Apparent thermalization due to plasma instabilities in the quark-gIuon plasma

Physical Review Letters

Volumn 94, Issue 7, 2005, Pages

  Arnold, Peter ^a   Lenaghan, Jonathan ^a   Moore, Guy D ^b   Yaffe, Laurence G ^c  

^a University of Virginia   (United States)

^b MCGILL UNIVERSITY   (Canada)

^c UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ENERGY DENSITY; EXCITATIONS; QUARK-GLUON PLASMA; RELATIVISTIC HEAVY-ION COLLIDER (RHIC);

ANISOTROPY; ELLIPSOMETRY; HYDRODYNAMICS; IONS; PERTURBATION TECHNIQUES; STABILITY; THERMOANALYSIS;

PLASMAS;

EID: 18244376604     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.94.072302     Document Type: Article

References (39)

1. See, for example, U. W. Heinz, nucl-th/0407067.
2. R. Baier, A. H. Mueller, D. Schiff and D. T. Son, Phys. Lett. B 539, 46 (2002); D. Molnar and M. Gyulassy, Nucl. Phys. A697, 495 (2002); A703, 893(E) (2002).
3. R. Baier, A. H. Mueller, D. Schiff and D. T. Son, Phys. Lett. B 539, 46 (2002); D. Molnar and M. Gyulassy, Nucl. Phys. A697, 495 (2002); A703, 893(E) (2002).
4. R. Baier, A. H. Mueller, D. Schiff and D. T. Son, Phys. Lett. B 539, 46 (2002); D. Molnar and M. Gyulassy, Nucl. Phys. A697, 495 (2002); A703, 893(E) (2002).
5. For other efforts to address this puzzle, see E. V. Shuryak and I. Zahed, Phys. Rev. C 70, 021901 (2004); E. Shuryak, Prog. Part. Nucl. Phys. 53, 273 (2004); Z. Xu and C. Greiner, hep-ph/0406278; F. Gastineau, E. Blanquier, and J. Aichelin, hep-ph/0404207.
6. For other efforts to address this puzzle, see E. V. Shuryak and I. Zahed, Phys. Rev. C 70, 021901 (2004); E. Shuryak, Prog. Part. Nucl. Phys. 53, 273 (2004); Z. Xu and C. Greiner, hep-ph/0406278; F. Gastineau, E. Blanquier, and J. Aichelin, hep-ph/0404207.
7. For other efforts to address this puzzle, see E. V. Shuryak and I. Zahed, Phys. Rev. C 70, 021901 (2004); E. Shuryak, Prog. Part. Nucl. Phys. 53, 273 (2004); Z. Xu and C. Greiner, hep-ph/0406278; F. Gastineau, E. Blanquier, and J. Aichelin, hep-ph/0404207.
8. For other efforts to address this puzzle, see E. V. Shuryak and I. Zahed, Phys. Rev. C 70, 021901 (2004); E. Shuryak, Prog. Part. Nucl. Phys. 53, 273 (2004); Z. Xu and C. Greiner, hep-ph/0406278; F. Gastineau, E. Blanquier, and J. Aichelin, hep-ph/0404207.
9. P. Arnold, G. D. Moore, and L. G. Yaffe, J. High Energy Phys. 01 (2003) 030.
10. f = 3 QCD. For the latter, see P. Arnold, G. D. Moore, and L. G. Yaffe, J. High Energy Phys. 05 (2003) 051.
11. P. Arnold, J. Lenaghan, and G. D. Moore, J. High Energy Phys. 08 (2003) 002.
12. S. Mrówczyński, Phys. Lett. B 314, 118 (1993); Phys. Rev. C 49, 2191 (1994); Phys. Lett. B 393, 26 (1997).
13. S. Mrówczyński, Phys. Lett. B 314, 118 (1993); Phys. Rev. C 49, 2191 (1994); Phys. Lett. B 393, 26 (1997).
14. S. Mrówczyński, Phys. Lett. B 314, 118 (1993); Phys. Rev. C 49, 2191 (1994); Phys. Lett. B 393, 26 (1997).
15. P. Romatschke and M. Strickland, Phys. Rev. D 68, 036004 (2003).
