Abstract
The imaginary part of the heavy quark-antiquark potential experienced by moving heavy quarkonia in strongly coupled plasmas dual to theories of gravity is computed by considering thermal worldsheet fluctuations of the holographic Nambu-Goto string. General results for a wide class of gravity duals are presented and an explicit formula for Im \( {V}_{Q\overline{Q}} \) is found in the case where the axis of the moving \( \overline{Q}Q \) pair has an arbitrary orientation with respect to its velocity in the plasma. These results are applied to the study of heavy quarkonia propagating through a strongly coupled \( \mathcal{N}=4 \) SYM plasma. Our results indicate that the onset of Im \( {V}_{Q\overline{Q}} \) decreases with increasing rapidity (though our analysis is limited to slowly moving quarkonia) and that, in general, a \( Q\overline{Q} \) pair is more strongly bound if its axis is aligned with its direction of motion through the strongly coupled plasma.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E.V. Shuryak, Quantum chromodynamics and the theory of superdense matter, Phys. Rept. 61 (1980) 71 [INSPIRE].
F. Karsch, M.T. Mehr and H. Satz, Color screening and deconfinement for bound states of heavy quarks, Z. Phys. C 37 (1988) 617 [INSPIRE].
K.G. Wilson, Confinement of quarks, Phys. Rev. D 10 (1974) 2445 [INSPIRE].
J.-L. Gervais and A. Neveu, The slope of the leading Regge trajectory in quantum chromodynamics, Nucl. Phys. B 163 (1980) 189 [INSPIRE].
A.M. Polyakov, Gauge fields as rings of glue, Nucl. Phys. B 164 (1980) 171 [INSPIRE].
M. Laine, O. Philipsen, P. Romatschke and M. Tassler, Real-time static potential in hot QCD, JHEP 03 (2007) 054 [hep-ph/0611300] [INSPIRE].
M. Laine, A resummed perturbative estimate for the quarkonium spectral function in hot QCD, JHEP 05 (2007) 028 [arXiv:0704.1720] [INSPIRE].
A. Beraudo, J.-P. Blaizot and C. Ratti, Real and imaginary-time \( Q\overline{Q} \) correlators in a thermal medium, Nucl. Phys. A 806 (2008) 312 [arXiv:0712.4394] [INSPIRE].
N. Brambilla, J. Ghiglieri, A. Vairo and P. Petreczky, Static quark-antiquark pairs at finite temperature, Phys. Rev. D 78 (2008) 014017 [arXiv:0804.0993] [INSPIRE].
P. Petreczky, C. Miao and A. Mócsy, Quarkonium spectral functions with complex potential, Nucl. Phys. A 855 (2011) 125 [arXiv:1012.4433] [INSPIRE].
N. Brambilla, M.A. Escobedo, J. Ghiglieri, J. Soto and A. Vairo, Heavy quarkonium in a weakly-coupled quark-gluon plasma below the melting temperature, JHEP 09 (2010) 038 [arXiv:1007.4156] [INSPIRE].
Y. Burnier, M. Laine and M. Vepsäläinen, Quarkonium dissociation in the presence of a small momentum space anisotropy, Phys. Lett. B 678 (2009) 86 [arXiv:0903.3467] [INSPIRE].
A. Dumitru, Y. Guo and M. Strickland, The imaginary part of the static gluon propagator in an anisotropic (viscous) QCD plasma, Phys. Rev. D 79 (2009) 114003 [arXiv:0903.4703] [INSPIRE].
O. Philipsen and M. Tassler, On quarkonium in an anisotropic quark gluon plasma, arXiv:0908.1746 [INSPIRE].
M. Laine, O. Philipsen, P. Romatschke and M. Tassler, Real-time static potential in hot QCD, JHEP 03 (2007) 054 [hep-ph/0611300] [INSPIRE].
A. Rothkopf, T. Hatsuda and S. Sasaki, Complex heavy-quark potential at finite temperature from lattice QCD, Phys. Rev. Lett. 108 (2012) 162001 [arXiv:1108.1579] [INSPIRE].
G. Aarts et al., What happens to the Υ and η b in the quark-gluon plasma? Bottomonium spectral functions from lattice QCD, JHEP 11 (2011) 103 [arXiv:1109.4496] [INSPIRE].
G. Aarts et al., Melting of P wave bottomonium states in the quark-gluon plasma from lattice NRQCD, JHEP 12 (2013) 064 [arXiv:1310.5467] [INSPIRE].
J. Noronha and A. Dumitru, Thermal width of the Υ at large ’t Hooft coupling, Phys. Rev. Lett. 103 (2009) 152304 [arXiv:0907.3062] [INSPIRE].
J.L. Albacete, Y.V. Kovchegov and A. Taliotis, Heavy quark potential at finite temperature in AdS/CFT revisited, Phys. Rev. D 78 (2008) 115007 [arXiv:0807.4747] [INSPIRE].
T. Hayata, K. Nawa and T. Hatsuda, Time-dependent heavy-quark potential at finite temperature from gauge-gravity duality, Phys. Rev. D 87 (2013) 101901 [arXiv:1211.4942] [INSPIRE].
S.I. Finazzo and J. Noronha, Estimates for the thermal width of heavy quarkonia in strongly coupled plasmas from holography, JHEP 11 (2013) 042 [arXiv:1306.2613] [INSPIRE].
K.B. Fadafan, D. Giataganas and H. Soltanpanahi, The imaginary part of the static potential in strongly coupled anisotropic plasma, JHEP 11 (2013) 107 [arXiv:1306.2929] [INSPIRE].
