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Nambu-Goldstone mesons in strong magnetic field

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Abstract

We study the \( q\overline{q} \) structure embedded in chiral mesons in response to external magnetic fields (m.f.), using the chiral Lagrangian with \( q\overline{q} \) degrees of freedom derived earlier. We show that GMOR relations hold true for neutral chiral mesons, while they are violated for the charged ones for eB > σ = 0.2GeV2. The standard chiral perturbation theory also fails in this region. Masses of π + and π 0 mesons are calculated and compared to lattice data.

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References

  1. S. Glashow and S. Weinberg, Breaking chiral symmetry, Phys. Rev. Lett. 20 (1968) 224 [INSPIRE].

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

  3. M. Gell-Mann and M. Lévy, The axial vector current in beta decay, Nuovo Cim. 16 (1960) 705 [INSPIRE].

    Article  MATH  Google Scholar 

  4. M. Gell-Mann, R. Oakes and B. Renner, Behavior of current divergences under SU(3) × SU(3), Phys. Rev. 175 (1968) 2195 [INSPIRE].

    Article  ADS  Google Scholar 

  5. J. Gasser and H. Leutwyler, Quark masses, Phys. Rept. 87 (1982) 77 [INSPIRE].

    Article  ADS  Google Scholar 

  6. J. Gasser and H. Leutwyler, Chiral perturbation theory to one loop, Annals Phys. 158 (1984) 142 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. 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 

  8. C.W. Bernard and M.F. Golterman, Chiral perturbation theory for the quenched approximation of QCD, Phys. Rev. D 46 (1992) 853 [hep-lat/9204007] [INSPIRE].

    ADS  Google Scholar 

  9. S.R. Sharpe, Quenched chiral logarithms, Phys. Rev. D 46 (1992) 3146 [hep-lat/9205020] [INSPIRE].

    ADS  Google Scholar 

  10. Y. Simonov, Chiral Lagrangian with confinement from the QCD Lagrangian, Phys. Rev. D 65 (2002) 094018 [hep-ph/0201170] [INSPIRE].

    ADS  Google Scholar 

  11. Y. Simonov, Resolution of the pion puzzle: the QCD string in Nambu-Goldstone mesons, Phys. Atom. Nucl. 67 (2004) 846 [Yad. Fiz. 67 (2004) 868] [hep-ph/0302090] [INSPIRE].

  12. Y. Simonov, New spectral representation and evaluation of f π and the quark condensate \( \left\langle {\overline{q}q} \right\rangle \) in the terms of string tension, Phys. Atom. Nucl. 67 (2004) 1027 [Yad. Fiz. 67 (2004) 1050] [hep-ph/0305281] [INSPIRE].

  13. S. Fedorov and Y. Simonov, Pseudoscalar mesons and their radial excitations from the effective chiral Lagrangian, JETP Lett. 78 (2003) 57 [Pisma Zh. Eksp. Teor. Fiz. 78 (2003) 67] [hep-ph/0306216] [INSPIRE].

  14. A.Y. Dubin, A. Kaidalov and Y. Simonov, The QCD string with quarks. 1. Spinless quarks, Phys. Atom. Nucl. 56 (1993) 1745 [Yad. Fiz. 56 (1993) 213] [hep-ph/9311344] [INSPIRE].

  15. A.Y. Dubin, A. Kaidalov and Y. Simonov, Dynamical regimes of the QCD string with quarks, Phys. Lett. B 323 (1994) 41 [INSPIRE].

    Article  ADS  Google Scholar 

  16. Y. Kalashnikova, A. Nefediev and Y. Simonov, QCD string in light-light and heavy-light mesons, Phys. Rev. D 64 (2001) 014037 [hep-ph/0103274] [INSPIRE].

    ADS  Google Scholar 

  17. Y. Simonov, Analysis of the QCD spectrum and chiral symmetry breaking with varying quark masses, Phys. Atom. Nucl. 76 (2013) 525 [arXiv:1205.0692] [INSPIRE].

