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Chiral dynamics predictions for η′ → ηππ

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Abstract

The hadronic decays η′ → ηππ are studied in the frameworks of large-N C Chiral Perturbation Theory, at lowest and next-to-leading orders, and Resonance Chiral Theory in the leading 1/N C approximation. Higher order effects such as ππ final state interactions are taken into account through a detailed unitarization procedure. The inclusion of finite-width effects in the case of RChT is also discussed. The Dalitz plot distribution and the differential branching ratio are computed in both approaches. The predicted Dalitz plot parameters obtained from the different treatments are compared with the most recent measured values. We find that the η′ → ηππ branching ratios are easily understood, while the Dalitz plot parameters require the inclusion of ππ loops in order to achieve a reasonable agreement. Our final predictions agree with the experimental measurements. We hope our results to be of relevance for present and future experimental analyses of these decays.

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References

  1. J. Gasser and H. Leutwyler, Chiral Perturbation Theory: Expansions in the Mass of the Strange Quark, Nucl. Phys. B 250 (1985) 465 [SPIRES].

    Article  ADS  Google Scholar 

  2. A. Pich, Chiral perturbation theory, Rept. Prog. Phys. 58 (1995) 563 [hep-ph/9502366] [SPIRES].

    Article  ADS  Google Scholar 

  3. G. Ecker, Chiral perturbation theory, Prog. Part. Nucl. Phys. 35 (1995) 1 [hep-ph/9501357] [SPIRES].

    Article  ADS  Google Scholar 

  4. R. Kaiser and H. Leutwyler, Large-N C in chiral perturbation theory, Eur. Phys. J. C 17 (2000) 623 [hep-ph/0007101] [SPIRES].

    Article  ADS  Google Scholar 

  5. G. Ecker, J. Gasser, H. Leutwyler, A. Pich and E. de Rafael, Chiral Lagrangians for Massive Spin 1 Fields, Phys. Lett. B 223 (1989) 425 [SPIRES].

    ADS  Google Scholar 

  6. A.M. Blik et al., Measurement of the matrix element for the decay η′ → ηπ 0 π 0 with the GAMS-4 π spectrometer, Phys. Atom. Nucl. 72 (2009) 231 [Yad. Fiz. 72 (2009) 258] [SPIRES].

    Article  ADS  Google Scholar 

  7. V. Dorofeev et al., Study of η′ → ηπ + π Dalitz plot, Phys. Lett. B 651 (2007) 22 [hep-ph/0607044] [SPIRES].

    ADS  Google Scholar 

  8. Serpukhov-Brussels-Los Alamos-Annecy(LAPP) collaboration, D. Alde et al., Matrix Element Of The η′(958) → ηπ 0 π 0 Decay, Phys. Lett. B 177 (1986) 115 [SPIRES].

    ADS  Google Scholar 

  9. CLEO collaboration, R.A. Briere et al., Rare decays of the eta′, Phys. Rev. Lett. 84 (2000) 26 [hep-ex/9907046] [SPIRES].

    Article  ADS  Google Scholar 

  10. for the KLOE-2 collaboration, G. Venanzoni, Status of KLOE-2, Chin. Phys. C 34 (2010) 918 [arXiv:1001.3591] [SPIRES].

    ADS  Google Scholar 

  11. H.-B. Li, η and η′ Physics at BES-III, J. Phys. G 36 (2009) 085009 [arXiv:0902.3032] [SPIRES].

    ADS  Google Scholar 

  12. A.H. Fariborz and J. Schechter, η′ → ηππ decay as a probe of a possible lowest-lying scalar nonet, Phys. Rev. D 60 (1999) 034002 [hep-ph/9902238] [SPIRES].

    ADS  Google Scholar 

  13. B. Borasoy and R. Nissler, Hadronic η and η′ decays, Eur. Phys. J. A 26 (2005) 383 [hep-ph/0510384] [SPIRES].

    ADS  Google Scholar 

  14. J.A. Cronin, Phenomenological model of strong and weak interactions in chiral U(3) × U(3), Phys. Rev. 161 (1967) 1483 [SPIRES].

    Article  ADS  Google Scholar 

  15. J. Schwinger, Chiral Transformations, Phys. Rev. 167 (1968) 1432 [SPIRES].

    Article  ADS  Google Scholar 

  16. P. Di Vecchia, F. Nicodemi, R. Pettorino and G. Veneziano, Large N, Chiral Approach To Pseudoscalar Masses, Mixings And Decays, Nucl. Phys. B 181 (1981) 318 [SPIRES].

