Abstract
QCD topological susceptibility at high temperature, χ t (T ), provides an important input for the estimate of the axion abundance in the present Universe. While the model independent determination of χ t (T ) should be possible from the first principles using lattice QCD, existing methods fail at high temperature, since not only the probability that non-trivial topological sectors appear in the configuration generation process but also the local topological fluctuations get strongly suppressed. We propose a novel method to calculate the temperature dependence of topological susceptibility at high temperature. A feasibility test is performed on a small lattice in the quenched approximation, and the results are compared with the prediction of the dilute instanton gas approximation. It is found that the method works well especially at very high temperature and the result is consistent with the instanton calculus down to T ∼ 2 T c within the statistical uncertainty.
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References
R.D. Peccei and H.R. Quinn, CP Conservation in the Presence of Instantons, Phys. Rev. Lett. 38 (1977) 1440 [INSPIRE].
R.D. Peccei and H.R. Quinn, Constraints Imposed by CP Conservation in the Presence of Instantons, Phys. Rev. D 16 (1977) 1791 [INSPIRE].
S. Weinberg, A New Light Boson?, Phys. Rev. Lett. 40 (1978) 223 [INSPIRE].
F. Wilczek, Axions and Family Symmetry Breaking, Phys. Rev. Lett. 49 (1982) 1549 [INSPIRE].
J.E. Kim, Weak Interaction Singlet and Strong CP Invariance, Phys. Rev. Lett. 43 (1979) 103 [INSPIRE].
M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Can Confinement Ensure Natural CP Invariance of Strong Interactions?, Nucl. Phys. B 166 (1980) 493 [INSPIRE].
M. Dine, W. Fischler and M. Srednicki, A Simple Solution to the Strong CP Problem with a Harmless Axion, Phys. Lett. B 104 (1981) 199 [INSPIRE].
A.R. Zhitnitsky, On Possible Suppression of the Axion Hadron Interactions (in Russian), Sov. J. Nucl. Phys. 31 (1980) 260 [INSPIRE].
J. Preskill, M.B. Wise and F. Wilczek, Cosmology of the Invisible Axion, Phys. Lett. B 120 (1983) 127 [INSPIRE].
L.F. Abbott and P. Sikivie, A Cosmological Bound on the Invisible Axion, Phys. Lett. B 120 (1983) 133 [INSPIRE].
M. Dine and W. Fischler, The Not So Harmless Axion, Phys. Lett. B 120 (1983) 137 [INSPIRE].
G. ’t Hooft, Computation of the Quantum Effects Due to a Four-Dimensional Pseudoparticle, Phys. Rev. D 14 (1976) 3432 [Erratum ibid. D 18 (1978) 2199] [INSPIRE].
R.D. Pisarski and L.G. Yaffe, The density of instantons at finite temperature, Phys. Lett. B 97 (1980) 110 [INSPIRE].
D.J. Gross, R.D. Pisarski and L.G. Yaffe, QCD and Instantons at Finite Temperature, Rev. Mod. Phys. 53 (1981) 43 [INSPIRE].
O. Wantz and E.P.S. Shellard, Axion Cosmology Revisited, Phys. Rev. D 82 (2010) 123508 [arXiv:0910.1066] [INSPIRE].
S. Aoki, H. Fukaya and Y. Taniguchi, Chiral symmetry restoration, eigenvalue density of Dirac operator and axial U(1) anomaly at finite temperature, Phys. Rev. D 86 (2012) 114512 [arXiv:1209.2061] [INSPIRE].
T. Kanazawa and N. Yamamoto, U(1) axial symmetry and Dirac spectra in QCD at high temperature, JHEP 01 (2016) 141 [arXiv:1508.02416] [INSPIRE].
R. Kitano and N. Yamada, Topology in QCD and the axion abundance, JHEP 10 (2015) 136 [arXiv:1506.00370] [INSPIRE].
E. Berkowitz, M.I. Buchoff and E. Rinaldi, Lattice QCD input for axion cosmology, Phys. Rev. D 92 (2015) 034507 [arXiv:1505.07455] [INSPIRE].
