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The evolution of meson masses in a strong magnetic field

  • M.A. Andreichikov
  • B.O. Kerbikov
  • E.V. Luschevskaya
  • Yu.A. Simonov
  • O.E. Solovjeva
Open Access
Regular Article - Theoretical Physics

Abstract

Spectra of \( q\overline{q} \) hadrons are investigated in the framework of the Hamiltonian obtained from the relativistic path integral in external homogeneous magnetic field. The spectra of all 12 spin-isospin s-wave states, generated by π and ρ mesons with different spin projections, are studied both analytically and numerically on the lattice as functions of (magnetic field) eB. Results are in agreement and demonstrate three types of behavior, with characteristic splittings predicted by the theory.

Keywords

QCD Phenomenology Heavy Ion Phenomenology 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    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].
  2. [2]
    V.A. Miransky and I.A. Shovkovy, Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals, Phys. Rept. 576 (2015) 1 [arXiv:1503.00732] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  3. [3]
    J.M. Lattimer and M. Prakash, Neutron Star Observations: Prognosis for Equation of State Constraints, Phys. Rept. 442 (2007) 109 [astro-ph/0612440] [INSPIRE].
  4. [4]
    A.Y. Potekhin, The physics of neutron stars, Phys. Usp. 53 (2010) 1235 [arXiv:1102.5735].ADSCrossRefGoogle Scholar
  5. [5]
    D. Lai, Physics in Very Strong Magnetic Fields: Introduction and Overview, Space Sci. Rev. 191 (2015) 13 [arXiv:1411.7995] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    A.K. Harding and D. Lai, Physics of Strongly Magnetized Neutron Stars, Rept. Prog. Phys. 69 (2006) 2631 [astro-ph/0606674] [INSPIRE].
  7. [7]
    D. Grasso and H.R. Rubinstein, Magnetic fields in the early universe, Phys. Rept. 348 (2001) 163 [astro-ph/0009061] [INSPIRE].
  8. [8]
    S.I. Godunov, B. Machet and M.I. Vysotsky, Critical nucleus charge in a superstrong magnetic field: effect of screening, Phys. Rev. D 85 (2012) 044058 [arXiv:1112.1891] [INSPIRE].ADSGoogle Scholar
  9. [9]
    M.I. Vysotsky and S.I. Godunov, Critical charge in a superstrong magnetic field, Phys. Usp. 57 (2014) 194.ADSCrossRefGoogle Scholar
  10. [10]
    A.E. Shabad and V.V. Usov, Modified Coulomb Law in a Strongly Magnetized Vacuum, Phys. Rev. Lett. 98 (2007) 180403 [arXiv:0704.2162] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    A.E. Shabad and V.V. Usov, Bethe-Salpeter approach for relativistic positronium in a strong magnetic field, Phys. Rev. D 73 (2006) 125021 [hep-th/0603070] [INSPIRE].ADSGoogle Scholar
  12. [12]
    B.M. Karnakov and V.S. Popov, A hydrogen atom in a superstrong magnetic field and the Zeldovich effect, JETP 97 (2003) 890.ADSCrossRefGoogle Scholar
  13. [13]
    V.S. Popov and B.M. Karnakov, On the spectrum of the hydrogen atom in an ultrastrong magnetic field, JETP 141 (2012) 1.ADSCrossRefGoogle Scholar
  14. [14]
    V.S. Popov and B.M. Karnakov, Hydrogen atom in a strong magnetic field, Phys. Usp. 57 (2014) 257.ADSCrossRefGoogle Scholar
  15. [15]
    M.A. Andreichikov, B.O. Kerbikov and Yu.A. Simonov, Magnetic field focusing of hyperfine interaction in hydrogen, JETP Lett. 99 (2014) 289.CrossRefGoogle Scholar
  16. [16]
