Local CP-violation and electric charge separation by magnetic fields from lattice QCD

  • G. S. Bali
  • F. Bruckmann
  • G. Endrődi
  • Z. Fodor
  • S. D. Katz
  • A. Schäfer
Open Access
Article

Abstract

We study local CP-violation on the lattice by measuring the local correlation between the topological charge density and the electric dipole moment of quarks, induced by a constant external magnetic field. This correlator is found to increase linearly with the external field, with the coefficient of proportionality depending only weakly on temperature. Results are obtained on lattices with various spacings, and are extrapolated to the continuum limit after the renormalization of the observables is carried out. This renormalization utilizes the gradient flow for the quark and gluon fields. Our findings suggest that the strength of local CP-violation in QCD with physical quark masses is about an order of magnitude smaller than a model prediction based on nearly massless quarks in domains of constant gluon backgrounds with topological charge. We also show numerical evidence that the observed local CP-violation correlates with spatially extended electric dipole structures in the QCD vacuum.

Keywords

Quark-Gluon Plasma Lattice QCD Lattice Gauge Field Theories Lattice Quantum Field Theory 

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]
    Y. Aoki, G. Endrődi, Z. Fodor, S. Katz and K. Szabó, The order of the quantum chromodynamics transition predicted by the standard model of particle physics, Nature 443 (2006) 675 [hep-lat/0611014] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    Y. Aoki, Z. Fodor, S. Katz and K. Szabó, The QCD transition temperature: Results with physical masses in the continuum limit, Phys. Lett. B 643 (2006) 46 [hep-lat/0609068] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    Wuppertal-Budapest collaboration, S. Borsányi et al., Is there still any T c mystery in lattice QCD? Results with physical masses in the continuum limit III, JHEP 09 (2010) 073 [arXiv:1005.3508] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    PHENIX collaboration, A. Adare et al., Detailed measurement of the e + e pair continuum in p + p and Au+Au collisions at \( \sqrt{{{s_{NN }}}} \) = 200 GeV and implications for direct photon production, Phys. Rev. C 81 (2010) 034911 [arXiv:0912.0244] [INSPIRE].ADSGoogle Scholar
  5. [5]
    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].ADSCrossRefGoogle Scholar
  6. [6]
    T. Vachaspati, Magnetic fields from cosmological phase transitions, Phys. Lett. B 265 (1991) 258 [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    R.C. Duncan and C. Thompson, Formation of very strongly magnetized neutron starsImplications for gamma-ray bursts, Astrophys. J. 392 (1992) L9 [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    D. Kharzeev, R. Pisarski and M.H. Tytgat, Possibility of spontaneous parity violation in hot QCD, Phys. Rev. Lett. 81 (1998) 512 [hep-ph/9804221] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    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
  10. [10]
    K. Fukushima, D.E. Kharzeev and H.J. Warringa, The chiral magnetic effect, Phys. Rev. D 78 (2008) 074033 [arXiv:0808.3382] [INSPIRE].ADSGoogle Scholar
  11. [11]
    D. Kharzeev, Parity violation in hot QCD: why it can happen and how to look for it, Phys. Lett. B 633 (2006) 260 [hep-ph/0406125] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    S.A. Voloshin, Parity violation in hot QCD: how to detect it, Phys. Rev. C 70 (2004) 057901 [hep-ph/0406311] [INSPIRE].ADSGoogle Scholar
  13. [13]
    STAR collaboration, S.A. Voloshin, Probe for the strong parity violation effects at RHIC with three particle correlations, Indian J. Phys. 85 (2011) 1103 [arXiv:0806.0029] [INSPIRE].CrossRefGoogle Scholar
  14. [14]
