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Chinese Physics C> 2017, Vol. 41> Issue(12) : 124101 DOI: 10.1088/1674-1137/41/12/124101

On the chiral covariant approach to ρρ scattering

  • 1.

      School of Physics and Nuclear Energy Engineering &

  • 2.

      Physics Department, The George Washington University, Washington, DC 20052, USA

  • 3.

      Departamento de Fí

  • We examine in detail a recent work (D. Gülmez, U. G. Meißner and J. A. Oller, Eur. Phys. J. C, 77:460 (2017)), where improvements to make ρρ scattering relativistically covariant are made. The paper has the remarkable conclusion that the J=2 state disappears with a potential which is much more attractive than for J=0, where a bound state is found. We trace this abnormal conclusion to the fact that an "on-shell" factorization of the potential is done in a region where this potential is singular and develops a large discontinuous and unphysical imaginary part. A method is developed, evaluating the loops with full ρ propagators, and we show that they do not develop singularities and do not have an imaginary part below threshold. With this result for the loops we define an effective potential, which when used with the Bethe-Salpeter equation provides a state with J=2 around the energy of the f2(1270). In addition, the coupling of the state to ρρ is evaluated and we find that this coupling and the T matrix around the energy of the bound state are remarkably similar to those obtained with a drastic approximation used previously, in which the q2 terms of the propagators of the exchanged ρ mesons are dropped, once the cut-off in the ρρ loop function is tuned to reproduce the bound state at the same energy.

  • References

    [1] J. A. Oller and E. Oset, Nucl. Phys. A, 620:438(1997) Erratum:[Nucl. Phys. A, 652:407(1999)]
    [2] N. Kaiser, Eur. Phys. J. A, 3:307(1998).
    [3] M. P. Locher, V. E. Markushin, and H. Q. Zheng, Eur. Phys. J. C, 4:317(1998)
    [4] J. Nieves and E. Ruiz Arriola, Phys. Lett. B, 455:30(1999)
    [5] T. Waas, N. Kaiser, and W. Weise, Phys. Lett. B, 379:34(1996)
    [6] E. Oset and A. Ramos, Nucl. Phys. A, 635:99(1998)
    [7] J. A. Oller and U. G. Meiner, Phys. Lett. B, 500:263(2001)
    [8] C. Garcia-Recio, J. Nieves, E. Ruiz Arriola, and M. J. Vicente Vacas, Phys. Rev. D, 67:076009(2003)
    [9] T. Hyodo, S. I. Nam, D. Jido, and A. Hosaka, Phys. Rev. C, 68:018201(2003)
    [10] J. A. Oller, E. Oset, and A. Ramos, Prog. Part. Nucl. Phys., 45:157(2000)
    [11] R. Molina, D. Nicmorus, and E. Oset, Phys. Rev. D, 78:114018(2008)
    [12] L. S. Geng and E. Oset, Phys. Rev. D, 79:074009(2009)
    [13] H. Nagahiro, J. Yamagata-Sekihara, E. Oset, S. Hirenzaki, and R. Molina, Phys. Rev. D, 79:114023(2009)
    [14] E. Oset, L. S. Geng, and R. Molina, J. Phys. Conf. Ser., 348:012004(2012)
    [15] D. Glmez, U. G. Meiner, and J. A. Oller, Eur. Phys. J. C, 77(7):460(2017) arXiv:1611.00168[hep-ph]
    [16] S. Weinberg, Phys. Rev., 130:776(1963); S. Weinberg, Phys. Rev. B, 137:672(1965)
    [17] V. Baru, J. Haidenbauer, C. Hanhart, Y. Kalashnikova, and A. E. Kudryavtsev, Phys. Lett. B, 586:53(2004)
    [18] D. Gamermann, J. Nieves, E. Oset and E. Ruiz Arriola, Phys. Rev. D, 81:014029(2010)
    [19] E. Klempt and A. Zaitsev, Phys. Rept., 454:1(2007)
    [20] V. Crede and C. A. Meyer, Prog. Part. Nucl. Phys., 63:74(2009)
    [21] J. J. Xie and E. Oset, Eur. Phys. J. A, 51:111(2015)
    [22] J. J. Xie, E. Oset, and L. S. Geng, Phys. Rev. C, 93(2):025202(2016)
    [23] M. Bando, T. Kugo, S. Uehara, K. Yamawaki, and T. Yanagida, Phys. Rev. Lett., 54:1215(1985)
    [24] M. Bando, T. Kugo, and K. Yamawaki, Phys. Rept., 164:217(1988)
    [25] U. G. Meiner, Phys. Rept., 161:213(1988)
    [26] S. Weinberg, Physica A, 96:327(1979)
    [27] J. Gasser and H. Leutwyler, Annals Phys., 158:142(1984)
    [28] S. Scherer, Adv. Nucl. Phys., 27:277(2003)
    [29] G. Ecker, J. Gasser, H. Leutwyler, A. Pich, and E. de Rafael, Phys. Lett. B, 223:425(1989)
    [30] G. F. Chew and S. Mandelstam, Phys. Rev., 119:467(1960)
    [31] J. A. Oller and E. Oset, Phys. Rev. D, 60:074023(1999)
    [32] J. R. Pelaez, Phys. Rept., 658:1(2016)
    [33] E. E. Salpeter and H. A. Bethe, Phys. Rev., 84:1232(1951)
    [34] T. Regge, Nuovo Cim., 14:951(1959)
    [35] T. Regge, Nuovo Cim., 18:947(1960)
    [36] M. M. Brisudova, L. Burakovsky, J. T. Goldman, and A. Szczepaniak, Phys. Rev. D, 67:094016(2003)
    [37] A. V. Barnes, D. J. Mellema, A. V. Tollestrup, R. L. Walker, O. I. Dahl, R. A. Johnson, R. W. Kenney, and M. Pripstein, Phys. Rev. Lett., 37:76(1976)
    [38] H. Navelet and P. R. Stevens, Nucl. Phys. B, 118:475(1977)
    [39] M. Guidal, J. M. Laget, and M. Vanderhaeghen, Nucl. Phys. A, 627:645(1997)
    [40] N. I. Kochelev, M. Battaglieri, and R. De Vita, Phys. Rev. C, 80:025201(2009)
    [41] C. R. Ji, R. Kaminski, L. Lesniak, A. Szczepaniak, and R. Williams, Phys. Rev. C, 58:1205(1998)
    [42] M. Battaglieri et al (CLAS Collaboration), Phys. Rev. D, 80:072005(2009)
    [43] J. Yamagata-Sekihara, J. Nieves, and E. Oset, Phys. Rev. D, 83:014003(2011)