    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].ADSCrossRefGoogle Scholar
  17. [17]
    V. Skokov, A. Yu. 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].ADSCrossRefGoogle Scholar
  18. [18]
    T. Tajima, Prospect for extreme field science, Eur. Phys. J. D 55 (2009) 519.ADSGoogle Scholar
  19. [19]
    K. Hattori, T. Kojo and N. Su, Mesons in strong magnetic fields: (I) General analyses, Nucl. Phys. A 951 (2016) 1 [arXiv:1512.07361] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    F.X. Lee, L. Zhou, W. Wilcox and J.C. Christensen, Magnetic polarizability of hadrons from lattice QCD in the background field method, Phys. Rev. D 73 (2006) 034503 [hep-lat/0509065] [INSPIRE].
  21. [21]
    P. Hagler, Hadron structure from lattice quantum chromodynamics, Phys. Rept. 490 (2010) 49 [arXiv:0912.5483] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    T. Primer, W. Kamleh, D. Leinweber and M. Burkardt, Magnetic properties of the neutron in a uniform background field, arXiv:1212.1963 [INSPIRE].
  23. [23]
    E.V. Luschevskaya and O.V. Larina, The ρ and A mesons in a strong abelian magnetic field in SU(2) lattice gauge theory, Nucl. Phys. B 884 (2014) 1 [arXiv:1203.5699] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  24. [24]
    E.V. Luschevskaya and O.V. Larina, Neutral ρ and A mesons in magnetic field in SU(2) lattice gauge theory, JETP Lett. 98 (2014) 652 [arXiv:1306.2936] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  25. [25]
    G.S. Bali et al., The QCD phase diagram for external magnetic fields, JHEP 02 (2012) 044 [arXiv:1111.4956] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  26. [26]
    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].ADSGoogle Scholar
  27. [27]
    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].ADSGoogle Scholar
  28. [28]
    M. D’Elia, Lattice QCD Simulations in External Background Fields, Lect. Notes Phys. 871 (2013) 181 [arXiv:1209.0374] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    P.V. Buividovich, M.N. Chernodub, E.V. Luschevskaya and M.I. 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].ADSCrossRefMATHGoogle Scholar
  30. [30]
    V.V. Braguta, P.V. Buividovich, T. Kalaydzhyan, S.V. Kuznetsov and M.I. 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].ADSCrossRefGoogle Scholar
  31. [31]
    E.M. Ilgenfritz, M. Kalinowski, M. Muller-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].ADSGoogle Scholar
  32. [32]
    Yu. A. 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 [hep-ph/0305281] [INSPIRE].
  33. [33]
    E.V. Luschevskaya, O.E. Solovjeva, O.A. Kochetkov and O.V. Teryaev, Magnetic polarizabilities of light mesons in SU(3) lattice gauge theory, Nucl. Phys. B 898 (2015) 627 [arXiv:1411.4284] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  34. [34]
    E.V. Luschevskaya, O.A. Kochetkov, O.V. Teryaev and O.E. Solovjeva, π ± and ρ 0,± mesons in a strong magnetic field on the lattice, JETP Lett. 101 (2015) 674 [INSPIRE].
  35. [35]
    E.V. Luschevskaya, O.E. Solovjeva and O.V. Teryaev, Lattice Stern-Gerlach experiment, arXiv:1608.03472 [INSPIRE].
  36. [36]