    STAR collaboration, B. Abelev et al., Azimuthal charged-particle correlations and possible local strong parity violation, Phys. Rev. Lett. 103 (2009) 251601 [arXiv:0909.1739] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    ALICE collaboration, I. Selyuzhenkov, Anisotropic flow and other collective phenomena measured in Pb-Pb collisions with ALICE at the LHC, Prog. Theor. Phys. Suppl. 193 (2012) 153 [arXiv:1111.1875] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    F. Wang, Effects of cluster particle correlations on local parity violation observables, Phys. Rev. C 81 (2010) 064902 [arXiv:0911.1482] [INSPIRE].ADSGoogle Scholar
  17. [17]
    B. Müller and A. Schäfer, Charge fluctuations from the chiral magnetic effect in nuclear collisions, Phys. Rev. C 82 (2010) 057902 [arXiv:1009.1053] [INSPIRE].Google Scholar
  18. [18]
    V. Voronyuk et al., (Electro-)magnetic field evolution in relativistic heavy-ion collisions, Phys. Rev. C 83 (2011) 054911 [arXiv:1103.4239] [INSPIRE].ADSGoogle Scholar
  19. [19]
    A. Bzdak, V. Koch and J. Liao, Charge-dependent correlations in relativistic heavy ion collisions and the chiral magnetic effect, Lect. Notes Phys. 871 (2013) 503 [arXiv:1207.7327] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    K. Fukushima, Views of the chiral magnetic effect, Lect. Notes Phys. 871 (2013) 241 [arXiv:1209.5064] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    D.E. Kharzeev, The chiral magnetic effect and anomaly-induced transport, Prog. Part. Nucl. Phys. 75 (2014) 133 [arXiv:1312.3348] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    K. Fukushima, M. Ruggieri and R. Gatto, Chiral magnetic effect in the PNJL model, Phys. Rev. D 81 (2010) 114031 [arXiv:1003.0047] [INSPIRE].ADSGoogle Scholar
  23. [23]
    H.-U. Yee, Holographic chiral magnetic conductivity, JHEP 11 (2009) 085 [arXiv:0908.4189] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    A. Rebhan, A. Schmitt and S.A. Stricker, Anomalies and the chiral magnetic effect in the Sakai-Sugimoto model, JHEP 01 (2010) 026 [arXiv:0909.4782] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    V.I. Zakharov, Chiral magnetic effect in hydrodynamic approximation, Lect. Notes Phys. 871 (2013) 295 [arXiv:1210.2186] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    T. Kalaydzhyan, Chiral superfluidity of the quark-gluon plasma, Nucl. Phys. A 913 (2013) 243 [arXiv:1208.0012] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    Z. Khaidukov, V. Kirilin, A. Sadofyev and V. Zakharov, On magnetostatics of chiral media, arXiv:1307.0138 [INSPIRE].
  28. [28]
    P. Buividovich, M. Chernodub, E. Luschevskaya and M. Polikarpov, Numerical evidence of chiral magnetic effect in lattice gauge theory, Phys. Rev. D 80 (2009) 054503 [arXiv:0907.0494] [INSPIRE].ADSGoogle Scholar
  29. [29]
    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].ADSCrossRefGoogle Scholar
  30. [30]
    A. Yamamoto, Chiral magnetic effect in lattice QCD with a chiral chemical potential, Phys. Rev. Lett. 107 (2011) 031601 [arXiv:1105.0385] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    P. Buividovich, Anomalous transport with overlap fermions, Nucl. Phys. A 925 (2014) 218 [arXiv:1312.1843] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    M. Abramczyk, T. Blum, G. Petropoulos and R. Zhou, Chiral magnetic effect in 2 + 1 flavor QCD + QED, PoS(LAT2009)181 [arXiv:0911.1348] [INSPIRE].
  33. [33]
    P. Buividovich, M. Chernodub, E. Luschevskaya and M. Polikarpov, Quark electric dipole moment induced by magnetic field, Phys. Rev. D 81 (2010) 036007 [arXiv:0909.2350] [INSPIRE].ADSGoogle Scholar
  34. [34]
    M. Lüscher, Properties and uses of the Wilson flow in lattice QCD, JHEP 08 (2010) 071 [arXiv:1006.4518] [INSPIRE].CrossRefGoogle Scholar
  35. [35]
    G. Basar, G.V. Dunne and D.E. Kharzeev, Electric dipole moment induced by a QCD instanton in an external magnetic field, Phys. Rev. D 85 (2012) 045026 [arXiv:1112.0532] [INSPIRE].ADSGoogle Scholar
  36. [36]