    Article  ADS  Google Scholar 

  17. S. Fajfer and J.M. Gerard, Hadronic decays of η and η′ in the large-N limit, Z. Phys. C 42 (1989) 431 [SPIRES].

    Google Scholar 

  18. P. Herrera-Siklody, η and η′ hadronic decays in U(3)L × U(3)R chiral perturbation theory, hep-ph/9902446 [SPIRES].

  19. J. Schechter and Y. Ueda, General treatment of the breaking of chiral symmetry and scale invariance in the SU(3) σ-model, Phys. Rev. D 3 (1971) 2874 [Erratum ibid D 8 (1973) 987] [SPIRES].

    ADS  Google Scholar 

  20. C.A. Singh and J. Pasupathy, On the Decay Modes of the Meson η′(958) and Chiral Symmetry Breaking, Phys. Rev. Lett. 35 (1975) 1193 [Erratum ibid 35 (1975) 1748] [SPIRES].

    Article  ADS  Google Scholar 

  21. P. Masjuan, Chiral Dynamics Predictions for η′ → ηππ, PoS(CD09)117 [arXiv:0910.0140] [SPIRES].

  22. R. Escribano, A preliminary analysis of η′ → ηππ in chiral theories, AIP Conf. Proc. 1257 (2010) 686 [arXiv:1003.5228] [SPIRES].

    Article  ADS  Google Scholar 

  23. Particle Data Group collaboration, L. Montanet et al., Review of particle properties. Particle Data Group, Phys. Rev. D 50 (1994) 1173 [SPIRES].

    ADS  Google Scholar 

  24. Particle Data Group collaboration, K. Nakamura et al., Review of particle physics, J. Phys. G 37 (2010) 075021 [SPIRES].

    ADS  Google Scholar 

  25. D.V. Amelin et al., Measurement of form factors for the decay η′ → ηπ π +, Phys. Atom. Nucl. 68 (2005) 372 [Yad. Fiz. 68 (2005) 401] [SPIRES].

    Article  ADS  Google Scholar 

  26. G.R. Kalbfleisch, Comments on the η′(958): Branching Ratio, Linear Matrix Element and Dipion Phase Shift, Phys. Rev. D 10 (1974) 916 [SPIRES].

    ADS  Google Scholar 

  27. CLEO collaboration, T.K. Pedlar et al., Charmonium decays to γπ 0 , γη and γη′, Phys. Rev. D 79 (2009) 111101 [arXiv:0904.1394] [SPIRES].

    ADS  Google Scholar 

  28. B. Kubis, Cusp effects in meson decays, EPJ Web Conf. 3 (2010) 01008 [arXiv:0912.3440] [SPIRES].

    Article  Google Scholar 

  29. B. Kubis and S.P. Schneider, The cusp effect in η′ → ηππ decays, Eur. Phys. J. C 62 (2009) 511 [arXiv:0904.1320] [SPIRES].

    Article  ADS  Google Scholar 

  30. P. Masjuan, J.J. Sanz-Cillero and J. Virto, Some Remarks on the Pade Unitarization of Low-Energy Amplitudes, Phys. Lett. B 668 (2008) 14 [arXiv:0805.3291] [SPIRES].

    ADS  Google Scholar 

  31. J.J. Sanz-Cillero, Pade Theory and Phenomenology of Resonance Poles, arXiv: 1002.3512 [SPIRES].

  32. J.A. Oller and E. Oset, N/D Description of Two Meson Amplitudes and Chiral Symmetry, Phys. Rev. D 60 (1999) 074023 [hep-ph/9809337] [SPIRES].

    ADS  Google Scholar 

  33. Z.H. Guo, J.A. Oller and J. Prades, Meson-meson scatterings from U(3) chiral perturbation theory, proceedings of the 15th International QCD Conference, Montpellier, France, 28 Jun–3 Jul 2010.

  34. J.A. Oller, E. Oset and J.E. Palomar, Pion and kaon vector form factors, Phys. Rev. D 63 (2001) 114009 [hep-ph/0011096] [SPIRES].