K.B. Fadafan and S.K. Tabatabaei, Thermal width of quarkonium from holography, Eur. Phys. J. C 74 (2014) 2842 [arXiv:1308.3971] [INSPIRE].
Y. Akamatsu and A. Rothkopf, Stochastic potential and quantum decoherence of heavy quarkonium in the quark-gluon plasma, Phys. Rev. D 85 (2012) 105011 [arXiv:1110.1203] [INSPIRE].
Y. Akamatsu, Heavy quark master equations in the Lindblad form at high temperatures, arXiv:1403.5783 [INSPIRE].
M. Strickland, Thermal Υ1s and χ b1 suppression at \( \sqrt{s_{NN}}=2.76 \) TeV Pb-Pb collisions at the LHC, Phys. Rev. Lett. 107 (2011) 132301 [arXiv:1106.2571] [INSPIRE].
M. Strickland and D. Bazow, Thermal bottomonium suppression at RHIC and LHC, Nucl. Phys. A 879 (2012) 25 [arXiv:1112.2761] [INSPIRE].
M. Margotta, K. McCarty, C. McGahan, M. Strickland and D. Yager-Elorriaga, Quarkonium states in a complex-valued potential, Phys. Rev. D 83 (2011) 105019 [Erratum ibid. D 84 (2011) 069902] [arXiv:1101.4651] [INSPIRE].
G. Aarts et al., S wave bottomonium states moving in a quark-gluon plasma from lattice NRQCD, JHEP 03 (2013) 084 [arXiv:1210.2903] [INSPIRE].
M.A. Escobedo, F. Giannuzzi, M. Mannarelli and J. Soto, Heavy quarkonium moving in a quark-gluon plasma, Phys. Rev. D 87 (2013) 114005 [arXiv:1304.4087] [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].
J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].
A. Brandhuber, N. Itzhaki, J. Sonnenschein and S. Yankielowicz, Wilson loops in the large-N limit at finite temperature, Phys. Lett. B 434 (1998) 36 [hep-th/9803137] [INSPIRE].
S.-J. Rey, S. Theisen and J.-T. Yee, Wilson-Polyakov loop at finite temperature in large-N gauge theory and anti-de Sitter supergravity, Nucl. Phys. B 527 (1998) 171 [hep-th/9803135] [INSPIRE].
Y. Kinar, E. Schreiber and J. Sonnenschein, \( Q\overline{Q} \) potential from strings in curved space-time — classical results, Nucl. Phys. B 566 (2000) 103 [hep-th/9811192] [INSPIRE].
J. Sonnenschein, What does the string/gauge correspondence teach us about Wilson loops?, hep-th/0003032 [INSPIRE].
H. Liu, K. Rajagopal and U.A. Wiedemann, An AdS/CFT calculation of screening in a hot wind, Phys. Rev. Lett. 98 (2007) 182301 [hep-ph/0607062] [INSPIRE].
H. Liu, K. Rajagopal and U.A. Wiedemann, Wilson loops in heavy ion collisions and their calculation in AdS/CFT, JHEP 03 (2007) 066 [hep-ph/0612168] [INSPIRE].
E. Caceres, M. Natsuume and T. Okamura, Screening length in plasma winds, JHEP 10 (2006) 011 [hep-th/0607233] [INSPIRE].
T. Faulkner and H. Liu, Meson widths from string worldsheet instantons, Phys. Lett. B 673 (2009) 161 [arXiv:0807.0063] [INSPIRE].
Q.J. Ejaz, T. Faulkner, H. Liu, K. Rajagopal and U.A. Wiedemann, A limiting velocity for quarkonium propagation in a strongly coupled plasma via AdS/CFT, JHEP 04 (2008) 089 [arXiv:0712.0590] [INSPIRE].
S. Gradshteyn and I.M. Ryzhik, Table of integrals, series, and products, A. Jeffrey and D. Zwillinger eds., seventh edition, Academic Press (2007).
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
D. Bak, A. Karch and L.G. Yaffe, Debye screening in strongly coupled \( \mathcal{N}=4 \) supersymmetric Yang-Mills plasma, JHEP 08 (2007) 049 [arXiv:0705.0994] [INSPIRE].
U. Gürsoy and E. Kiritsis, Exploring improved holographic theories for QCD: part I, JHEP 02 (2008) 032 [arXiv:0707.1324] [INSPIRE].
U. Gürsoy, E. Kiritsis and F. Nitti, Exploring improved holographic theories for QCD: part II, JHEP 02 (2008) 019 [arXiv:0707.1349] [INSPIRE].
U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Deconfinement and gluon plasma dynamics in improved holographic QCD, Phys. Rev. Lett. 101 (2008) 181601 [arXiv:0804.0899] [INSPIRE].
S.S. Gubser and A. Nellore, Mimicking the QCD equation of state with a dual black hole, Phys. Rev. D 78 (2008) 086007 [arXiv:0804.0434] [INSPIRE].
J. Noronha, Connecting Polyakov loops to the thermodynamics of SU(N c ) gauge theories using the gauge-string duality, Phys. Rev. D 81 (2010) 045011 [arXiv:0910.1261] [INSPIRE].
M. Ali-Akbari, D. Giataganas and Z. Rezaei, Imaginary potential of heavy quarkonia moving in strongly coupled plasma, Phys. Rev. D 90 (2014) 086001 [arXiv:1406.1994] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1406.2683
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Finazzo, S.I., Noronha, J. Thermal suppression of moving heavy quark pairs in a strongly coupled plasma. J. High Energ. Phys. 2015, 51 (2015). https://doi.org/10.1007/JHEP01(2015)051
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2015)051