Abstract
I propose an alternative method for measuring the CP violating phase ϕ2 (α) without ambiguity in an extended SU(2) isospin triangle analysis, which can ultimately be achieved by exploiting interference effects between B0 → ρ0ρ0 and B0 → a ±1 π∓ in a time-dependent flavour-tagged amplitude analysis. Under certain assumptions on the effective ϕ2 in each channel, I demonstrate with an idealised amplitude model that potential deviations in the measured ϕ2 due to penguin contamination in B0 → a ±1 π∓ are sufficiently large within current experimental uncertainties that this programme could be executed with Run 3 data at LHCb and easily at Belle II.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Cabibbo, Unitary Symmetry and Leptonic Decays, Phys. Rev. Lett. 10 (1963) 531 [INSPIRE].
M. Kobayashi and T. Maskawa, CP Violation in the Renormalizable Theory of Weak Interaction, Prog. Theor. Phys. 49 (1973) 652 [INSPIRE].
BaBar collaboration, J.P. Lees et al., Measurement of CP Asymmetries and Branching Fractions in Charmless Two-Body B-Meson Decays to Pions and Kaons, Phys. Rev. D 87 (2013) 052009 [arXiv:1206.3525] [INSPIRE].
Belle collaboration, J. Dalseno et al., Measurement of the CP-violation parameters in B 0 → π + π − decays, Phys. Rev. D 88 (2013) 092003 [arXiv:1302.0551] [INSPIRE].
LHCb collaboration, Measurement of CP asymmetries in two-body B 0( s) -meson decays to charged pions and kaons, Phys. Rev. D 98 (2018) 032004 [arXiv:1805.06759] [INSPIRE].
BaBar collaboration, B. Aubert et al., Study of B 0 → π 0 π 0 , B ± → π ± π 0 and B ± → K ± π 0 Decays and Isospin Analysis of B → ππ Decays, Phys. Rev. D 76 (2007) 091102 [arXiv:0707.2798] [INSPIRE].
Belle collaboration, Y.T. Duh et al., Measurements of branching fractions and direct CP asymmetries for B → Kπ, B → ππ and B → KK decays, Phys. Rev. D 87 (2013) 031103 [arXiv:1210.1348] [INSPIRE].
Belle collaboration, T. Julius et al., Measurement of the branching fraction and CP asymmetry in B 0 → π 0 π 0 decays and an improved constraint on ϕ 2, Phys. Rev. D 96 (2017) 032007 [arXiv:1705.02083] [INSPIRE].
BaBar collaboration, J.P. Lees et al., Measurement of CP-violating asymmetries in B 0 → (ρπ)0 decays using a time-dependent Dalitz plot analysis, Phys. Rev. D 88 (2013) 012003 [arXiv:1304.3503] [INSPIRE].
Belle collaboration, A. Kusaka et al., Measurement of CP Asymmetry in a Time-Dependent Dalitz Analysis of B 0 → (ρπ)0 and a Constraint on the CKM Angle ϕ 2, Phys. Rev. Lett. 98 (2007) 221602 [hep-ex/0701015] [INSPIRE].
BaBar collaboration, B. Aubert et al., A Study of B 0 → ρ + ρ − Decays and Constraints on the CKM Angle α, Phys. Rev. D 76 (2007) 052007 [arXiv:0705.2157] [INSPIRE].
Belle collaboration, P. Vanhoefer et al., Study of B 0 → ρ + ρ − decays and implications for the CKM angle ϕ 2, Phys. Rev. D 93 (2016) 032010 [Erratum ibid. D 94 (2016) 099903] [arXiv:1510.01245] [INSPIRE].
BaBar collaboration, B. Aubert et al., Improved Measurement of B + → ρ + ρ 0 and Determination of the Quark-Mixing Phase Angle α, Phys. Rev. Lett. 102 (2009) 141802 [arXiv:0901.3522] [INSPIRE].
Belle collaboration, J. Zhang et al., Observation of B ∓ → ρ ∓ ρ 0 Decays, Phys. Rev. Lett. 91 (2003) 221801 [hep-ex/0306007] [INSPIRE].
BaBar collaboration, B. Aubert et al., Measurement of the Branching Fraction, Polarization and CP Asymmetries in B 0 → ρ 0 ρ 0 Decay and Implications for the CKM Angle α, Phys. Rev. D 78 (2008) 071104 [arXiv:0807.4977] [INSPIRE].
Belle collaboration, P. Vanhoefer et al., Study of B 0 → ρ 0 ρ 0 decays, implications for the CKM angle ϕ 2 and search for other B 0 decay modes with a four-pion final state, Phys. Rev. D 89 (2014) 072008 [Erratum ibid. D 89 (2014) 119903] [arXiv:1212.4015] [INSPIRE].
LHCb collaboration, Observation of the B 0 → ρ 0 ρ 0 decay from an amplitude analysis of B 0 → (π + π −)(π + π −) decays, Phys. Lett. B 747 (2015) 468 [arXiv:1503.07770] [INSPIRE].
BaBar collaboration, B. Aubert et al., Measurements of CP-Violating Asymmetries in B 0 → a ±1 (1260)π ∓ decays, Phys. Rev. Lett. 98 (2007) 181803 [hep-ex/0612050] [INSPIRE].
