Abstract
The resonant substructure of D 0 → π+π−π+π− decays is studied using data collected by the CLEO-c detector. An amplitude analysis is performed in order to disentangle the various intermediate state contributions. To limit the model complexity a data driven regularization procedure is applied. The prominent contributions are the decay modes D 0 → a 1(1260)+ π−, D 0 → σ f 0(1370) and D 0 → ρ(770)0 ρ(770)0. The broad resonances a 1(1260)+, π(1300)+ and a 1(1640)+ are studied in detail, including quasi-modelindependent parametrizations of their lineshapes. The mass and width of the a 1(1260)+ meson are determined to be m a1(1260)+ = [1225 ± 9 (stat) ± 17 (syst) ± 10 (model)] MeV/c 2 and Γa1(1260)+ = [430 ± 24 (stat) ± 25 (syst) ± 18 (model)] MeV. The amplitude model of D 0 → K + K −π+π− decays obtained from CLEO II.V, CLEO III, and CLEO-c data is revisited with improved lineshape parametrizations. The largest components are the decay modes D 0 → ϕ(1020)ρ(770)0, D 0 → K 1(1270)+ K − and D 0 → K(1400)+ K −.
The fractional CP -even content of the decay D 0 → π+π−π+π− is calculated from the amplitude model to be F 4π+ = [72.9 ± 0.9(stat) ± 1.5(syst) ± 1.0(model)] %, consistent with that obtained from a previous model-independent measurement. For D 0 → K + K −π+π− decays, the CP -even fraction is measured for the first time and found to be F KKππ+ = [75.3 ± 1.8 (stat) ± 3.3 (syst) ± 3.5 (model)] %.
The global decay rate asymmetries between D 0 and \( {\overline{D}}^0 \) decays are measured to be \( {\mathcal{A}}_{CP}^{4\uppi}=\left[+0.54\pm 1.04\ \left(\mathrm{stat}\right)\pm 0.51\ \left(\mathrm{syst}\right)\right]\% \) and \( {\mathcal{A}}_{CP}^{KK\pi \pi}=\left[+1.84\pm 1.74\ \left(\mathrm{stat}\right)\pm 0.30\ \left(\mathrm{syst}\right)\right]\% \). A search for CP asymmetries in the amplitude components yields no evidence for CP violation in either decay mode.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Gronau and D. Wyler, On determining a weak phase from CP asymmetries in charged B decays, Phys. Lett. B 265 (1991) 172 [INSPIRE].
M. Gronau and D. London, How to determine all the angles of the unitarity triangle from B d → DK s and B 0 s → Dϕ, Phys. Lett. B 253 (1991) 483 [INSPIRE].
D. Atwood, I. Dunietz and A. Soni, Enhanced CP-violation with \( B\to\ {\mathrm{KD}}^0\left({\overline{\mathrm{D}}}^0\right) \) modes and extraction of the CKM angle γ, Phys. Rev. Lett. 78 (1997) 3257 [hep-ph/9612433] [INSPIRE].
A. Giri, Y. Grossman, A. Soffer and J. Zupan, Determining γ using B ± → DK± with multibody D decays, Phys. Rev. D 68 (2003) 054018 [hep-ph/0303187] [INSPIRE].
Belle collaboration, A. Poluektov et al., Measurement of \( \phi \) 3 with Dalitz plot analysis of B ± → D (∗) K ± decay, Phys. Rev. D 70 (2004) 072003 [hep-ex/0406067] [INSPIRE].
J. Rademacker and G. Wilkinson, Determining the unitarity triangle γ with a four-body amplitude analysis of B ± → (K + K − π + π −) D K ± decays, Phys. Lett. B 647 (2007) 400 [hep-ph/0611272] [INSPIRE].
D. Atwood and A. Soni, Role of charm factory in extracting CKM phase information via B→DK, Phys. Rev. D 68 (2003)033003 [hep-ph/0304085] [INSPIRE].
A. Bondar and A. Poluektov, Feasibility study of model-independent approach to \( \phi \) 3 measurement using Dalitz plot analysis, Eur. Phys. J. C 47 (2006) 347 [hep-ph/0510246] [INSPIRE].
A. Bondar and A. Poluektov, On model-independent measurement of the angle \( \phi \) 3 using Dalitz plot analysis, hep-ph/0703267 [INSPIRE].
S. Harnew and J. Rademacker, Model independent determination of the CKM phase γ using input from \( {D}^0\hbox{--} {\overline{D}}^0 \) mixing, JHEP 03 (2015) 169 [arXiv:1412.7254] [INSPIRE].
Particle Data Group collaboration, C. Patrignani et al., Review of Particle Physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].
FOCUS collaboration, J.M. Link et al., Study of the D 0 → π − π + π − π + decay, Phys. Rev. D 75 (2007) 052003 [hep-ex/0701001] [INSPIRE].
CLEO collaboration, M. Artuso et al., Amplitude analysis of D 0 → K + K − π + π −, Phys. Rev. D 85 (2012) 122002 [arXiv:1201.5716] [INSPIRE].
