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Octet baryon masses in next-to-next-to-next-to-leading order covariant baryon chiral perturbation theory

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Abstract

We study the ground-state octet baryon masses and sigma terms using the covariant baryon chiral perturbation theory (ChPT) with the extended-on-mass-shell (EOMS) renormalization scheme up to next-to-next-to-next-to-leading order (N3LO). By adjusting the available 19 low-energy constants (LECs), a reasonable fit of the n f  = 2+1 lattice quantum chromodynamics (LQCD) results from the PACS-CS, LHPC, HSC, QCDSF-UKQCD and NPLQCD collaborations is achieved. Finite-volume corrections to the lattice data are calculated self-consistently. Our study shows that the N3LO BChPT describes better the light quark mass evolution of the lattice data than the NNLO BChPT does and the various lattice simulations seem to be consistent with each other. We also predict the pion and strangeness sigma terms of the octet baryons using the LECs determined in the fit of their masses. The predicted pion- and strangeness-nucleon sigma terms are σ πN  = 43(1)(6) MeV and σ sN  = 126(24)(54) MeV, respectively.

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References

  1. K.G. Wilson, Confinement of Quarks, Phys. Rev. D 10 (1974) 2445 [INSPIRE].

    ADS  Google Scholar 

  2. C. Gattringer and C.B. Lang, Quantum Chromodynamics on the Lattice - An Introductory Presentation, Springer, Heidelberg Germany (2010).

    Google Scholar 

  3. ETM collaboration, C. Alexandrou et al., Low-lying baryon spectrum with two dynamical twisted mass fermions, Phys. Rev. D 80 (2009) 114503 [arXiv:0910.2419] [INSPIRE].

    ADS  Google Scholar 

  4. S. Dürr et al., Ab-Initio Determination of Light Hadron Masses, Science 322 (2008) 1224 [arXiv:0906.3599] [INSPIRE].

    Article  ADS  Google Scholar 

  5. PACS-CS collaboration, S. Aoki et al., 2+1 Flavor Lattice QCD toward the Physical Point, Phys. Rev. D 79 (2009) 034503 [arXiv:0807.1661] [INSPIRE].

    ADS  Google Scholar 

  6. PACS-CS collaboration, S. Aoki et al., Physical Point Simulation in 2+1 Flavor Lattice QCD, Phys. Rev. D 81 (2010) 074503 [arXiv:0911.2561] [INSPIRE].

    ADS  Google Scholar 

  7. A. Walker-Loud et al., Light hadron spectroscopy using domain wall valence quarks on an Asqtad sea, Phys. Rev. D 79 (2009) 054502 [arXiv:0806.4549] [INSPIRE].

    ADS  Google Scholar 

  8. Hadron Spectrum collaboration, H.-W. Lin et al., First results from 2+1 dynamical quark flavors on an anisotropic lattice: Light-hadron spectroscopy and setting the strange-quark mass, Phys. Rev. D 79 (2009) 034502 [arXiv:0810.3588] [INSPIRE].

    ADS  Google Scholar 

  9. W. Bietenholz et al., Tuning the strange quark mass in lattice simulations, Phys. Lett. B 690 (2010) 436 [arXiv:1003.1114] [INSPIRE].

    ADS  Google Scholar 

  10. W. Bietenholz et al., Flavour blindness and patterns of flavour symmetry breaking in lattice simulations of up, down and strange quarks, Phys. Rev. D 84 (2011) 054509 [arXiv:1102.5300] [INSPIRE].

    ADS  Google Scholar 

  11. S. Beane et al., High Statistics Analysis using Anisotropic Clover Lattices: (IV) Volume Dependence of Light Hadron Masses, Phys. Rev. D 84 (2011) 014507 [arXiv:1104.4101] [INSPIRE].

    ADS  Google Scholar 

  12. Particle Data Group collaboration, J. Beringer et al., Review of Particle Physics (RPP), Phys. Rev. D 86 (2012) 010001 [INSPIRE].

    ADS  Google Scholar 

  13. Z. Fodor and C. Hölbling, Light Hadron Masses from Lattice QCD, Rev. Mod. Phys. 84 (2012) 449 [arXiv:1203.4789] [INSPIRE].

    Article  ADS  Google Scholar 

  14. S. Weinberg, Phenomenological Lagrangians, Physica A 96 (1979) 327 [INSPIRE].

    ADS  Google Scholar 

  15. J. Gasser and H. Leutwyler, Chiral Perturbation Theory to One Loop, Annals Phys. 158 (1984) 142 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. J. Gasser, M. Sainio and A. Svarc, Nucleons with Chiral Loops, Nucl. Phys. B 307 (1988) 779 [INSPIRE].

