. Lopes] (Poster – May 20, 2013)
• FPCP 2013 [I. Nasteva] (Slides – May 20, 2013) — arXiv:1308.0740
• LISHEP 2013 [F. Rodrigues] (Slides – Mar 20, 2013)
• RETINHA24 2012 [F. Rodrigues] (Slides – Dec 04, 2012)
• (Video) Evidence of CP violation in B→hhh charmless decays (LHC Seminar [A. Gomes] – WebCast – Oct 2, 2012)
• CKM 2012 [J. Miranda] (Slides – Sep 30, 2012) — arXiv:1301.0283
• ICHEP 2012 [F. Rodrigues] (Slides – Jul 7, 2012) — PoS(ICHEP2012)248

• Undergraduate Laboratory Experiment: Measuring Matter Antimatter Asymmetries at the Large Hadron Collider
  (using B→3h data)
• Matéria e antimatéria: uma relação não muito simétrica (Informe CBPF – November 18, 2014)
• At IF-USP [I. Bediaga] (Slides – Aug 29, 2013)
• Charmless baryonic B decays(CERN Courier – Aug 19, 2013)
• Back From Hibernation, and a Puzzling Asymmetry (Quantum Diaries – March 4, 2013)
• Large CP-violation effects appear in three-body B decays (CERN Courier – Nov 6, 2012)
• Matter antimatter asymmetry in three-body charmless B decays becomes more and more interesting (LHCb public site – Oct 3, 2012 )
• Assimetrias em partículas podem explicar por que a matéria prevalece sobre a antimatéria no universo (CBPF news – Jul 18, 2012)
• So many attempts, so little luck (Quantum Diaries – Jul 8, 2012)
• Evidence for matter antimatter asymmetry in three-body charmless B decays (LHCb public site – Jul 7, 2012 (2))
• Matter-antimatter puzzle: LHCb improves resolution( CERN Bulletin (Issue No. 28-29/2012) – Jul 2, 2012)