16. See, for example, the discussion in the context of bottom-up thermalization in R. Baier, A. H. Mueller, D. Schiff, and D. T. Son, Phys. Lett. B 502, 51 (2001).
17. S. Mrówczyński, Phys. Rev. D 39, 1940 (1989).
18. We suppress species labels (quark vs gluon) on the distribution f, as well as associated species sums and color Casimirs which should appear in Eqs. (3) and (5)-(7). See Ref. [4] for details. For excitations in color representation R, the distribution f is a color density matrix transforming in the R × R̄ representation; the field strengths in Eq. (2) are matrices in the representation 31.
19. 2.
20. E. S. Weibel, Phys. Rev. Lett. 2, 83 (1959).
21. ∞.
22. ∞, gives the stated inequality.
23. 4.
24. Expansion of the plasma may also cut off instability growth, if the expansion rate is faster than the rate of the processes under discussion. See J. Randrup and S. Mrówczyński, Phys. Rev. C 68, 034909 (2003).
25. Estimates of gauge-field amplitudes should be understood as applying in gauges, such as Coulomb gauge, which make the gauge field as smooth as possible.
26. S. Mrówczyński, A. Rebhan, and M. Strickland, Phys. Rev. D 70, 025004 (2004).
27. hard/g.
28. J. P. Blaizot and E. Iancu, Phys. Lett. B 326, 138 (1994).
29. P. Arnold and J. Lenaghan, Phys. Rev. D 70, 114007 (2004).
30. A. Rebhan, P. Romatschke, and M. Strickland, hep-ph/0412016.
31. P. Arnold, G. D. Moore, and L. G. Yaffe (to be published).
32. 2] ≫ 1 patches will be required to receive an O(1) change in direction. This is the usual case where the soft gauge field is perturbatively small on the scale of hard momenta.
33. This is analogous to "violent relaxation" in gravitational dynamics. See, for example, D. Lynden-Bell, Mon. Not. R. Astron. Soc. 136, 101 (1967); M. Trenti and G. Bertin, astro-ph/0406236.
34. This is analogous to "violent relaxation" in gravitational dynamics. See, for example, D. Lynden-Bell, Mon. Not. R. Astron. Soc. 136, 101 (1967); M. Trenti and G. Bertin, astro-ph/0406236.
35. F. Califano, and N. Attico, F. Pegoraro, G. Bertin, and S. V. Bulanov, Phys. Rev. Lett. 86, 5293 (2001).
36. A. Krasnitz and R. Venugopalan, Nucl. Phys. B557, 237 (1999); A. Krasnitz, Y. Nara, and R. Venugopalan, Nucl. Phys. A717, 268 (2003); A727, 427 (2003); T. Lappi, Phys. Rev. C 67, 054903 (2003).
37. A. Krasnitz and R. Venugopalan, Nucl. Phys. B557, 237 (1999); A. Krasnitz, Y. Nara, and R. Venugopalan, Nucl. Phys. A717, 268 (2003); A727, 427 (2003); T. Lappi, Phys. Rev. C 67, 054903 (2003).
38. A. Krasnitz and R. Venugopalan, Nucl. Phys. B557, 237 (1999); A. Krasnitz, Y. Nara, and R. Venugopalan, Nucl. Phys. A717, 268 (2003); A727, 427 (2003); T. Lappi, Phys. Rev. C 67, 054903 (2003).
39. A. Krasnitz and R. Venugopalan, Nucl. Phys. B557, 237 (1999); A. Krasnitz, Y. Nara, and R. Venugopalan, Nucl. Phys. A717, 268 (2003); A727, 427 (2003); T. Lappi, Phys. Rev. C 67, 054903 (2003).