Abstract
By subtracting from a recent lattice measurement of the thermal vector-current correlator the known 5-loop vacuum contribution, we demonstrate that the remainder is small and shows no visible short-distance divergence. It can therefore in principle be subjected to model-independent analytic continuation. Testing a particular implementation, we obtain estimates for the flavour-diffusion coefficient (2πTD≳0.8) and electrical conductivity which are significantly smaller than previous results. Although systematic errors remain beyond control at present, some aspects of our approach could be of a wider applicability.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J.I. Kapusta, C. Gale, Finite-Temperature Field Theory: Principles and Applications (Cambridge University Press, Cambridge, 2006)
H.B. Meyer, Transport properties of the quark–gluon plasma: a lattice QCD perspective. Eur. Phys. J. A 47, 86 (2011). 1104.3708
S. Gupta, The electrical conductivity and soft photon emissivity of the QCD plasma. Phys. Lett. B 597, 57 (2004). hep-lat/0301006
G. Aarts, C. Allton, J. Foley, S. Hands, S. Kim, Spectral functions at small energies and the electrical conductivity in hot, quenched lattice QCD. Phys. Rev. Lett. 99, 022002 (2007). hep-lat/0703008
H.-T. Ding, A. Francis, O. Kaczmarek, F. Karsch, E. Laermann, W. Soeldner, Thermal dilepton rate and electrical conductivity: An analysis of vector current correlation functions in quenched lattice QCD. Phys. Rev. D 83, 034504 (2011). 1012.4963
G. Cuniberti, E. De Micheli, G.A. Viano, Reconstructing the thermal Green functions at real times from those at imaginary times. Commun. Math. Phys. 216, 59 (2001). cond-mat/0109175
Y. Burnier, M. Laine, L. Mether, A test on analytic continuation of thermal imaginary-time data. Eur. Phys. J. C 71, 1619 (2011). 1101.5534
S. Caron-Huot, Asymptotics of thermal spectral functions. Phys. Rev. D 79, 125009 (2009). 0903.3958
P.A. Baikov, K.G. Chetyrkin, J.H. Kühn, Hadronic Z- and τ-decays in order \(\alpha_{s}^{4}\). Phys. Rev. Lett. 101, 012002 (2008). 0801.1821
J. Casalderrey-Solana, D. Teaney, Heavy quark diffusion in strongly coupled \(\mathcal{N}=4\) Yang-Mills. Phys. Rev. D 74, 085012 (2006). hep-ph/0605199
S. Caron-Huot, M. Laine, G.D. Moore, A way to estimate the heavy quark thermalization rate from the lattice. J. High Energy Phys. 04, 053 (2009). 0901.1195
A. Francis, O. Kaczmarek, M. Laine, J. Langelage, Towards a non-perturbative measurement of the heavy quark momentum diffusion coefficient, in PoS Lattice 2011 (2011), 202. 1109.3941
D. Banerjee, S. Datta, R. Gavai, P. Majumdar, Heavy quark momentum diffusion coefficient from lattice QCD. Phys. Rev. D 85, 014510 (2012). 1109.5738
F. Karsch, E. Laermann, P. Petreczky, S. Stickan, Infinite temperature limit of meson spectral functions calculated on the lattice. Phys. Rev. D 68, 014504 (2003). hep-lat/0303017
A. Vuorinen, Quark number susceptibilities of hot QCD up to g 6lng. Phys. Rev. D 67, 074032 (2003). hep-ph/0212283
Y. Burnier, M. Laine, J. Langelage, L. Mether, Colour-electric spectral function at next-to-leading order. J. High Energy Phys. 08, 094 (2010). 1006.0867
M. Laine, A. Vuorinen, Y. Zhu, Next-to-leading order thermal spectral functions in the perturbative domain. J. High Energy Phys. 09, 084 (2011). 1108.1259
R. Baier, B. Pire, D. Schiff, Dilepton production at finite temperature: Perturbative treatment at order α s . Phys. Rev. D 38, 2814 (1988)
Y. Gabellini, T. Grandou, D. Poizat, Electron-positron annihilation in thermal QCD. Ann. Phys. 202, 436 (1990)
T. Altherr, P. Aurenche, Finite temperature QCD corrections to lepton-pair formation in a quark-gluon plasma. Z. Phys. C 45, 99 (1989)
G. Aarts, J.M. MartÃnez Resco, Transport coefficients, spectral functions and the lattice. J. High Energy Phys. 04, 053 (2002). hep-ph/0203177
P.A. Baikov, K.G. Chetyrkin, J.H. Kühn, R(s) and hadronic τ-decays in order \(\alpha^{4}_{s}\): technical aspects. Nucl. Phys. B, Proc. Suppl. 189, 49 (2009). 0906.2987
T. van Ritbergen, J.A.M. Vermaseren, S.A. Larin, The four-loop β-function in quantum chromodynamics. Phys. Lett. B 400, 379 (1997). hep-ph/9701390
P.A. Baikov, K.G. Chetyrkin, J.H. Kühn, Adler Function, DIS sum rules and Crewther relations. Nucl. Phys. B, Proc. Suppl. 205–206, 237 (2010). 1007.0478
S. Borsanyi, G. Endrodi, Z. Fodor, S.D. Katz, K.K. Szabo, Lattice SU(3) thermodynamics and the onset of perturbative behaviour. 1104.0013
W. Florkowski, B.L. Friman, Spatial dependence of the finite temperature meson correlation function. Z. Phys., A Hadrons Nucl. 347, 271 (1994)
P.B. Arnold, L.G. Yaffe, Effective theories for real-time correlations in hot plasmas. Phys. Rev. D 57, 1178 (1998). hep-ph/9709449
M. Laine, Y. Schröder, Two-loop QCD gauge coupling at high temperatures. J. High Energy Phys. 03, 067 (2005). hep-ph/0503061
A. Francis, O. Kaczmarek, On the temperature dependence of the electrical conductivity in hot quenched lattice QCD. 1112.4802
P.B. Arnold, G.D. Moore, L.G. Yaffe, Transport coefficients in high temperature gauge theories. 1. Leading log results. J. High Energy Phys. 11, 001 (2000). hep-ph/0010177
P.B. Arnold, G.D. Moore, L.G. Yaffe, Transport coefficients in high temperature gauge theories. 2. Beyond leading log. J. High Energy Phys. 05, 051 (2003). hep-ph/0302165
P. Kovtun, D.T. Son, A.O. Starinets, Holography and hydrodynamics: Diffusion on stretched horizons. J. High Energy Phys. 10, 064 (2003). hep-th/0309213
G.D. Moore, J.-M. Robert, Dileptons, spectral weights, and conductivity in the quark-gluon plasma. hep-ph/0607172
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Burnier, Y., Laine, M. Towards flavour-diffusion coefficient and electrical conductivity without ultraviolet contamination. Eur. Phys. J. C 72, 1902 (2012). https://doi.org/10.1140/epjc/s10052-012-1902-8
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjc/s10052-012-1902-8