    Article  ADS  Google Scholar 

  18. H. Leutwyler, Principles of chiral perturbation theory, hep-ph/9406283 [INSPIRE].

  19. V. Bernard, N. Kaiser and U.-G. Meissner, Chiral dynamics in nucleons and nuclei, Int. J. Mod. Phys. E 4 (1995) 193 [hep-ph/9501384] [INSPIRE].

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  22. A. Pich, Effective field theory: Course, hep-ph/9806303 [INSPIRE].

  23. V. Bernard and U.-G. Meissner, Chiral perturbation theory, Ann. Rev. Nucl. Part. Sci. 57 (2007) 33 [hep-ph/0611231] [INSPIRE].

    Article  ADS  Google Scholar 

  24. V. Bernard, Chiral Perturbation Theory and Baryon Properties, Prog. Part. Nucl. Phys. 60 (2008) 82 [arXiv:0706.0312] [INSPIRE].

    Article  ADS  Google Scholar 

  25. S. Scherer and M.R. Schindler, A Primer for Chiral Perturbation Theory, Springer, Heidelberg Germany (2012).

    MATH  Google Scholar 

  26. E.E. Jenkins and A.V. Manohar, Baryon chiral perturbation theory using a heavy fermion Lagrangian, Phys. Lett. B 255 (1991) 558 [INSPIRE].

    ADS  Google Scholar 

  27. T. Becher and H. Leutwyler, Baryon chiral perturbation theory in manifestly Lorentz invariant form, Eur. Phys. J. C 9 (1999) 643 [hep-ph/9901384] [INSPIRE].

    ADS  Google Scholar 

  28. J. Gegelia and G. Japaridze, Matching heavy particle approach to relativistic theory, Phys. Rev. D 60 (1999) 114038 [hep-ph/9908377] [INSPIRE].

    ADS  Google Scholar 

  29. T. Fuchs, J. Gegelia, G. Japaridze and S. Scherer, Renormalization of relativistic baryon chiral perturbation theory and power counting, Phys. Rev. D 68 (2003) 056005 [hep-ph/0302117] [INSPIRE].

    ADS  Google Scholar 

  30. V. Bernard, T.R. Hemmert and U.-G. Meissner, Cutoff schemes in chiral perturbation theory and the quark mass expansion of the nucleon mass, Nucl. Phys. A 732 (2004) 149 [hep-ph/0307115] [INSPIRE].

    ADS  Google Scholar 

  31. R.D. Young, D.B. Leinweber and A.W. Thomas, Convergence of chiral effective field theory, Prog. Part. Nucl. Phys. 50 (2003) 399 [hep-lat/0212031] [INSPIRE].

    Article  ADS  Google Scholar 

  32. D.B. Leinweber, A.W. Thomas and R.D. Young, Physical nucleon properties from lattice QCD, Phys. Rev. Lett. 92 (2004) 242002 [hep-lat/0302020] [INSPIRE].

    Article  ADS  Google Scholar 

  33. R. Young and A. Thomas, Octet baryon masses and sigma terms from an SU(3) chiral extrapolation, Phys. Rev. D 81 (2010) 014503 [arXiv:0901.3310] [INSPIRE].

    ADS  Google Scholar 

  34. A. Semke and M. Lutz, Baryon self energies in the chiral loop expansion, Nucl. Phys. A 778 (2006) 153 [nucl-th/0511061] [INSPIRE].

    ADS  Google Scholar 

  35. E.E. Jenkins, Baryon masses in chiral perturbation theory, Nucl. Phys. B 368 (1992) 190 [INSPIRE].

    Article  ADS  Google Scholar 

  36. V. Bernard, N. Kaiser and U.G. Meissner, Critical analysis of baryon masses and sigma terms in heavy baryon chiral perturbation theory, Z. Phys. C 60 (1993) 111 [hep-ph/9303311] [INSPIRE].

    ADS  Google Scholar 

  37. M.K. Banerjee and J. Milana, Baryon mass splittings in chiral perturbation theory, Phys. Rev. D 52 (1995) 11.

    Google Scholar 

  38. B. Borasoy and U.-G. Meissner, Chiral expansion of baryon masses and sigma terms, Annals Phys. 254 (1997) 192 [hep-ph/9607432] [INSPIRE].