    B. Ioffe and A.V. Smilga, Nucleon magnetic moments and magnetic properties of vacuum in QCD, Nucl. Phys. B 232 (1984) 109 [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    E. Witten, Dyons of charge eθ/2π, Phys. Lett. B 86 (1979) 283 [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    S. Borsányi et al., The QCD equation of state with dynamical quarks, JHEP 11 (2010) 077 [arXiv:1007.2580] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    S. Borsányi et al., Full result for the QCD equation of state with 2 + 1 flavors, Phys. Lett. B 730 (2014) 99 [arXiv:1309.5258] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    Y. Aoki, Z. Fodor, S. Katz and K. Szabó, The equation of state in lattice QCD: with physical quark masses towards the continuum limit, JHEP 01 (2006) 089 [hep-lat/0510084] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    G. Bali et al., The QCD phase diagram for external magnetic fields, JHEP 02 (2012) 044 [arXiv:1111.4956] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    T.A. DeGrand, A. Hasenfratz and T.G. Kovacs, Topological structure in the SU(2) vacuum, Nucl. Phys. B 505 (1997) 417 [hep-lat/9705009] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    G. Bali et al., Magnetic susceptibility of QCD at zero and at finite temperature from the lattice, Phys. Rev. D 86 (2012) 094512 [arXiv:1209.6015] [INSPIRE].ADSGoogle Scholar
  44. [44]
    F. Bruckmann, F. Gruber, N. Cundy, A. Schäfer and T. Lippert, Topology of dynamical lattice configurations including results from dynamical overlap fermions, Phys. Lett. B 707 (2012) 278 [arXiv:1107.0897] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    M. Lüscher, Chiral symmetry and the Yang-Mills gradient flow, JHEP 04 (2013) 123 [arXiv:1302.5246] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    G. Bali et al., QCD quark condensate in external magnetic fields, Phys. Rev. D 86 (2012) 071502 [arXiv:1206.4205] [INSPIRE].ADSGoogle Scholar
  47. [47]
    F. Bruckmann, G. Endrődi and T.G. Kovács, Inverse magnetic catalysis and the Polyakov loop, JHEP 04 (2013) 112 [arXiv:1303.3972] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    G. Bali, F. Bruckmann, G. Endrődi, F. Gruber and A. Schäfer, Magnetic field-induced gluonic (inverse) catalysis and pressure (an)isotropy in QCD, JHEP 04 (2013) 130 [arXiv:1303.1328] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    G. Bali, K. Schilling, J. Fingberg, U.M. Heller and F. Karsch, Computation of the spatial string tension in high temperature SU(2) gauge theory, Int. J. Mod. Phys. C 4 (1993) 1179 [hep-lat/9308003] [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    S. Dürr et al., Ab-initio determination of light hadron masses, Science 322 (2008) 1224 [arXiv:0906.3599] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    T. Schäfer and E.V. Shuryak, Instantons in QCD, Rev. Mod. Phys. 70 (1998) 323 [hep-ph/9610451] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    MILC collaboration, A. Bazavov et al., Topological susceptibility with the asqtad action, Phys. Rev. D 81 (2010) 114501 [arXiv:1003.5695] [INSPIRE].ADSGoogle Scholar
  53. [53]
    S. Borsányi et al., High-precision scale setting in lattice QCD, JHEP 09 (2012) 010 [arXiv:1203.4469] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    G. ’t Hooft, Some twisted selfdual solutions for the Yang-Mills equations on a hypertorus, Commun. Math. Phys. 81 (1981) 267.ADSCrossRefMATHMathSciNetGoogle Scholar
  55. [55]
    J.S. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev. 82 (1951) 664 [INSPIRE].ADSCrossRefMATHMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  • G. S. Bali
    • 1
    • 2
  • F. Bruckmann
    • 1
  • G. Endrődi
    • 1
  • Z. Fodor
    • 3
    • 4
    • 5
  • S. D. Katz
    • 4
    • 6
  • A. Schäfer
    • 1
  1. 1.Institute for Theoretical PhysicsUniversität RegensburgRegensburgGermany
  2. 2.Tata Institute of Fundamental ResearchMumbaiIndia
  3. 3.Bergische Universität Wuppertal, Theoretical PhysicsWuppertalGermany
  4. 4.Eötvös University, Theoretical PhysicsBudapestHungary
  5. 5.Jülich Supercomputing Centre, Forschungszentrum JülichJülichGermany
  6. 6.MTA-ELTE Lendület Lattice Gauge Theory Research GroupBudapestHungary

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