  • References

    [1] J. A. Oller and E. Oset, Nucl. Phys. A, 620:438(1997) Erratum:[Nucl. Phys. A, 652:407(1999)]
    [2] N. Kaiser, Eur. Phys. J. A, 3:307(1998).
    [3] M. P. Locher, V. E. Markushin, and H. Q. Zheng, Eur. Phys. J. C, 4:317(1998)
    [4] J. Nieves and E. Ruiz Arriola, Phys. Lett. B, 455:30(1999)
    [5] T. Waas, N. Kaiser, and W. Weise, Phys. Lett. B, 379:34(1996)
    [6] E. Oset and A. Ramos, Nucl. Phys. A, 635:99(1998)
    [7] J. A. Oller and U. G. Meiner, Phys. Lett. B, 500:263(2001)
    [8] C. Garcia-Recio, J. Nieves, E. Ruiz Arriola, and M. J. Vicente Vacas, Phys. Rev. D, 67:076009(2003)
    [9] T. Hyodo, S. I. Nam, D. Jido, and A. Hosaka, Phys. Rev. C, 68:018201(2003)
    [10] J. A. Oller, E. Oset, and A. Ramos, Prog. Part. Nucl. Phys., 45:157(2000)
    [11] R. Molina, D. Nicmorus, and E. Oset, Phys. Rev. D, 78:114018(2008)
    [12] L. S. Geng and E. Oset, Phys. Rev. D, 79:074009(2009)
    [13] H. Nagahiro, J. Yamagata-Sekihara, E. Oset, S. Hirenzaki, and R. Molina, Phys. Rev. D, 79:114023(2009)
    [14] E. Oset, L. S. Geng, and R. Molina, J. Phys. Conf. Ser., 348:012004(2012)
    [15] D. Glmez, U. G. Meiner, and J. A. Oller, Eur. Phys. J. C, 77(7):460(2017) arXiv:1611.00168[hep-ph]
    [16] S. Weinberg, Phys. Rev., 130:776(1963); S. Weinberg, Phys. Rev. B, 137:672(1965)
    [17] V. Baru, J. Haidenbauer, C. Hanhart, Y. Kalashnikova, and A. E. Kudryavtsev, Phys. Lett. B, 586:53(2004)
    [18] D. Gamermann, J. Nieves, E. Oset and E. Ruiz Arriola, Phys. Rev. D, 81:014029(2010)
    [19] E. Klempt and A. Zaitsev, Phys. Rept., 454:1(2007)
    [20] V. Crede and C. A. Meyer, Prog. Part. Nucl. Phys., 63:74(2009)
    [21] J. J. Xie and E. Oset, Eur. Phys. J. A, 51:111(2015)
    [22] J. J. Xie, E. Oset, and L. S. Geng, Phys. Rev. C, 93(2):025202(2016)
    [23] M. Bando, T. Kugo, S. Uehara, K. Yamawaki, and T. Yanagida, Phys. Rev. Lett., 54:1215(1985)
    [24] M. Bando, T. Kugo, and K. Yamawaki, Phys. Rept., 164:217(1988)
    [25] U. G. Meiner, Phys. Rept., 161:213(1988)
    [26] S. Weinberg, Physica A, 96:327(1979)
    [27] J. Gasser and H. Leutwyler, Annals Phys., 158:142(1984)
    [28] S. Scherer, Adv. Nucl. Phys., 27:277(2003)
    [29] G. Ecker, J. Gasser, H. Leutwyler, A. Pich, and E. de Rafael, Phys. Lett. B, 223:425(1989)
    [30] G. F. Chew and S. Mandelstam, Phys. Rev., 119:467(1960)
    [31] J. A. Oller and E. Oset, Phys. Rev. D, 60:074023(1999)
    [32] J. R. Pelaez, Phys. Rept., 658:1(2016)
    [33] E. E. Salpeter and H. A. Bethe, Phys. Rev., 84:1232(1951)
    [34] T. Regge, Nuovo Cim., 14:951(1959)
    [35] T. Regge, Nuovo Cim., 18:947(1960)
    [36] M. M. Brisudova, L. Burakovsky, J. T. Goldman, and A. Szczepaniak, Phys. Rev. D, 67:094016(2003)
    [37] A. V. Barnes, D. J. Mellema, A. V. Tollestrup, R. L. Walker, O. I. Dahl, R. A. Johnson, R. W. Kenney, and M. Pripstein, Phys. Rev. Lett., 37:76(1976)
    [38] H. Navelet and P. R. Stevens, Nucl. Phys. B, 118:475(1977)
    [39] M. Guidal, J. M. Laget, and M. Vanderhaeghen, Nucl. Phys. A, 627:645(1997)
    [40] N. I. Kochelev, M. Battaglieri, and R. De Vita, Phys. Rev. C, 80:025201(2009)
    [41] C. R. Ji, R. Kaminski, L. Lesniak, A. Szczepaniak, and R. Williams, Phys. Rev. C, 58:1205(1998)
    [42] M. Battaglieri et al (CLAS Collaboration), Phys. Rev. D, 80:072005(2009)
    [43] J. Yamagata-Sekihara, J. Nieves, and E. Oset, Phys. Rev. D, 83:014003(2011)