    E.V. Luschevskaya, O.E. Solovjeva and O.V. Teryaev, Magnetic polarizability of pion, Phys. Lett. B 761 (2016) 393 [arXiv:1511.09316] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    E.V. Luschevskaya and O.V. Larina, The ρ and A mesons in a strong abelian magnetic field in SU(2) lattice gauge theory, Nucl. Phys. B 884 (2014) 1 [arXiv:1203.5699] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  38. [38]
    O.V. Teryaev, Hadron spin and external fields, Int. J. Mod. Phys. Conf. Ser. 39 (2015) 1560083.CrossRefGoogle Scholar
  39. [39]
    C. Bonati, M. D’Elia and A. Rucci, Heavy quarkonia in strong magnetic fields, Phys. Rev. D 92 (2015) 054014 [arXiv:1506.07890] [INSPIRE].ADSGoogle Scholar
  40. [40]
    H. Neuberger, Exactly massless quarks on the lattice, Phys. Lett. B 417 (1998) 141 [hep-lat/9707022] [INSPIRE].
  41. [41]
    Y. Hidaka and A. Yamamoto, Charged vector mesons in a strong magnetic field, Phys. Rev. D 87 (2013) 094502 [arXiv:1209.0007] [INSPIRE].ADSGoogle Scholar
  42. [42]
    B.B. Brandt, G. Bali, G. Endrödi and B. Glässle, QCD spectroscopy and quark mass renormalisation in external magnetic fields with Wilson fermions, PoS (LATTICE2015) 265 [arXiv:1510.03899] [INSPIRE].
  43. [43]
    F.X. Lee, S. Moerschbacher and W. Wilcox, Magnetic moments of vector, axial and tensor mesons in lattice QCD, Phys. Rev. D 78 (2008) 094502 [arXiv:0807.4150] [INSPIRE].ADSGoogle Scholar
  44. [44]
    I.A. Shushpanov and A.V. Smilga, Quark condensate in a magnetic field, Phys. Lett. B 402 (1997) 351 [hep-ph/9703201] [INSPIRE].
  45. [45]
    N.O. Agasian and I.A. Shushpanov, Quark and gluon condensates in a magnetic field, JETP Lett. 70 (1999) 717 [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    N.O. Agasian and I.A. 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].
  47. [47]
    N.O. Agasian and I.A. Shushpanov, Gell-Mann-Oakes-Renner relation in a magnetic field at finite temperature, JHEP 10 (2001) 006 [hep-ph/0107128] [INSPIRE].
  48. [48]
    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].
  49. [49]
    N.O. Agasian, Chiral thermodynamics in a magnetic field, Phys. Atom. Nucl. 64 (2001) 554 [hep-ph/0112341] [INSPIRE].
  50. [50]
    J.O. Andersen, Chiral perturbation theory in a magnetic background - finite-temperature effects, JHEP 10 (2012) 005 [arXiv:1205.6978] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    J.O. Andersen, Thermal pions in a magnetic background, Phys. Rev. D 86 (2012) 025020 [arXiv:1202.2051] [INSPIRE].ADSGoogle Scholar
  52. [52]
    T.M. Aliev, A. Ozpineci and M. Savci, Magnetic and quadrupole moments of light spin-1 mesons in light cone QCD sum rules, Phys. Lett. B 678 (2009) 470 [arXiv:0902.4627] [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    T.M. Aliev, K. Azizi and M. Savci, Magnetic dipole moment of the light tensor mesons in light cone QCD sum rules, J. Phys. G 37 (2010) 075008 [arXiv:0909.2413] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    H.-M. Choi and C.-R. Ji, Electromagnetic structure of the rho meson in the light front quark model, Phys. Rev. D 70 (2004) 053015 [hep-ph/0402114] [INSPIRE].
  55. [55]
    J.P. B.C. de Melo and T. Frederico, Covariant and light front approaches to the rho meson electromagnetic form-factors, Phys. Rev. C 55 (1997) 2043 [nucl-th/9706032] [INSPIRE].
  56. [56]
    M.S. Bhagwat and P. Maris, Vector meson form factors and their quark-mass dependence, Phys. Rev. C 77 (2008) 025203 [nucl-th/0612069] [INSPIRE].