    Article  ADS  Google Scholar 

  39. A. Walker-Loud, Octet baryon masses in partially quenched chiral perturbation theory, Nucl. Phys. A 747 (2005) 476 [hep-lat/0405007] [INSPIRE].

    ADS  Google Scholar 

  40. P. Ellis and K. Torikoshi, Baryon masses in chiral perturbation theory with infrared regularization, Phys. Rev. C 61 (2000) 015205 [nucl-th/9904017] [INSPIRE].

    ADS  Google Scholar 

  41. M. Frink and U.-G. Meissner, Chiral extrapolations of baryon masses for unquenched three flavor lattice simulations, JHEP 07 (2004) 028 [hep-lat/0404018] [INSPIRE].

    Article  ADS  Google Scholar 

  42. M. Frink, U.-G. Meissner and I. Scheller, Baryon masses, chiral extrapolations and all that, Eur. Phys. J. A 24 (2005) 395 [hep-lat/0501024] [INSPIRE].

    ADS  Google Scholar 

  43. B. Lehnhart, J. Gegelia and S. Scherer, Baryon masses and nucleon sigma terms in manifestly Lorentz-invariant baryon chiral perturbation theory, J. Phys. G 31 (2005) 89 [hep-ph/0412092] [INSPIRE].

    ADS  Google Scholar 

  44. J. Martin Camalich, L.S. Geng and M. Vicente Vacas, The lowest-lying baryon masses in covariant SU(3)-flavor chiral perturbation theory, Phys. Rev. D 82 (2010) 074504 [arXiv:1003.1929] [INSPIRE].

    ADS  Google Scholar 

  45. A. Semke and M.F.M. Lutz, On the possibility of a discontinuous quark-mass dependence of baryon octet and decuplet masses, Nucl. Phys. A 789 (2007) 251

    ADS  Google Scholar 

  46. A. Semke and M. Lutz, On the quark-mass dependence of the baryon ground-state masses, Phys. Rev. D 85 (2012) 034001 [arXiv:1111.0238] [INSPIRE].

    ADS  Google Scholar 

  47. P.C. Bruns, L. Greil and A. Schafer, Chiral extrapolation of baryon mass ratios, arXiv:1209.0980 [INSPIRE].

  48. M. Lutz and A. Semke, On the consistency of recent QCD lattice data of the baryon ground-state masses, Phys. Rev. D 86 (2012) 091502 [arXiv:1209.2791] [INSPIRE].

    ADS  Google Scholar 

  49. PACS-CS collaboration, K.-I. Ishikawa et al., SU(2) and SU(3) chiral perturbation theory analyses on baryon masses in 2+1 flavor lattice QCD, Phys. Rev. D 80 (2009) 054502 [arXiv:0905.0962] [INSPIRE].

    ADS  Google Scholar 

  50. J. Alarcon, L.S. Geng, J.M. Camalich and J. Oller, On the strangeness content of the nucleon, arXiv:1209.2870 [INSPIRE].

  51. J.A. Oller, M. Verbeni and J. Prades, Meson-baryon effective chiral lagrangians to \( \mathcal{O} \)(q 3), JHEP 09 (2006) 079 [hep-ph/0608204] [INSPIRE].

    Article  ADS  Google Scholar 

  52. L.S. Geng, J. Martin Camalich, L. Álvarez-Ruso and M. Vicente Vacas, Leading SU(3)-breaking corrections to the baryon magnetic moments in Chiral Perturbation Theory, Phys. Rev. Lett. 101 (2008) 222002 [arXiv:0805.1419] [INSPIRE].

    Article  ADS  Google Scholar 

  53. L.S. Geng, M. Altenbuchinger and W. Weise, Light quark mass dependence of the D and D s decay constants, Phys. Lett. B 696 (2011) 390 [arXiv:1012.0666] [INSPIRE].

    ADS  Google Scholar 

  54. L.S. Geng, J. Martin-Camalich, L. Álvarez-Ruso and M. Vicente-Vacas, The Lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments in chiral perturbation theory, arXiv:1001.0465 [INSPIRE].

  55. J. Bijnens and I. Jemos, A new global fit of the \( L_i^r \) at next-to-next-to-leading order in Chiral Perturbation Theory, Nucl. Phys. B 854 (2012) 631 [arXiv:1103.5945] [INSPIRE].

    Article  ADS  Google Scholar 

  56. QCDSF-UKQCD collaboration, A. Ali Khan et al., The Nucleon mass in N(f) = 2 lattice QCD: Finite size effects from chiral perturbation theory, Nucl. Phys. B 689 (2004) 175 [hep-lat/0312030] [INSPIRE].