    ADS  Google Scholar 

  35. Z.H. Guo and J.A. Oller, Resonances from meson-meson scattering in U(3) CHPT, arXiv:1104.2849 [SPIRES].

  36. H. Leutwyler, Bounds on the light quark masses, Phys. Lett. B 374 (1996) 163 [hep-ph/9601234] [SPIRES].

    ADS  Google Scholar 

  37. R. Kaiser and H. Leutwyler, Pseudoscalar decay constants at large-N C , hep-ph/9806336 [SPIRES].

  38. J. Bijnens, η and η′ decays and what can we learn from them?, Acta Phys. Slov. 56 (2006) 305 [hep-ph/0511076] [SPIRES].

    Google Scholar 

  39. F. Ambrosino et al., A global fit to determine the pseudoscalar mixing angle and the gluonium content of the η′ meson, JHEP 07 (2009) 105 [arXiv:0906.3819] [SPIRES].

    ADS  Google Scholar 

  40. J. Bijnens, Chiral perturbation theory and anomalous processes, Int. J. Mod. Phys. A 8 (1993) 3045 [SPIRES].

    ADS  Google Scholar 

  41. P. Herrera-Siklody, J.I. Latorre, P. Pascual and J. Taron, Chiral effective Lagrangian in the large-N/c limit: The nonet case, Nucl. Phys. B 497 (1997) 345 [hep-ph/9610549] [SPIRES].

    Article  ADS  Google Scholar 

  42. P. Herrera-Siklody, J.I. Latorre, P. Pascual and J. Taron, ηη′ mixing from U(3)L × U(3)R chiral perturbation theory, Phys. Lett. B 419 (1998) 326 [hep-ph/9710268] [SPIRES].

    ADS  Google Scholar 

  43. A. Pich, Effective field theory, hep-ph/9806303 [SPIRES].

  44. J. Bijnens, E. Pallante and J. Prades, Hadronic light by light contributions to the muon g-2 in the large-N C limit, Phys. Rev. Lett. 75 (1995) 1447 [Erratum ibid 75 (1995) 3781] [hep-ph/9505251] [SPIRES].

    Article  ADS  Google Scholar 

  45. J. Gasser, M.A. Ivanov and M.E. Sainio, Low-energy photon photon collisions to two loops revisited, Nucl. Phys. B 728 (2005) 31 [hep-ph/0506265] [SPIRES].

    Article  ADS  Google Scholar 

  46. J. Gasser, M.A. Ivanov and M.E. Sainio, Revisiting γγπ + π at low energies, Nucl. Phys. B 745 (2006) 84 [hep-ph/0602234] [SPIRES].

    Article  ADS  Google Scholar 

  47. H. Leutwyler, On the 1/N-expansion in chiral perturbation theory, Nucl. Phys. Proc. Suppl. 64 (1998) 223 [hep-ph/9709408] [SPIRES].

    Article  ADS  Google Scholar 

  48. G. Ecker, Chiral perturbation theory, Prog. Part. Nucl. Phys. 35 (1995) 1 [hep-ph/9501357] [SPIRES].

    Article  ADS  Google Scholar 

  49. J. Bijnens, G. Ecker and J. Gasser, Chiral perturbation theory, hep-ph/9411232 [SPIRES].

  50. A. Pich, Low-Energy Constants from Resonance Chiral Theory, PoS(Confinement8)026 [arXiv:0812.2631] [SPIRES].

  51. J. Bijnens, E. Gamiz, E. Lipartia and J. Prades, QCD short-distance constraints and hadronic approximations, JHEP 04 (2003) 055 [hep-ph/0304222] [SPIRES].

    Article  ADS  Google Scholar 

  52. S. Peris, Large-N c QCD and Pade approximant theory, Phys. Rev. D 74 (2006) 054013 [hep-ph/0603190] [SPIRES].

    ADS  Google Scholar 

  53. P. Masjuan and S. Peris, A Rational Approach to Resonance Saturation in large-N c QCD, JHEP 05 (2007) 040 [arXiv:0704.1247] [SPIRES].

    Article  ADS  Google Scholar 

  54. P. Masjuan and S. Peris, A rational approximation to VVAA and its O(p 6) low-energy constant, Phys. Lett. B 663 (2008) 61 [arXiv:0801.3558] [SPIRES].

    ADS  Google Scholar 

  55. P. Masjuan Queralt, Rational Approximations in Quantum Chromodynamics, arXiv:1005.5683 [SPIRES].

  56. G. Ecker, J. Gasser, A. Pich and E. de Rafael, The Role of Resonances in Chiral Perturbation Theory, Nucl. Phys. B 321 (1989) 311 [SPIRES].

