Abstract
Finite temperature charmonium spectral functions in the pseudoscalar and vector channels are studied in lattice QCD with 2+1 flavours of dynamical Wilson quarks, on fine isotropic lattices (with a lattice spacing of 0.057fm), with a non-physical pion mass of m π ≈ 545 MeV. The highest temperature studied is approximately 1.4T c . Up to this temperature no significant variation of the spectral function is seen in the pseudoscalar channel. The vector channel shows some temperature dependence, which seems to be consistent with a temperature dependent low frequency peak related to heavy quark transport, plus a temperature independent term at ω > 0. These results are in accord with previous calculations using the quenched approximation.
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References
D.J. Schwarz, The first second of the universe, Annalen Phys. 12 (2003) 220 [astro-ph/0303574] [INSPIRE].
Y. Aoki, G. Endrodi, Z. Fodor, S.D. Katz and K.K. Szabo, The order of the quantum chromodynamics transition predicted by the standard model of particle physics, Nature 443 (2006) 675 [hep-lat/0611014] [INSPIRE].
Y. Aoki, Z. Fodor, S.D. Katz and K.K. Szabo, The equation of state in lattice QCD: With physical quark masses towards the continuum limit, JHEP 01 (2006) 089 [hep-lat/0510084] [INSPIRE].
Y. Aoki et al., The QCD transition temperature: results with physical masses in the continuum limit II., JHEP 06 (2009) 088 [arXiv:0903.4155] [INSPIRE].
S. Borsányi et al., The QCD equation of state with dynamical quarks, JHEP 11 (2010) 077 [arXiv:1007.2580] [INSPIRE].
A. Bazavov et al., The chiral and deconfinement aspects of the QCD transition, Phys. Rev. D 85 (2012) 054503 [arXiv:1111.1710] [INSPIRE].
S. Borsányi, Z. Fodor, S.D. Katz, S. Krieg, C. Ratti and K. Szabó, Fluctuations of conserved charges at finite temperature from lattice QCD, JHEP 01 (2012) 138 [arXiv:1112.4416] [INSPIRE].
HotQCD collaboration, A. Bazavov et al., Fluctuations and Correlations of net baryon number, electric charge and strangeness: A comparison of lattice QCD results with the hadron resonance gas model, Phys. Rev. D 86 (2012) 034509 [arXiv:1203.0784] [INSPIRE].
T. Umeda et al., Fixed Scale Approach to Equation of State in Lattice QCD, Phys. Rev. D 79 (2009) 051501 [arXiv:0809.2842] [INSPIRE].
WHOT-QCD collaboration, S. Ejiri et al., Equation of State and Heavy-Quark Free Energy at Finite Temperature and Density in Two Flavor Lattice QCD with Wilson Quark Action, Phys. Rev. D 82 (2010) 014508 [arXiv:0909.2121] [INSPIRE].
WHOT-QCD collaboration, Y. Maezawa et al., Free energies of heavy quarks in full-QCD lattice simulations with Wilson-type quark action, Nucl. Phys. A 830 (2009) 247C-250C [arXiv:0907.4203] [INSPIRE].
V.G. Bornyakov et al., Probing the finite temperature phase transition with N(f) = 2 nonperturbatively improved Wilson fermions, Phys. Rev. D 82 (2010) 014504 [arXiv:0910.2392] [INSPIRE].
WHOT-QCD collaboration, T. Umeda et al., EOS in 2 + 1 flavor QCD with improved Wilson quarks by the fixed-scale approach, PoS(Lattice 2010)218 [arXiv:1011.2548] [INSPIRE].
Y. Maezawa et al., Application of fixed scale approach to static quark free energies in quenched and 2 + 1 flavor lattice QCD with improved Wilson quark action, Prog. Theor. Phys. 128 (2012) 955 [arXiv:1112.2756] [INSPIRE].
WHOT-QCD collaboration, T. Umeda et al., Equation of state in 2+1 flavor QCD with improved Wilson quarks by the fixed scale approach, Phys. Rev. D 85 (2012) 094508 [arXiv:1202.4719] [INSPIRE].
S. Borsányi et al., QCD thermodynamics with continuum extrapolated Wilson fermions I, JHEP 08 (2012) 126 [arXiv:1205.0440] [INSPIRE].