    Article  ADS  Google Scholar 

  57. M. Procura, B. Musch, T. Wollenweber, T. Hemmert and W. Weise, Nucleon mass: From lattice QCD to the chiral limit, Phys. Rev. D 73 (2006) 114510 [hep-lat/0603001] [INSPIRE].

    ADS  Google Scholar 

  58. L.S. Geng, X.-l. Ren, J. Martin-Camalich and W. Weise, Finite-volume effects on octet-baryon masses in covariant baryon chiral perturbation theory, Phys. Rev. D 84 (2011) 074024 [arXiv:1108.2231] [INSPIRE].

    ADS  Google Scholar 

  59. H. Ohki et al., Nucleon sigma term and strange quark content in 2+1-flavor QCD with dynamical overlap fermions, PoS(LAT2009)124 [arXiv:0910.3271] [INSPIRE].

  60. G. Amoros, J. Bijnens and P. Talavera, QCD isospin breaking in meson masses, decay constants and quark mass ratios, Nucl. Phys. B 602 (2001) 87 [hep-ph/0101127] [INSPIRE].

    Article  ADS  Google Scholar 

  61. M. Procura, T.R. Hemmert and W. Weise, Nucleon mass, sigma term and lattice QCD, Phys. Rev. D 69 (2004) 034505 [hep-lat/0309020] [INSPIRE].

    ADS  Google Scholar 

  62. J. Giedt, A.W. Thomas and R.D. Young, Dark matter, the CMSSM and lattice QCD, Phys. Rev. Lett. 103 (2009) 201802 [arXiv:0907.4177] [INSPIRE].

    Article  ADS  Google Scholar 

  63. S. Dürr et al., Sigma term and strangeness content of octet baryons, Phys. Rev. D 85 (2012) 014509 [arXiv:1109.4265] [INSPIRE].

    ADS  Google Scholar 

  64. P. Shanahan, A. Thomas and R. Young, Sigma terms from an SU(3) chiral extrapolation, arXiv:1205.5365 [INSPIRE].

  65. A. Semke and M. Lutz, Strangeness in the baryon ground states, Phys. Lett. B 717 (2012) 242 [arXiv:1202.3556] [INSPIRE].

    ADS  Google Scholar 

  66. R. Horsley et al., Hyperon sigma terms for 2+1 quark flavours, Phys. Rev. D 85 (2012) 034506 [arXiv:1110.4971] [INSPIRE].

    ADS  Google Scholar 

  67. J. Gasser, H. Leutwyler and M. Sainio, Sigma term update, Phys. Lett. B 253 (1991) 252 [INSPIRE].

    ADS  Google Scholar 

  68. J. Alarcon, J. Martin Camalich and J. Oller, The chiral representation of the πN scattering amplitude and the pion-nucleon sigma term, Phys. Rev. D 85 (2012) 051503 [arXiv:1110.3797] [INSPIRE].

    ADS  Google Scholar 

  69. QCDSF collaboration, G.S. Bali et al., The strange and light quark contributions to the nucleon mass from Lattice QCD, Phys. Rev. D 85 (2012) 054502 [arXiv:1111.1600] [INSPIRE].

    ADS  Google Scholar 

  70. G. Bali et al., Nucleon mass and sigma term from lattice QCD with two light fermion flavors, Nucl. Phys. B 866 (2013) 1 [arXiv:1206.7034] [INSPIRE].

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Research Center for Nuclear Science and Technology & School of Physics and Nuclear Energy Engineering, Beihang University, Beijing, 100191, China

    X.-L. Ren, L. S. Geng & J. Meng

  2. Department of Physics and Astronomy, University of Sussex, BN1 9QH, Brighton, U.K.

    J. Martin Camalich

  3. State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing, 100871, China

    J. Meng

  4. Department of Physics, University of Stellenbosch, Stellenbosch, South Africa

    J. Meng

  5. Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki, Osaka, 567-0047, Japan

    H. Toki

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  1. X.-L. Ren
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  2. L. S. Geng
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Correspondence to L. S. Geng.

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Ren, XL., Geng, L.S., Camalich, J.M. et al. Octet baryon masses in next-to-next-to-next-to-leading order covariant baryon chiral perturbation theory. J. High Energ. Phys. 2012, 73 (2012). https://doi.org/10.1007/JHEP12(2012)073

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