    Article  ADS  Google Scholar 

  57. V. Cirigliano et al., Towards a consistent estimate of the chiral low-energy constants, Nucl. Phys. B 753 (2006) 139 [hep-ph/0603205] [SPIRES].

    Article  ADS  Google Scholar 

  58. G. ’t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B 72 (1974) 461 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  59. G. ’t Hooft, A Two-Dimensional Model for Mesons, Nucl. Phys. B 75 (1974) 461 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  60. E. Witten, Baryons in the 1/n Expansion, Nucl. Phys. B 160 (1979) 57 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  61. L.Y. Xiao and J.J. Sanz-Cillero, Renormalizable Sectors in Resonance Chiral Theory: Sππ Decay Amplitude, Phys. Lett. B 659 (2008) 452 [arXiv:0705.3899] [SPIRES].

    ADS  Google Scholar 

  62. V. Bernard, N. Kaiser and U.G. Meissner, Chiral perturbation theory in the presence of resonances: Application to ππ and πK scattering, Nucl. Phys. B 364 (1991) 283 [SPIRES].

    Article  ADS  Google Scholar 

  63. J.J. Sanz-Cillero, Pion and kaon decay constants: Lattice vs. resonance chiral theory, Phys. Rev. D 70 (2004) 094033 [hep-ph/0408080] [SPIRES].

    ADS  Google Scholar 

  64. Z.-H. Guo and J.J. Sanz-Cillero, ππ scattering lengths at O(p 6) revisited, Phys. Rev. D 79 (2009) 096006 [arXiv:0903.0782] [SPIRES].

    ADS  Google Scholar 

  65. V. Cirigliano, G. Ecker, H. Neufeld and A. Pich, Meson resonances, large-N c and chiral symmetry, JHEP 06 (2003) 012 [hep-ph/0305311] [SPIRES].

    Article  ADS  Google Scholar 

  66. M. Jamin, J.A. Oller and A. Pich, Strangeness-changing scalar form factors, Nucl. Phys. B 622 (2002) 279 [hep-ph/0110193] [SPIRES].

    Article  ADS  Google Scholar 

  67. M. Jamin, J.A. Oller and A. Pich, S-wave Kπ scattering in chiral perturbation theory with resonances, Nucl. Phys. B 587 (2000) 331 [hep-ph/0006045] [SPIRES].

    Article  ADS  Google Scholar 

  68. G. Ecker and C. Zauner, Tensor meson exchange at low energies, Eur. Phys. J. C 52 (2007) 315 [arXiv:0705.0624] [SPIRES].

    Article  ADS  Google Scholar 

  69. R. Escribano, Scalar and vector meson exchange in VP 0 P 0 γ decays, Phys. Rev. D 74 (2006) 114020 [hep-ph/0606314] [SPIRES].

    ADS  Google Scholar 

  70. I. Caprini, G. Colangelo and H. Leutwyler, Mass and width of the lowest resonance in QCD, Phys. Rev. Lett. 96 (2006) 132001 [hep-ph/0512364] [SPIRES].

    Article  ADS  Google Scholar 

  71. C. Shen, Recent results from BESIII, PoS(HQL 2010)006 [arXiv:1012.1377] [SPIRES].

  72. D. Gómez Dumm, A. Pich and J. Portolés, The hadronic off-shell width of meson resonances, Phys. Rev. D 62 (2000) 054014 [hep-ph/0003320] [SPIRES].

    ADS  Google Scholar 

  73. J.J. Sanz-Cillero and A. Pich, Rho Meson Properties in the Chiral Theory Framework, Eur. Phys. J. C 27 (2003) 587 [hep-ph/0208199] [SPIRES].

    ADS  Google Scholar 

  74. J.J. Sanz-Cillero, Renormalization group equations in resonance chiral theory, Phys. Lett. B 681 (2009) 100 [arXiv:0905.3676] [SPIRES].

    ADS  Google Scholar 

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Correspondence to Pere Masjuan.

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Escribano, R., Masjuan, P. & Sanz-Cillero, J.J. Chiral dynamics predictions for η′ → ηππ . J. High Energ. Phys. 2011, 94 (2011). https://doi.org/10.1007/JHEP05(2011)094

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