S. Dürr et al., Ab-Initio Determination of Light Hadron Masses, Science 322 (2008) 1224 [arXiv:0906.3599] [INSPIRE].
T. Matsui and H. Satz, J/ψ Suppression by quark-gluon Plasma Formation, Phys. Lett. B 178 (1986) 416 [INSPIRE].
M. Le Bellac, Thermal Field Theory, Cambridge University Press, (1996).
M. Asakawa, T. Hatsuda and Y. Nakahara, Maximum entropy analysis of the spectral functions in lattice QCD, Prog. Part. Nucl. Phys. 46 (2001) 459 [hep-lat/0011040] [INSPIRE].
G. Aarts and J.M. Martinez Resco, Transport coefficients, spectral functions and the lattice, JHEP 04 (2002) 053 [hep-ph/0203177] [INSPIRE].
R.K. Bryan, Maximum-entropy analysis of oversampled data problems, Eur. Biophys J. 18 (1990) 165.
A. Jakovác, P. Petreczky, K. Petrov and A. Velytsky, Quarkonium correlators and spectral functions at zero and finite temperature, Phys. Rev. D 75 (2007) 014506 [hep-lat/0611017] [INSPIRE].
T. Umeda, A Constant contribution in meson correlators at finite temperature, Phys. Rev. D 75 (2007) 094502 [hep-lat/0701005] [INSPIRE].
A. Rothkopf, Improved Maximum Entropy Analysis with an Extended Search Space, J. Comput. Phys. 238 (2013) 106 [arXiv:1110.6285] [INSPIRE].
G. Aarts, C. Allton, J. Foley, S. Hands and S. Kim, Spectral functions at small energies and the electrical conductivity in hot, quenched lattice QCD, Phys. Rev. Lett. 99 (2007) 022002 [hep-lat/0703008] [INSPIRE].
J. Engels and O. Vogt, Longitudinal and transverse spectral functions in the three-dimensional O(4) model, Nucl. Phys. B 832 (2010) 538 [arXiv:0911.1939] [INSPIRE].
T. Umeda, K. Nomura and H. Matsufuru, Charmonium at finite temperature in quenched lattice QCD, Eur. Phys. J. C 39S1 (2005) 9 [hep-lat/0211003] [INSPIRE].
M. Asakawa and T. Hatsuda, J/ψ and η(c) in the deconfined plasma from lattice QCD, Phys. Rev. Lett. 92 (2004) 012001 [hep-lat/0308034] [INSPIRE].
G. Aarts, C. Allton, M.B. Oktay, M. Peardon and J.-I. Skullerud, Charmonium at high temperature in two-flavor QCD, Phys. Rev. D 76 (2007) 094513 [arXiv:0705.2198] [INSPIRE].
A. Kelly, J.-I. Skullerud, C. Allton, D. Mehta and M.B. Oktay, Spectral functions of charmonium from 2 flavour anisotropic lattice data, arXiv:1312.0791 [INSPIRE].
H. Iida, T. Doi, N. Ishii, H. Suganuma and K. Tsumura, Charmonium properties in deconfinement phase in anisotropic lattice QCD, Phys. Rev. D 74 (2006) 074502 [hep-lat/0602008] [INSPIRE].
WHOT-QCD collaboration, H. Ohno et al., Charmonium spectral functions with the variational method in zero and finite temperature lattice QCD, Phys. Rev. D 84 (2011) 094504 [arXiv:1104.3384] [INSPIRE].
H.T. Ding, A. Francis, O. Kaczmarek, F. Karsch, H. Satz and W. Soeldner, Charmonium properties in hot quenched lattice QCD, Phys. Rev. D 86 (2012) 014509 [arXiv:1204.4945] [INSPIRE].
G. Aarts et al., Charmonium spectral functions in two-flavour QCD, Nucl. Phys. A 785 (2007) 198 [hep-lat/0608009] [INSPIRE].
A. Amato, G. Aarts, C. Allton, P. Giudice, S. Hands J.-I. Skullerud, Electrical conductivity of the quark-gluon plasma across the deconfinement transition, Phys. Rev. Lett. 111 (2013) 172001 [arXiv:1307.6763] [INSPIRE].