FOCUS collaboration, J.M. Link et al., Study of the D 0 → K + K − π + π − decay, Phys. Lett. B 610 (2005) 225 [hep-ex/0411031] [INSPIRE].
CLEO collaboration, Y. Kubota et al., The CLEO-II detector, Nucl. Instrum. Meth. A 320 (1992) 66 [INSPIRE].
T.S. Hill, The CLEO-II silicon vertex detector, Nucl. Instrum. Meth. A 418 (1998) 32 [INSPIRE].
CLEO-III collaboration, G. Viehhauser, CLEO III operation, Nucl. Instrum. Meth. A 462 (2001) 146 [INSPIRE].
M. Artuso et al., The CLEO RICH detector, Nucl. Instrum. Meth. A 554 (2005) 147 [physics/0506132] [INSPIRE].
R.A. Briere et al., CLEO-c and CESR-c: A new frontier of weak and strong interactions, Cornell LEPP preprint CLNS 01/1742 (2001).
R. Brun et al., GEANT 3.21, CERN DD/EE/84-1 (1984).
CLEO collaboration, J. Libby et al., Model-independent determination of the strong-phase difference between D 0 and \( {\overline{D}}^0\to {K}_S^0{,}_L{h}^{+}{h}^{-}\left(h=\pi, K\right) \) and its impact on the measurement of the CKM angle γ/ \( \phi \) 3, Phys. Rev. D 82 (2010) 112006 [arXiv:1010.2817] [INSPIRE].
ARGUS collaboration, H. Albrecht et al., Search for Hadronic b → u Decays, Phys. Lett. B 241 (1990) 278 [INSPIRE].
CLEO collaboration, D. Cronin-Hennessy et al., Measurement of Charm Production Cross Sections in e + e − Annihilation at Energies between 3.97 and 4.26-GeV, Phys. Rev. D 80 (2009) 072001 [arXiv:0801.3418] [INSPIRE].
MARK-III collaboration, D. Coffman et al., Resonant substructure in \( \overline{K}\pi \pi \pi \) decays of D mesons, Phys. Rev. D 45 (1992) 2196 [INSPIRE].
FOCUS collaboration, J.M. Link et al., Study of the decay mode D 0 → K − K − K + π +, Phys. Lett. B 575 (2003) 190 [hep-ex/0308054] [INSPIRE].
C. Zemach, Use of angular momentum tensors, Phys. Rev. 140 (1965) B97.
W. Rarita and J. Schwinger, On a theory of particles with half integral spin, Phys. Rev. 60 (1941) 61 [INSPIRE].
S.U. Chung, A General formulation of covariant helicity coupling amplitudes, Phys. Rev. D 57 (1998) 431 [INSPIRE].
M.E. Peskin and D.V. Schroeder, An Introduction To Quantum Field Theory (Frontiers in Physics), Westview Press, Boulder U.S.A. (1995).
M. Beneke, J. Rohrer and D. Yang, Branching fractions, polarisation and asymmetries ofB → V V decays, Nucl. Phys. B 774 (2007) 64 [hep-ph/0612290] [INSPIRE].
LHCb collaboration, Measurement of CP asymmetries and polarisation fractions in \( {B}_s^0\to {K}^{\ast 0}{\overline{K}}^{\ast 0} \) decays, JHEP 07 (2015) 166 [arXiv:1503.05362] [INSPIRE].
E. Byckling and K. Kajantie, Particle Kinematics, John Wiley & Sons, New York U.S.A. (1973).
S. Mandelstam, J.E. Paton, R.F. Peierls and A.Q. Sarker, Isobar approximation of production processes, Annals Phys. 18 (1962) 198.
D. Herndon, P. Söding and R.J. Cashmore, A generalized isobar model formalism, Phys. Rev. D 11 (1975) 3165 [INSPIRE].
J.J. Brehm, Unitarity and the Isobar Model: Two-Body Discontinuities, Annals Phys. 108 (1977) 454 [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].
J.D. Jackson, Remarks on the phenomenological analysis of resonances, Nuovo Cim. 34 (1964) 1644.
N. Isgur, C. Morningstar and C. Reader, The a 1 in τ decay, Phys. Rev. D 39 (1989) 1357 [INSPIRE].
M. Vojik and P. Lichard, Three-pion decays of the tau lepton, the a 1(1260) properties and the a 1 ρπ Lagrangian, arXiv:1006.2919 [INSPIRE].
P. Lichard and M. Vojik, An alternative parametrization of the pion form-factor and the mass and width of ρ(770), hep-ph/0611163 [INSPIRE].
D.V. Bugg, The mass of the sigma pole, J. Phys. G 34 (2007) 151 [hep-ph/0608081] [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].
S.M. Flatté, Coupled-channel analysis of the πη and \( K\overline{K} \) systems near \( K\overline{K} \) threshold, Phys. Lett. B 63 (1976) 224 [INSPIRE].
