The Λ(1405) state in a chiral unitary approach with off-shell corrections to dimensional regularized loop functions

  • The Bethe-Salpeter equation is solved in the framework of the unitary coupled-channel approximation by using the pseudoscalar meson-baryon octet interaction. The loop function of the intermediate meson and baryon is deduced in a dimensional regularization scheme, where the relativistic kinetic effect and off-shell corrections are taken into account. Based on the experimental data at the K-p threshold, the subtraction constants in the loop function are determined. The squared amplitude is suppressed strongly and only one Λ(1405) state is generated dynamically in the strangeness S=-1 and isospin I=0 sector.
  • [1] R. H. Dalitz, T. C. Wong, G. Rajasekaran, Phys. Rev., 153: 1617 (1967)
    [2] R. H. Dalitz and S. F. Tuan, Ann. Phys. (N. Y.) 10: 307 (1960)
    [3] L. S. Kisslinger and E. M. Henley, Eur. Phys. J. A, 47: 8 (2011)
    [4] I. Zychor et al, Phys. Lett. B, 660: 167 (2008)
    [5] N. Isgur and G. Karl, Phys. Rev. D, 18: 4187 (1978)
    [6] J. A. Oller, U.-G Meiner ner, Phys. Letter. B, 500: 263 (2001)
    [7] D. Jido, J. A. Oller, E. Oset, A. Ramos. U.-G Meiner ner, Nuclear Physics A, 725: 181 (2003)
    [8] L. S. Geng and E. Oset, Eur. Phys. J. A, 34: 405 (2007)
    [9] E. Oset, A. Ramos, C. Bennhold. Phys. Lett. B, 527: 99 (2002); E. Oset, A. Ramos, C. Bennhold. Erratum, Phys. Lett. B, 530: 260 (2002)
    [10] T. Hyodo, A. Hosaka, E. Oset, A. Ramos, and M. J. Vicente Vacas, Phys. Rev. C, 68: 065203 (2003)
    [11] A. Cieply and J. Smejkal, Eur. Phys. J. A, 43: 191 (2010)
    [12] M. Hassanvand et al, Phys Rev. C, 87: 055202 (2013)
    [13] R. H. Dalitz and A. Deloff. J. Phys. G, 17: 289 (1991)
    [14] G. Alexander, G. R. Kalbfleisch, D. H. Miller et al, Phys. Rev. Lett., 8: 447 (1962)
    [15] K. Moriya et al (CLAS Collaboration), Phys. Rev. C, 87(3): 035206 (2013)
    [16] M. Bazzi et al (SIDDHARTA Collaboration), Phys. Lett. B, 704: 113 (2011)
    [17] Y. Ikeda, T. Hyodo, and W. Weise, Nucl. Phys. A, 881: 98 (2012)
    [18] M. Mai and U. G. Meiner ner, Nucl. Phys. A, 900: 51 (2013)
    [19] Z. H. Guo and J. A. Oller, Phys. Rev. C, 87(3): 035202 (2013)
    [20] M. Mai and U. G. Meiner ner, Eur. Phys. J. A, 51(3): 30 (2015)
    [21] A. Cieply, M. Mai, U. G. Meiner ner, and J. Smejkal, Nucl. Phys. A, 954: 17 (2016)
    [22] A. Pich, Rep. Prog. Phys., 58: 563 (1995)
    [23] G. Ecker, Prog. Part. Nucl. Phys., 35: 1 (1995)
    [24] V. Bernard, N. Kaiser, and U. G. Meiner ner, Int. J. Mod. Phys. E, 4: 193 (1995)
    [25] P. C. Bruns, M. Mai, and U. G. Meiner ner, Phys. Lett. B, 697: 254 (2011)
    [26] E. Oset, A. Ramos, Nucl. Phys. A, 635: 99 (1998)
    [27] U. G. Meiner ner, U. Raha, and A. Rusetsky, Eur. Phys. J. C, 35: 349 (2004)
    [28] D. N. Tovee et al, Nucl. Phys. B, 33: 493 (1971)
    [29] R. J. Nowak et al, Nucl. Phys. B, 139: 61 (1978)
    [30] K. A. Olive et al (Particle Data Group), Chin. Phys. C, 38: 090001 (2014)
    [31] G. Passarino and M. J. G. Veltman, Nucl. Phys. B, 160: 151 (1979)
  • [1] R. H. Dalitz, T. C. Wong, G. Rajasekaran, Phys. Rev., 153: 1617 (1967)
    [2] R. H. Dalitz and S. F. Tuan, Ann. Phys. (N. Y.) 10: 307 (1960)
    [3] L. S. Kisslinger and E. M. Henley, Eur. Phys. J. A, 47: 8 (2011)
    [4] I. Zychor et al, Phys. Lett. B, 660: 167 (2008)
    [5] N. Isgur and G. Karl, Phys. Rev. D, 18: 4187 (1978)
    [6] J. A. Oller, U.-G Meiner ner, Phys. Letter. B, 500: 263 (2001)
    [7] D. Jido, J. A. Oller, E. Oset, A. Ramos. U.-G Meiner ner, Nuclear Physics A, 725: 181 (2003)
