The perturbative series for finite-temperature field theories has very poor convergence properties and one needs a way to reorganize it. In this talk, I review two ways of reorganizing the perturbative series for field theories at finite temperature and chemical potential, namely hard-thermal-loop perturbation theory (HTLpt) and dimensional reduction (DR). I will present results for the pressure, trace anomaly, speed of sound, and the quark susceptibilities from a 3-loop HTLpt calculation and for the quark susceptibilities using DR at four loops. A careful comparison with available lattice data shows good agreement for a number of physical quantities.
REFERENCES
1.
2.
S. A.
Chin
, Phys. Lett. B
78
, 552
–555
(1978
).3.
J. I.
Kapusta
, Nucl. Phys. B
148
, 461
–498
(1979
).4.
T.
Toimela
, Phys. Lett. B
124
, 407
–409
(1983
).5.
P.
Arnold
, C. X.
Zhai
, Phys. Rev. D
50
, 7603
–7623
(1994
).6.
P.
Arnold
, C. X.
Zhai
, Phys. Rev. D
51
, 1906
–1918
(1995
).7.
C. X.
Zhai
and B. M.
Kastening
, Phys. Rev. D
52
, 7232
–7246
(1995
).8.
E.
Braaten
, and A.
Nieto
, Phys. Rev. D
53
, 3421
–3437
(1996
).9.
K.
Kajantie
, M.
Laine
, K.
Rummukainen
and Y.
Schröder
, Phys. Rev. D
67
, 105008
(2003
).10.
A.
Vuorinen
, Phys. Rev. D
67
, 074032
(2003
).11.
A.
Vuorinen
, Phys. Rev. D
68
, 054017
(2003
).12.
A.
Ipp
, K.
Kajantie
, A.
Rebhan
, and A.
Vuorinen
, Phys. Rev. D
74
, 045016
(2006
).13.
A. D.
Linde
, Phys. Lett. B
96
, 289
–292
(1980
).14.
J. O.
Andersen
and M.
Strickland
, Ann. Phys.
317
, 281
–353
(2005
).15.
U.
Kraemmer
and A.
Rebhan
, Rept. Prog. Phys.
67
, 351
–431
(2004
).16.
J. O.
Andersen
, L. E.
Leganger
, M.
Strickland
, and N.
Su
, JHEP
08
, 053
(2011
).17.
S.
Mogliacci
, J. O.
Andersen
, M.
Strickland
, N.
Su
, and A.
Vuorinen
, JHEP
12
, 055
(2013
).18.
N.
Haque
, J. O.
Andersen
, M. G.
Mustafa
, M.
Strickland
, and N.
Su
, Phys. Rev. D
89
, 061701
(2014
).19.
N.
Haque
, A.
Bandyopadhyay
, J. O.
Andersen
, M. G.
Mustafa
, M.
Strickland
, and N.
Su
, JHEP
05
, 027
(2014
).20.
E.
Braaten
, and R. D.
Pisarski
, Nucl. Phys. B
, 337
, 569
–634
(1990
).21.
F.
Karsch
, A.
Patkos
and P.
Petreczky
, Phys. Lett. B
401
, 69
–73
, (1997
).22.
S.
Chiku
and T.
Hatsuda
, Phys. Rev. D
58
, 076001
(1998
).23.
J. O.
Andersen
, E.
Braaten
and M.
Strickland
, Phys. Rev. D
63
, 105008
(2001
).24.
J. O.
Andersen
and L.
Kyllingstad
, Phys. Rev. D
78
, 076008
(2008
).25.
J. O.
Andersen
and M.
Strickland
, Phys. Rev. D
64
, 105012
(2001
).26.
V. I.
Yukalov
, Teor. Mat. Fiz.
26
, 403
–413
, (1976
).27.
P. M.
Stevenson
, Phys. Rev. D
23
, 2916
–2944
(1981
).28.
A.
Duncan
and M.
Moshe
, Phys. Lett. B
215
, 352
–358
(1988
).29.
J. O.
Andersen
, E.
Braaten
, and M.
Strickland
, Phys. Rev. Lett.
83
, 2139
–2142
(1999
).30.
J. C.
Taylor
, and S. M. H.
Wong
, Nucl. Phys. B
346
, 115
–128
(1990
).31.
E.
Braaten
, and R. D.
Pisarski
, Phys. Rev. D
45
, 1827
–1830
(1992
).32.
33.
J. O.
Andersen
, M.
Strickland
, and N.
Su
, JHEP
1008
, 113
(2010
).34.
E.
Braaten
, and A.
Nieto
, Phys. Rev. D
, 51
, 6990
–7006
(1995
).35.
K.
Kajantie
, M.
Laine
, K.
Rummukainen
, and M. E.
Shaposhnikov
, Nucl. Phys. B
, 458
, 90
–136
(1996
).36.
A.
Hart
, M.
Laine
, and O.
Philipsen
, Nucl. Phys. B
586
, 443
–474
(2000
)37.
A.
Vuorinen
and L. G.
Yaffe
, Phys. Rev. D
74
, 025011
(2006
).38.
P.
de Forcrand
, A.
Kurkela
and A.
Vuorinen
, Phys. Rev. D
77
, 125014
(2008
).39.
K.
Kajantie
, M.
Laine
, K.
Rummukainen
, and Y.
Schröder
, Phys. Rev. D
, 67
, 105008
(2003
).40.
K.
Kajantie
, M.
Laine
, K.
Rummukainen
, and Y.
Schröder
, JHEP
04
, 036
(2003
).41.
A.
Bazavov
, N.
Brambilla
, X. Garcia i
Tormo
, P.
Petreczky
, J.
Soto
, and A.
Vairo
, Phys. Rev. D
86
, 114031
(2012
).42.
S.
Borsányi
et al., JHEP
11
, 077
(2010
).43.
S.
Borsányi
et al., JHEP
08
, 53
(2012
).44.
S.
Borsányi
, Z.
Fodor
, S. D.
Katz
, S.
Krieg
, C.
Ratti
, and K.
Szabo
, JHEP
01
, 138
(2012
).45.
A.
Bazavov
et al., Phys. Rev. Lett.
111
, 082301
(2013
).46.
A.
Bazavov
et al., Phys. Rev. D
88
, 094021
(2013
).47.
C.
Bernard
et al., Phys. Rev. D
71
, 034504
(2005
).48.
49.
A.
Bazavov
et al., Phys. Rev. Lett.
109
, 192302
(2012
).
This content is only available via PDF.
© 2016 AIP Publishing LLC.
2016
AIP Publishing LLC
You do not currently have access to this content.