  57. [57]
    J.N. Hedditch, W. Kamleh, B.G. Lasscock, D.B. Leinweber, A.G. Williams and J.M. Zanotti, Pseudoscalar and vector meson form-factors from lattice QCD, Phys. Rev. D 75 (2007) 094504 [hep-lat/0703014] [INSPIRE].
  58. [58]
    J. Alford and M. Strickland, Charmonia and Bottomonia in a Magnetic Field, Phys. Rev. D 88 (2013) 105017 [arXiv:1309.3003] [INSPIRE].ADSGoogle Scholar
  59. [59]
    C.S. Machado, F.S. Navarra, E.G. de Oliveira, J. Noronha and M. Strickland, Heavy quarkonium production in a strong magnetic field, Phys. Rev. D 88 (2013) 034009 [arXiv:1305.3308] [INSPIRE].ADSGoogle Scholar
  60. [60]
    M. Kawaguchi and S. Matsuzaki, Vector Meson Masses from Hidden Local Symmetry in Constant Magnetic Field, arXiv:1511.06990 [INSPIRE].
  61. [61]
    S.S. Avancini, R.L.S. Farias, M. Benghi Pinto, W.R. Tavares and V.S. Timóteo, π 0 pole mass calculation in a strong magnetic field and lattice constraints, Phys. Lett. B 767 (2017) 247 [arXiv:1606.05754] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  62. [62]
    Yu. A. Simonov, B.O. Kerbikov and M.A. Andreichikov, Quark-Antiquark System in Ultra-Intense Magnetic Field, arXiv:1210.0227 [INSPIRE].
  63. [63]
    M.A. Andreichikov, B.O. Kerbikov, V.D. Orlovsky and Yu. A. Simonov, Meson Spectrum in Strong Magnetic Fields, Phys. Rev. D 87 (2013) 094029 [arXiv:1304.2533] [INSPIRE].ADSGoogle Scholar
  64. [64]
    M.A. Andreichikov, V.D. Orlovsky and Yu. A. Simonov, Asymptotic Freedom in Strong Magnetic Fields, Phys. Rev. Lett. 110 (2013) 162002 [arXiv:1211.6568] [INSPIRE].ADSCrossRefGoogle Scholar
  65. [65]
    C. Bonati, M. D’Elia, M. Mariti, M. Mesiti, F. Negro and F. Sanfilippo, Anisotropy of the quark-antiquark potential in a magnetic field, Phys. Rev. D 89 (2014) 114502 [arXiv:1403.6094] [INSPIRE].ADSGoogle Scholar
  66. [66]
    Yu. A. Simonov and M.A. Trusov, Confinement and αs in a strong magnetic field, Phys. Lett. B 747 (2015) 48 [arXiv:1503.08531] [INSPIRE].ADSCrossRefGoogle Scholar
  67. [67]
    Yu. A. Simonov, Relativistic path integral and relativistic Hamiltonians in QCD and QED, Phys. Rev. D 88 (2013) 025028 [arXiv:1303.4952] [INSPIRE].ADSGoogle Scholar
  68. [68]
    Yu. A. Simonov, Spin interactions in mesons in strong magnetic field, Phys. Rev. D 88 (2013) 053004 [arXiv:1304.0365] [INSPIRE].ADSGoogle Scholar
  69. [69]
    V.D. Orlovsky and Yu. A. Simonov, Nambu-Goldstone mesons in strong magnetic field, JHEP 09 (2013) 136 [arXiv:1306.2232] [INSPIRE].ADSCrossRefGoogle Scholar
  70. [70]
    Yu. A. Simonov, Chiral Lagrangian with confinement from the QCD Lagrangian, Phys. Rev. D 65 (2002) 094018 [hep-ph/0201170] [INSPIRE].
  71. [71]
    Yu.A. Simonov, Nonperturbative approach to the parton model, Int. J. Mod. Phys. 31 (2016) 1650016.ADSMathSciNetCrossRefMATHGoogle Scholar
  72. [72]
    Yu.A. Simonov, Results of searches for extra spatial dimensions in the CMS experiment at the LHC, Phys. Atom. Nucl. 79 (2016) 266.ADSCrossRefGoogle Scholar
  73. [73]
    Yu. A. Simonov, Asymptotic freedom and IR freezing in QCD: the role of gluon paramagnetism, Phys. Atom. Nucl. 74 (2011) 1223 [arXiv:1011.5386] [INSPIRE].ADSCrossRefGoogle Scholar
  74. [74]
    A.M. Badalian and Yu. A. Simonov, Magnetic moments of mesons, Phys. Rev. D 87 (2013) 074012 [arXiv:1211.4349] [INSPIRE].ADSGoogle Scholar