G. Aarts, C. Allton, S. Kim, M.P. Lombardo, S.M. Ryan J.-I. Skullerud, Melting of P wave bottomonium states in the quark-gluon plasma from lattice NRQCD, JHEP 12 (2013) 064 [arXiv:1310.5467] [INSPIRE].
K. Symanzik, Continuum Limit and Improved Action in Lattice Theories. 1. Principles and Φ4 Theory, Nucl. Phys. B 226 (1983) 187 [INSPIRE].
M. Lüscher and P. Weisz, On-Shell Improved Lattice Gauge Theories, Commun. Math. Phys. 97 (1985) 59 [Erratum ibid. 98 (1985) 433] [INSPIRE].
B. Sheikholeslami and R. Wohlert, Improved Continuum Limit Lattice Action for QCD with Wilson Fermions, Nucl. Phys. B 259 (1985) 572 [INSPIRE].
C. Morningstar and M.J. Peardon, Analytic smearing of SU(3) link variables in lattice QCD, Phys. Rev. D 69 (2004) 054501 [hep-lat/0311018] [INSPIRE].
R. Hoffmann, A. Hasenfratz and S. Schaefer, Non-perturbative improvement of nHYP smeared Wilson fermions, PoS(LATTICE 2007)104 [arXiv:0710.0471] [INSPIRE].
S. Capitani, S. Dürr and C. Hölbling, Rationale for UV-filtered clover fermions, JHEP 11 (2006) 028 [hep-lat/0607006] [INSPIRE].
S. Dürr et al., Scaling study of dynamical smeared-link clover fermions, Phys. Rev. D 79 (2009) 014501 [arXiv:0802.2706] [INSPIRE].
S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth, Hybrid Monte Carlo, Phys. Lett. B 195 (1987) 216 [INSPIRE].
M.A. Clark and A.D. Kennedy, Accelerating dynamical fermion computations using the rational hybrid Monte Carlo (RHMC) algorithm with multiple pseudofermion fields, Phys. Rev. Lett. 98 (2007) 051601 [hep-lat/0608015] [INSPIRE].
J.C. Sexton and D.H. Weingarten, Hamiltonian evolution for the hybrid Monte Carlo algorithm, Nucl. Phys. B 380 (1992) 665 [INSPIRE].
T. Takaishi and P. de Forcrand, Testing and tuning new symplectic integrators for hybrid Monte Carlo algorithm in lattice QCD, Phys. Rev. E 73 (2006) 036706 [hep-lat/0505020] [INSPIRE].
T.A. DeGrand, A Conditioning Technique for Matrix Inversion for Wilson Fermions, Comput. Phys. Commun. 52 (1988) 161 [INSPIRE].
C.T.H. Davies et al., Precise Charm to Strange Mass Ratio and Light Quark Masses from Full Lattice QCD, Phys. Rev. Lett. 104 (2010) 132003 [arXiv:0910.3102] [INSPIRE].
S. Dürr et al., Lattice QCD at the physical point: light quark masses, Phys. Lett. B 701 (2011) 265 [arXiv:1011.2403] [INSPIRE].
S. Dürr et al., Lattice QCD at the physical point: Simulation and analysis details, JHEP 08 (2011) 148 [arXiv:1011.2711] [INSPIRE].
S. Borsányi et al., Anisotropy tuning with the Wilson flow, arXiv:1205.0781 [INSPIRE].
G.I. Egri et al., Lattice QCD as a video game, Comput. Phys. Commun. 177 (2007) 631 [hep-lat/0611022] [INSPIRE].
F. Karsch, E. Laermann, P. Petreczky and S. Stickan, Infinite temperature limit of meson spectral functions calculated on the lattice, Phys. Rev. D 68 (2003) 014504 [hep-lat/0303017] [INSPIRE].
G. Aarts and J.M. Martinez Resco, Continuum and lattice meson spectral functions at nonzero momentum and high temperature, Nucl. Phys. B 726 (2005) 93 [hep-lat/0507004] [INSPIRE].
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Borsányi, S., Dürr, S., Fodor, Z. et al. Charmonium spectral functions from 2+1 flavour lattice QCD. J. High Energ. Phys. 2014, 132 (2014). https://doi.org/10.1007/JHEP04(2014)132
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DOI: https://doi.org/10.1007/JHEP04(2014)132