Belle collaboration, J. Dalseno et al., Measurement of Branching Fraction and First Evidence of CP-violation in B 0 → a ±1 (1260)π ∓ Decays, Phys. Rev. D 86 (2012) 092012 [arXiv:1205.5957] [INSPIRE].
BaBar collaboration, B. Aubert et al., Measurement of branching fractions of B decays to K 1(1270)π and K 1(1400)π and determination of the CKM angle α from B 0 → a 1(1260)± π ∓, Phys. Rev. D 81 (2010) 052009 [arXiv:0909.2171] [INSPIRE].
M. Gronau and J.L. Rosner, Improving the measurement of the CKM phase ϕ 2 = α in B → ππ and B → ρρ decays, Phys. Lett. B 763 (2016) 228 [arXiv:1608.06224] [INSPIRE].
J. Charles, O. Deschamps, S. Descotes-Genon and V. Niess, Isospin analysis of charmless B-meson decays, Eur. Phys. J. C 77 (2017) 574 [arXiv:1705.02981] [INSPIRE].
UTfit collaboration, M. Bona et al., The Unitarity Triangle Fit in the Standard Model and Hadronic Parameters from Lattice QCD: A Reappraisal after the Measurements of Δm s and BR(B → τν τ), JHEP 10 (2006) 081 [hep-ph/0606167] [INSPIRE] and online at http://utfit.org/UTfit/WebHome.
A.F. Falk, Z. Ligeti, Y. Nir and H.R. Quinn, Comment on extracting α from B → ρρ, Phys. Rev. D 69 (2004) 011502(R) [hep-ph/0310242] [INSPIRE].
M. Gronau and D. London, Isospin analysis of CP asymmetries in B decays, Phys. Rev. Lett. 65 (1990) 3381 [INSPIRE].
H. Ishino, M. Hazumi, M. Nakao and T. Yoshikawa, New Measurements Using External Photon Conversion at a High Luminosity B Factory, hep-ex/0703039 [INSPIRE].
A.E. Snyder and H.R. Quinn, Measuring CP asymmetry in B → ρπ decays without ambiguities, Phys. Rev. D 48 (1993) 2139 [INSPIRE].
M. Gronau and J. Zupan, Weak phase alpha from B 0 → a ±1 (1260)π ∓, Phys. Rev. D 73 (2006) 057502 [hep-ph/0512148] [INSPIRE].
M. Gronau and J.L. Rosner, Controlling ρ width effects for a precise value of α in B → ρρ, Phys. Lett. B 766 (2017) 345 [arXiv:1612.08524] [INSPIRE].
M. Pivk and F.R. Le Diberder, Isospin constraints from/on B → ππ, Eur. Phys. J. C 39 (2005) 397 [hep-ph/0406263] [INSPIRE].
F. Von Hippel and C. Quigg, Centrifugal-barrier effects in resonance partial decay widths, shapes and production amplitudes, Phys. Rev. D 5 (1972) 624 [INSPIRE].
G.J. Gounaris and J.J. Sakurai, Finite width corrections to the vector meson dominance prediction for ρ → e + e −, Phys. Rev. Lett. 21 (1968) 244 [INSPIRE].
W. Rarita and J. Schwinger, On a theory of particles with half integral spin, Phys. Rev. 60 (1941) 61 [INSPIRE].
P. d’Argent et al., Amplitude Analyses of D 0 → π + π − π + π − and D 0 → K + K − π + π − Decays, JHEP 05 (2017) 143 [arXiv:1703.08505] [INSPIRE].
Particle Data Group collaboration, M. Tanabashi et al., Review of Particle Physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
H.-Y. Cheng and K.-C. Yang, Hadronic charmless B decays B → AP, Phys. Rev. D 76 (2007) 114020 [arXiv:0709.0137] [INSPIRE].
HFLAV collaboration, Y. Amhis et al., Averages of b-hadron, c-hadron and τ-lepton properties as of summer 2016, Eur. Phys. J. C 77 (2017) 895 [arXiv:1612.07233] [INSPIRE].
F. James, Monte Carlo phase space, CERN-68-15 [INSPIRE].
M. Williams, Numerical Object Oriented Quantum Field Theory Calculations, Comput. Phys. Commun. 180 (2009) 1847 [arXiv:0805.2956] [INSPIRE] and online at https://github.com/jdalseno/qft.
Belle II collaboration, E. Kou et al., The Belle II Physics Book, BELLE2-PUB-PH-2018-001 (2018) [arXiv:1808.10567] [INSPIRE].
LHCb collaboration, Expression of Interest for a Phase-II LHCb Upgrade: Opportunities in flavour physics and beyond, in the HL-LHC era, CERN-LHCC-2017-003 (2017).
LHCb collaboration, Physics case for an LHCb Upgrade II — Opportunities in flavour physics, and beyond, in the HL-LHC era, CERN-LHCC-2018-027 (2018) [arXiv:1808.08865] [INSPIRE].
LHCb collaboration, LHCb Trigger and Online Upgrade Technical Design Report, CERN-LHCC-2014-016 (2014) [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1808.09391
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Dalseno, J. Resolving the ϕ2 (α) ambiguity in B → ρρ. J. High Energ. Phys. 2018, 193 (2018). https://doi.org/10.1007/JHEP11(2018)193
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2018)193