S. Borsányi et al., Axion cosmology, lattice QCD and the dilute instanton gas, Phys. Lett. B 752 (2016) 175 [arXiv:1508.06917] [INSPIRE].
C. Bonati et al., Axion phenomenology and θ-dependence from N f = 2 + 1 lattice QCD, JHEP 03 (2016) 155 [arXiv:1512.06746] [INSPIRE].
P. Petreczky, H.-P. Schadler and S. Sharma, The topological susceptibility in finite temperature QCD and axion cosmology, arXiv:1606.03145 [INSPIRE].
A. Laio, G. Martinelli and F. Sanfilippo, Metadynamics surfing on topology barriers: the CP N−1 case, JHEP 07 (2016) 089 [arXiv:1508.07270] [INSPIRE].
A.A. Belavin, A.M. Polyakov, A.S. Schwartz and Yu.S. Tyupkin, Pseudoparticle Solutions of the Yang-Mills Equations, Phys. Lett. B 59 (1975) 85 [INSPIRE].
C.W. Bernard, Gauge Zero Modes, Instanton Determinants and QCD Calculations, Phys. Rev. D 19 (1979) 3013 [INSPIRE].
M. Lüscher, Dimensional Regularization in the Presence of Large Background Fields, Annals Phys. 142 (1982) 359 [INSPIRE].
R.D. Carlitz and D.B. Creamer, Light Quarks and Instantons, Annals Phys. 118 (1979) 429 [INSPIRE].
V.A. Novikov, M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Calculations in External Fields in Quantum Chromodynamics. Technical Review, Fortsch. Phys. 32 (1984) 585 [INSPIRE].
O.-K. Kwon, C.-k. Lee and H. Min, Massive field contributions to the QCD vacuum tunneling amplitude, Phys. Rev. D 62 (2000) 114022 [hep-ph/0008028] [INSPIRE].
G.V. Dunne, J. Hur, C. Lee and H. Min, Calculation of QCD instanton determinant with arbitrary mass, Phys. Rev. D 71 (2005) 085019 [hep-th/0502087] [INSPIRE].
B.J. Harrington and H.K. Shepard, Periodic Euclidean Solutions and the Finite Temperature Yang-Mills Gas, Phys. Rev. D 17 (1978) 2122 [INSPIRE].
JLQCD collaboration, H. Fukaya et al., Lattice gauge action suppressing near-zero modes of H(W), Phys. Rev. D 74 (2006) 094505 [hep-lat/0607020] [INSPIRE].
G. Cossu et al., Finite temperature study of the axial U(1) symmetry on the lattice with overlap fermion formulation, Phys. Rev. D 87 (2013) 114514 [arXiv:1304.6145] [INSPIRE].
CP-PACS collaboration, M. Okamoto et al., Equation of state for pure SU(3) gauge theory with renormalization group improved action, Phys. Rev. D 60 (1999) 094510 [hep-lat/9905005] [INSPIRE].
H. Neuberger, More about exactly massless quarks on the lattice, Phys. Lett. B 427 (1998) 353 [hep-lat/9801031] [INSPIRE].
R. Brower, S. Chandrasekharan, J.W. Negele and U.J. Wiese, QCD at fixed topology, Phys. Lett. B 560 (2003) 64 [hep-lat/0302005] [INSPIRE].
S. Aoki, H. Fukaya, S. Hashimoto and T. Onogi, Finite volume QCD at fixed topological charge, Phys. Rev. D 76 (2007) 054508 [arXiv:0707.0396] [INSPIRE].
A. Dromard and M. Wagner, Extracting hadron masses from fixed topology simulations, Phys. Rev. D 90 (2014) 074505 [arXiv:1404.0247] [INSPIRE].
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Frison, J., Kitano, R., Matsufuru, H. et al. Topological susceptibility at high temperature on the lattice. J. High Energ. Phys. 2016, 21 (2016). https://doi.org/10.1007/JHEP09(2016)021
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DOI: https://doi.org/10.1007/JHEP09(2016)021