  75. [75]
    B.O. Kerbikov and Yu. A. Simonov, Baryon magnetic moments in the QCD string approach, Phys. Rev. D 62 (2000) 093016 [hep-ph/0001243] [INSPIRE].
  76. [76]
    M.A. Andreichikov, B.O. Kerbikov, V.D. Orlovsky and Yu. A. Simonov, Neutron in Strong Magnetic Fields, Phys. Rev. D 89 (2014) 074033 [arXiv:1312.2212] [INSPIRE].ADSGoogle Scholar
  77. [77]
    W.E. Lamb, Fine Structure of the Hydrogen Atom. III, Phys. Rev. 85 (1952) 259 [INSPIRE].
  78. [78]
    L.P. Gor’kov and I.E. Dzyaloshinskii, Contribution to the Theory of the Mott Exciton in a Strong Magnetic Field, Sov. Phys. JETP 26 (1968) 449.ADSGoogle Scholar
  79. [79]
    J.E. Avron, I.W. Herbst and B. Simon, Separation of center of mass in homogeneous magnetic fields, Ann. Phys. 114 (1978) 431.ADSMathSciNetCrossRefMATHGoogle Scholar
  80. [80]
    H. Grotch and R.A. Hegstrom, Hydrogenic Atoms in a Magnetic Field, Phys. Rev. A 4 (1971) 59 [INSPIRE].ADSCrossRefGoogle Scholar
  81. [81]
    Yu. A. Simonov, Neutral 3-body system in a strong magnetic field: factorization and exact solutions, Phys. Lett. B 719 (2013) 464 [arXiv:1211.5297] [INSPIRE].ADSCrossRefGoogle Scholar
  82. [82]
    Yu. A. Simonov, Spin interactions in mesons in strong magnetic field, Phys. Rev. D 88 (2013) 053004 [arXiv:1304.0365] [INSPIRE].ADSGoogle Scholar
  83. [83]
    B.O. Kerbikov, M.I. Polikarpov and L.V. Shevchenko, Multi-Quark Masses and Wave Functions Through Modified Greens Function Monte Carlo Method, Nucl. Phys. B 331 (1990) 19 [INSPIRE].ADSCrossRefGoogle Scholar
  84. [84]
    A.M. Badalian and B.L.G. Bakker, Light meson orbital excitations in the QCD string approach, Phys. Rev. D 66 (2002) 034025 [hep-ph/0202246] [INSPIRE].
  85. [85]
    A.M. Badalian and B.L.G. Bakker, Higher excitations of the D and D s mesons, Phys. Rev. D 84 (2011) 034006 [arXiv:1104.1918] [INSPIRE].ADSGoogle Scholar
  86. [86]
    A.M. Badalian, B.L.G. Bakker and Yu. A. Simonov, Light meson radial Regge trajectories, Phys. Rev. D 66 (2002) 034026 [hep-ph/0204088] [INSPIRE].
  87. [87]
    A.M. Badalian, B.L.G. Bakker and I.V. Danilkin, The Hyperfine Splittings in Bottomonium and the B(q) (q = n, s, c) Mesons, Phys. Rev. D 81 (2010) 071502 [Erratum ibid. D 81 (2010) 099902] [arXiv:0911.4634] [INSPIRE].
  88. [88]
    Yu. A. Simonov, Pion decay constants in a strong magnetic field, Phys. Atom. Nucl. 79 (2016) 455 [arXiv:1503.06616] [INSPIRE].ADSCrossRefGoogle Scholar
  89. [89]
    Yu. A. Simonov, Analysis of the QCD spectrum and chiral symmetry breaking with varying quark masses, Phys. Atom. Nucl. 76 (2013) 525 [arXiv:1205.0692] [INSPIRE].ADSCrossRefGoogle Scholar
  90. [90]
    Yu. A. Simonov, Resolution of the pion puzzle: The QCD string in Nambu-Goldstone mesons, Phys. Atom. Nucl. 67 (2004) 846 [hep-ph/0302090] [INSPIRE].

Copyright information

© The Author(s) 2017

Authors and Affiliations

  • M.A. Andreichikov
    • 1
  • B.O. Kerbikov
    • 1
    • 2
    • 3
  • E.V. Luschevskaya
    • 1
    • 2
  • Yu.A. Simonov
    • 1
  • O.E. Solovjeva
    • 1
  1. 1.Institute for Theoretical and Experimental PhysicsMoscowRussia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudniyRussia
  3. 3.Lebedev Physical InstituteRussian Academy of SciencesMoscowRussia

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