    Article  ADS  Google Scholar 

  18. D.E. Kharzeev, K. Landsteiner, A. Schmitt and H.-U. Yee, ‘Strongly interacting matter in magnetic fields’: an overview, Lect. Notes Phys. 871 (2013) 1 [arXiv:1211.6245] [INSPIRE].

    Article  ADS  Google Scholar 

  19. J.M. Lattimer and M. Prakash, Neutron star observations: prognosis for equation of state constraints, Phys. Rept. 442 (2007) 109 [astro-ph/0612440] [INSPIRE].

    Article  ADS  Google Scholar 

  20. D. Grasso and H.R. Rubinstein, Magnetic fields in the early universe, Phys. Rept. 348 (2001) 163 [astro-ph/0009061] [INSPIRE].

    Article  ADS  Google Scholar 

  21. D.E. Kharzeev, L.D. McLerran and H.J. Warringa, The effects of topological charge change in heavy ion collisions: ‘event by event P and CP-violation’, Nucl. Phys. A 803 (2008) 227 [arXiv:0711.0950] [INSPIRE].

    Article  ADS  Google Scholar 

  22. V. Skokov, A.Y. Illarionov and V. Toneev, Estimate of the magnetic field strength in heavy-ion collisions, Int. J. Mod. Phys. A 24 (2009) 5925 [arXiv:0907.1396] [INSPIRE].

    Article  ADS  Google Scholar 

  23. B.M. Karnakov and V.S. Popov, A hydrogen atom in a superstrong magnetic field and the Zeldovich effect, JETP 97 (2003) 890 [Zh. Eksp. Teor. Fiz. 124 (2003) 996].

    Google Scholar 

  24. B.M. Karnakov and V.S. Popov, On the spectrum of the hydrogen atom in an ultrastrong magnetic field, JETP 114 (2012) 1 [Zh. Eksp. Teor. Fiz. 141 (2012) 5].

    Google Scholar 

  25. Y. Simonov, B. Kerbikov and M. Andreichikov, Quark-antiquark system in ultra-intense magnetic field, arXiv:1210.0227 [INSPIRE].

  26. M. Andreichikov, V. Orlovsky and Y. Simonov, Asymptotic freedom in strong magnetic field, Phys. Rev. Lett. 110 (2013) 162002 [arXiv:1211.6568] [INSPIRE].

    Article  ADS  Google Scholar 

  27. M. Andreichikov, B. Kerbikov, V. Orlovsky and Y.A. Simonov, Meson spectrum in strong magnetic fields, Phys. Rev. D 87 (2013) 094029 [arXiv:1304.2533] [INSPIRE].

    ADS  Google Scholar 

  28. A. Badalian and Y. Simonov, Magnetic moments of mesons, Phys. Rev. D 87 (2013) 074012 [arXiv:1211.4349] [INSPIRE].

    ADS  Google Scholar 

  29. Y. Simonov, Magnetic test of chiral dynamics in QCD, arXiv:1212.3118 [INSPIRE].

  30. M. D’Elia, S. Mukherjee and F. Sanfilippo, QCD phase transition in a strong magnetic background, Phys. Rev. D 82 (2010) 051501 [arXiv:1005.5365] [INSPIRE].

    ADS  Google Scholar 

  31. M. D’Elia and F. Negro, Chiral properties of strong interactions in a magnetic background, Phys. Rev. D 83 (2011) 114028 [arXiv:1103.2080] [INSPIRE].

    ADS  Google Scholar 

  32. M. D’Elia, Lattice QCD simulations in external background fields, Lect. Notes Phys. 871 (2013) 181 [arXiv:1209.0374] [INSPIRE].

    Article  ADS  Google Scholar 

  33. P. Buividovich, M. Chernodub, E. Luschevskaya and M. Polikarpov, Numerical study of chiral symmetry breaking in non-Abelian gauge theory with background magnetic field, Phys. Lett. B 682 (2010) 484 [arXiv:0812.1740] [INSPIRE].

    Article  ADS  Google Scholar 

  34. V. Braguta, P. Buividovich, T. Kalaydzhyan, S. Kuznetsov and M. Polikarpov, The chiral magnetic effect and chiral symmetry breaking in SU(3) quenched lattice gauge theory, Phys. Atom. Nucl. 75 (2012) 488 [arXiv:1011.3795] [INSPIRE].