BES collaboration, M. Ablikim et al., Resonances in J/ψ → \( \phi \) π + π − and \( \phi \) K + K −, Phys. Lett. B 607 (2005) 243 [hep-ex/0411001] [INSPIRE].
D.V. Bugg, A Study in Depth of f 0(1370), Eur. Phys. J. C 52 (2007) 55 [arXiv:0706.1341] [INSPIRE].
LHCb collaboration, Analysis of the resonant components in B s → J/ψπ + π −, Phys. Rev. D 86 (2012) 052006 [arXiv:1204.5643] [INSPIRE].
CLEO collaboration, D.M. Asner et al., Hadronic structure in the decay τ − → τ -neutrino π − π 0 π 0 and the sign of the τ-neutrino helicity, Phys. Rev. D 61 (2000) 012002 [hep-ex/9902022] [INSPIRE].
B.S. Zou and D.V. Bugg, Covariant tensor formalism for partial wave analyses of ψ decay to mesons, Eur. Phys. J. A 16 (2003) 537 [hep-ph/0211457] [INSPIRE].
V. Filippini, A. Fontana and A. Rotondi, Covariant spin tensors in meson spectroscopy, Phys. Rev. D 51 (1995) 2247 [INSPIRE].
J.-J. Zhu, Explicit expressions of spin wave functions, hep-ph/9906250 [INSPIRE].
S. Malder et al., First determination of the CP content of D → π + π − π + π − and updated determination of the CP contents of D → π + π − π 0 and D → K + K − π 0, Phys. Lett. B 747 (2015) 9 [arXiv:1504.05878] [INSPIRE].
T. Gershon, J. Libby and G. Wilkinson, Contributions to the width difference in the neutral D system from hadronic decays, Phys. Lett. B 750 (2015) 338 [arXiv:1506.08594] [INSPIRE].
CLEO collaboration, G. Bonvicini et al., Updated measurements of absolute D + and D 0 hadronic branching fractions and \( \sigma \left({e}^{+}{e}^{-}\to D\overline{D}\right) \) at E cm = 3774 MeV, Phys. Rev. D 89 (2014) 072002 [arXiv:1312.6775] [INSPIRE].
CLEO collaboration, T.E. Coan et al., Study of exclusive radiative B meson decays, Phys. Rev. Lett. 84 (2000) 5283 [hep-ex/9912057] [INSPIRE].
B. Guegan, J. Hardin, J. Stevens and M. Williams, Model selection for amplitude analysis, 2015 JINST 10 P09002 [arXiv:1505.05133] [INSPIRE].
R. Tibshirani, Regression shrinkage and selection via the Lasso, J. Roy. Stat. Soc. B 58 (1994) 267.
G. Schwarz, Estimating the dimension of a model, Ann. Statist. 6 (1978) 461.
H. Akaike, A new look at the statistical model identification, IEEE Trans. Automat. Control 19 (1974) 716.
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].
COMPASS collaboration, M. Alekseev et al., Observation of a J P C = 1∓ exotic resonance in diffractive dissociation of 190-GeV/c π − into π − π − π +, Phys. Rev. Lett. 104 (2010) 241803 [arXiv:0910.5842] [INSPIRE].
CLEO collaboration, D.M. Asner et al., Hadronic structure in the decay τ − → τ -neutrino π − π 0 π 0 and the sign of the τ-neutrino helicity, Phys. Rev. D 61 (2000) 012002 [hep-ex/9902022] [INSPIRE].
ALEPH collaboration, S. Schael et al., Branching ratios and spectral functions of τ decays: Final ALEPH measurements and physics implications, Phys. Rept. 421 (2005) 191 [hep-ex/0506072] [INSPIRE].
ARGUS collaboration, H. Albrecht et al., Analysis of the decay tau − → π − π − π + τ -neutrino and determination of the a 1(1260) resonance parameters, Z. Phys. C 58 (1993) 61 [INSPIRE].
OPAL collaboration, R. Akers et al., Measurement of the hadronic decay current in τ − →π − π − π + τ-neutrino, Z. Phys. C 67 (1995) 45 [INSPIRE].
C.A. Baker et al., Evidence for a J P C = 1++ I = 1 meson at 1640-MeV, Phys. Lett. B 449 (1999) 114 [INSPIRE].
S.U. Chung et al., Exotic and \( q\overline{q} \) resonances in the π + π − π − system produced in π − p collisions at 18-GeV/c/, Phys. Rev. D 65 (2002) 072001 [INSPIRE].
LHCb collaboration, Observation of the resonant character of the Z(4430)− state, Phys. Rev. Lett. 112 (2014) 222002 [arXiv:1404.1903] [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 authors
Additional information
ArXiv ePrint: 1703.08505
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, 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 license, and indicate if changes were made.
About this article
Cite this article
d’Argent, P., Skidmore, N., Benton, J. et al. Amplitude analyses of D 0 → π + π − π + π − and D 0 → K + K − π + π − decays. J. High Energ. Phys. 2017, 143 (2017). https://doi.org/10.1007/JHEP05(2017)143
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2017)143