    [8] L. S. Geng and E. Oset, Eur. Phys. J. A, 34: 405 (2007)
    [9] E. Oset, A. Ramos, C. Bennhold. Phys. Lett. B, 527: 99 (2002); E. Oset, A. Ramos, C. Bennhold. Erratum, Phys. Lett. B, 530: 260 (2002)
    [10] T. Hyodo, A. Hosaka, E. Oset, A. Ramos, and M. J. Vicente Vacas, Phys. Rev. C, 68: 065203 (2003)
    [11] A. Cieply and J. Smejkal, Eur. Phys. J. A, 43: 191 (2010)
    [12] M. Hassanvand et al, Phys Rev. C, 87: 055202 (2013)
    [13] R. H. Dalitz and A. Deloff. J. Phys. G, 17: 289 (1991)
    [14] G. Alexander, G. R. Kalbfleisch, D. H. Miller et al, Phys. Rev. Lett., 8: 447 (1962)
    [15] K. Moriya et al (CLAS Collaboration), Phys. Rev. C, 87(3): 035206 (2013)
    [16] M. Bazzi et al (SIDDHARTA Collaboration), Phys. Lett. B, 704: 113 (2011)
    [17] Y. Ikeda, T. Hyodo, and W. Weise, Nucl. Phys. A, 881: 98 (2012)
    [18] M. Mai and U. G. Meiner ner, Nucl. Phys. A, 900: 51 (2013)
    [19] Z. H. Guo and J. A. Oller, Phys. Rev. C, 87(3): 035202 (2013)
    [20] M. Mai and U. G. Meiner ner, Eur. Phys. J. A, 51(3): 30 (2015)
    [21] A. Cieply, M. Mai, U. G. Meiner ner, and J. Smejkal, Nucl. Phys. A, 954: 17 (2016)
    [22] A. Pich, Rep. Prog. Phys., 58: 563 (1995)
    [23] G. Ecker, Prog. Part. Nucl. Phys., 35: 1 (1995)
    [24] V. Bernard, N. Kaiser, and U. G. Meiner ner, Int. J. Mod. Phys. E, 4: 193 (1995)
    [25] P. C. Bruns, M. Mai, and U. G. Meiner ner, Phys. Lett. B, 697: 254 (2011)
    [26] E. Oset, A. Ramos, Nucl. Phys. A, 635: 99 (1998)
    [27] U. G. Meiner ner, U. Raha, and A. Rusetsky, Eur. Phys. J. C, 35: 349 (2004)
    [28] D. N. Tovee et al, Nucl. Phys. B, 33: 493 (1971)
    [29] R. J. Nowak et al, Nucl. Phys. B, 139: 61 (1978)
    [30] K. A. Olive et al (Particle Data Group), Chin. Phys. C, 38: 090001 (2014)
    [31] G. Passarino and M. J. G. Veltman, Nucl. Phys. B, 160: 151 (1979)
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Fang-Yong Dong, Bao-Xi Sun and Jing-Long Pang. The Λ(1405) state in a chiral unitary approach with off-shell corrections to dimensional regularized loop functions[J]. Chinese Physics C, 2017, 41(7): 074108. doi: 10.1088/1674-1137/41/7/074108
Fang-Yong Dong, Bao-Xi Sun and Jing-Long Pang. The Λ(1405) state in a chiral unitary approach with off-shell corrections to dimensional regularized loop functions[J]. Chinese Physics C, 2017, 41(7): 074108.  doi: 10.1088/1674-1137/41/7/074108 shu
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Received: 2016-11-14
Revised: 2017-04-03
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The Λ(1405) state in a chiral unitary approach with off-shell corrections to dimensional regularized loop functions

  • 1.  College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
  • 2. College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
  • 3. Department of Physics, Peking University, Beijing 100871, China
  • 4.  Department of Physics, Peking University, Beijing 100871, China

Abstract: The Bethe-Salpeter equation is solved in the framework of the unitary coupled-channel approximation by using the pseudoscalar meson-baryon octet interaction. The loop function of the intermediate meson and baryon is deduced in a dimensional regularization scheme, where the relativistic kinetic effect and off-shell corrections are taken into account. Based on the experimental data at the K-p threshold, the subtraction constants in the loop function are determined. The squared amplitude is suppressed strongly and only one Λ(1405) state is generated dynamically in the strangeness S=-1 and isospin I=0 sector.

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