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Get Citation
Li-Sheng Geng, Raquel Molina and Eulogio Oset. On the chiral covariant approach to ρρ scattering[J]. Chinese Physics C, 2017, 41(12): 124101. doi: 10.1088/1674-1137/41/12/124101
Li-Sheng Geng, Raquel Molina and Eulogio Oset. On the chiral covariant approach to ρρ scattering[J]. Chinese Physics C, 2017, 41(12): 124101.  doi: 10.1088/1674-1137/41/12/124101 shu
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Received: 2017-06-05
Revised: 2017-08-31
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    Supported by National Natural Science Foundation of China (11375024, 11522539), the Spanish Ministerio de Economia y Competitividad and European FEDER funds (FIS2011-28853-C02-01, FIS2011-28853-C02-02, FIS2014-57026-REDT, FIS2014-51948-C2-1-P, FIS2014-51948-C2-2-P), the Generalitat Valenciana in the program Prometeo Ⅱ-2014/068, We acknowledge the support of the European Community-Research Infrastructure Integrating Activity Study of Strongly Interacting Matter (acronym HadronPhysics3, Grant Agreement n. 283286) under the Seventh Framework Programme of the EU

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On the chiral covariant approach to ρρ scattering

    Corresponding author: Li-Sheng Geng,
  • 1.  School of Physics and Nuclear Energy Engineering &
  • 2.  Physics Department, The George Washington University, Washington, DC 20052, USA
  • 3.  Departamento de Fí
  • Received Date: 2017-06-05
  • Accepted Date: 2017-08-31
  • Available Online: 2017-12-05
Fund Project:  Supported by National Natural Science Foundation of China (11375024, 11522539), the Spanish Ministerio de Economia y Competitividad and European FEDER funds (FIS2011-28853-C02-01, FIS2011-28853-C02-02, FIS2014-57026-REDT, FIS2014-51948-C2-1-P, FIS2014-51948-C2-2-P), the Generalitat Valenciana in the program Prometeo Ⅱ-2014/068, We acknowledge the support of the European Community-Research Infrastructure Integrating Activity Study of Strongly Interacting Matter (acronym HadronPhysics3, Grant Agreement n. 283286) under the Seventh Framework Programme of the EU

Abstract: We examine in detail a recent work (D. Gülmez, U. G. Meißner and J. A. Oller, Eur. Phys. J. C, 77:460 (2017)), where improvements to make ρρ scattering relativistically covariant are made. The paper has the remarkable conclusion that the J=2 state disappears with a potential which is much more attractive than for J=0, where a bound state is found. We trace this abnormal conclusion to the fact that an "on-shell" factorization of the potential is done in a region where this potential is singular and develops a large discontinuous and unphysical imaginary part. A method is developed, evaluating the loops with full ρ propagators, and we show that they do not develop singularities and do not have an imaginary part below threshold. With this result for the loops we define an effective potential, which when used with the Bethe-Salpeter equation provides a state with J=2 around the energy of the f2(1270). In addition, the coupling of the state to ρρ is evaluated and we find that this coupling and the T matrix around the energy of the bound state are remarkably similar to those obtained with a drastic approximation used previously, in which the q2 terms of the propagators of the exchanged ρ mesons are dropped, once the cut-off in the ρρ loop function is tuned to reproduce the bound state at the same energy.

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