    Article  ADS  Google Scholar 

  35. E.-M. Ilgenfritz, M. Kalinowski, M. Müller-Preussker, B. Petersson and A. Schreiber, Two-color QCD with staggered fermions at finite temperature under the influence of a magnetic field, Phys. Rev. D 85 (2012) 114504 [arXiv:1203.3360] [INSPIRE].

    ADS  Google Scholar 

  36. G. Bali et al., QCD quark condensate in external magnetic fields, Phys. Rev. D 86 (2012) 071502 [arXiv:1206.4205] [INSPIRE].

    ADS  Google Scholar 

  37. Y.A. Simonov, Relativistic path integral and relativistic Hamiltonians in QCD and QED, Phys. Rev. D 88 (2013) 025028 [arXiv:1303.4952] [INSPIRE].

    ADS  Google Scholar 

  38. Y. Hidaka and A. Yamamoto, Charged vector mesons in a strong magnetic field, Phys. Rev. D 87 (2013) 094502 [arXiv:1209.0007] [INSPIRE].

    ADS  Google Scholar 

  39. Y.A. Simonov, Spin interactions in mesons in strong magnetic field, Phys. Rev. D 88 (2013) 053004 [arXiv:1304.0365] [INSPIRE].

    ADS  Google Scholar 

  40. G. Bali et al., The QCD phase diagram for external magnetic fields, JHEP 02 (2012) 044 [arXiv:1111.4956] [INSPIRE].

    Article  ADS  Google Scholar 

  41. I. Shushpanov and A.V. Smilga, Quark condensate in a magnetic field, Phys. Lett. B 402 (1997) 351 [hep-ph/9703201] [INSPIRE].

    Article  ADS  Google Scholar 

  42. N.O. Agasian and I. Shushpanov, Quark and gluon condensates in a magnetic field, JETP Lett. 70 (1999) 717 [Pisma Zh. Eksp. Teor. Fiz. 70 (1999) 711] [INSPIRE].

  43. N.O. Agasian and I. Shushpanov, The quark and gluon condensates and low-energy QCD theorems in a magnetic field, Phys. Lett. B 472 (2000) 143 [hep-ph/9911254] [INSPIRE].

    Article  ADS  Google Scholar 

  44. N.O. Agasian and I. Shushpanov, Gell-Mann-Oakes-Renner relation in a magnetic field at finite temperature, JHEP 10 (2001) 006 [hep-ph/0107128] [INSPIRE].

    Article  ADS  Google Scholar 

  45. N.O. Agasian, Phase structure of the QCD vacuum in a magnetic field at low temperature, Phys. Lett. B 488 (2000) 39 [hep-ph/0005300] [INSPIRE].

    Article  ADS  Google Scholar 

  46. N.O. Agasian, Chiral thermodynamics in a magnetic field, Phys. Atom. Nucl. 64 (2001) 554 [Yad. Fiz. 64 (2001) 608] [hep-ph/0112341] [INSPIRE].

  47. J.O. Andersen, Chiral perturbation theory in a magnetic background — finite-temperature effects, JHEP 10 (2012) 005 [arXiv:1205.6978] [INSPIRE].

    Article  ADS  Google Scholar 

  48. J.O. Andersen, Thermal pions in a magnetic background, Phys. Rev. D 86 (2012) 025020 [arXiv:1202.2051] [INSPIRE].

    ADS  Google Scholar 

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Authors and Affiliations

  1. Institute of Theoretical and Experimental Physics, B. Cheremushkinskaya 25, 117218, Moscow, Russia

    V.D. Orlovsky & Yu.A. Simonov

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  1. V.D. Orlovsky
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  2. Yu.A. Simonov
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Correspondence to V.D. Orlovsky.

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ArXiv ePrint: 1306.2232

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Orlovsky, V., Simonov, Y. Nambu-Goldstone mesons in strong magnetic field. J. High Energ. Phys. 2013, 136 (2013). https://doi.org/10.1007/JHEP09(2013)136

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  • DOI: https://doi.org/10.1007/JHEP09(2013)136

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