A fresh look on three-loop sum-integrals - INSPIRE

DataBETA

A fresh look on three-loop sum-integrals

York Schroder
(
- Bielefeld U.
)

Jul, 2012

19 pages

Published in:

JHEP 08 (2012) 095

e-Print:

1207.5666 [hep-ph]

DOI:

10.1007/JHEP08(2012)095

Report number:

BI-TP-2012-29

View in:

reference search13 citations

Citations per year

Abstract: (arXiv)

In order to prepare the ground for evaluating classes of three-loop sum-integrals that are presently needed for thermodynamic observables, we take a fresh and systematic look on the few known cases, and review their evaluation in a unified way using coherent notation. We do this for three important cases of massless bosonic three-loop vacuum sum-integrals that have been frequently used in the literature, and aim for a streamlined exposition as compared to the original evaluations. In passing, we speculate on options for generalization of the computational techniques that have been employed.

Note:

19 pages

boson: massless
thermodynamical
coherence

References(31)

Figures(0)

[1]

The Three loop free energy for high temperature QED and QCD with fermions

- Phys.Rev.D 51 (1995) 1906-1918
•
e-Print:
- hep-ph/9410360
•
DOI:
- 10.1103/PhysRevD.51.1906

[2]

Free energy of QCD at high temperature

Eric Braaten
(
- Ohio State U.
)
,
Agustin Nieto
(
- Ohio State U.
)

- Phys.Rev.D 53 (1996) 3421-3437
•
e-Print:
- hep-ph/9510408
•
DOI:
- 10.1103/PhysRevD.53.3421

[3]

Two-loop QCD gauge coupling at high temperatures

M. Laine
(
- Bielefeld U.
)
,
Y. Schroder
(
- Bielefeld U.
)

- JHEP 03 (2005) 067
•
e-Print:
- hep-ph/0503061
•
DOI:
- 10.1088/1126-6708/2005/03/067

[3]

Quark mass thresholds in QCD thermodynamics

Mikko Laine
(
- Bielefeld U.
)
,
York Schroder
(
- Bielefeld U.
)

- Phys.Rev.D 73 (2006) 085009
•
e-Print:
- hep-ph/0603048
•
DOI:
- 10.1103/PhysRevD.73.085009

[4]

High-precision calculation of multiloop Feynman integrals by difference equations

S. Laporta
(
- Bologna U.
)

- Int.J.Mod.Phys.A 15 (2000) 5087-5159
•
e-Print:
- hep-ph/0102033
•
DOI:
- 10.1142/S0217751X00002159

[4]

Evaluating multiloop Feynman integrals by Mellin-Barnes representation

Vladimir A. Smirnov
(
- SINP, Moscow
)

- Nucl.Phys.B Proc.Suppl. 135 (2004) 252-256,
•
e-Print:
- hep-ph/0406052
•
DOI:
- 10.1016/j.nuclphysbps.2004.09.024

[4]

Feynman Diagrams and Differential Equations

Mario Argeri
(
- Naples U.
)
,
Pierpaolo Mastrolia
(
- Zurich U.
)

- Int.J.Mod.Phys.A 22 (2007) 4375-4436
•
e-Print:
- 0707.4037
•
DOI:
- 10.1142/S0217751X07037147

[4]

Sector Decomposition

Gudrun Heinrich
(
- Durham U., IPPP
)

- Int.J.Mod.Phys.A 23 (2008) 1457-1486
•
e-Print:
- 0803.4177
•
DOI:
- 10.1142/S0217751X08040263

[5]

IBP methods at finite temperature

M. Nishimura
(
- TUCSS, Sakata and
- Bielefeld U.
)
,
Y. Schroder
(
- TUCSS, Sakata and
- Bielefeld U.
)

- JHEP 09 (2012) 051
•
e-Print:
- 1207.4042
•
DOI:
- 10.1007/JHEP09(2012)051

[6]

Loops for Hot QCD

Y. Schroder
(
- Bielefeld U.
)

- Nucl.Phys.B Proc.Suppl. 183 (2008) 296-301
•
e-Print:
- 0807.0500
•
DOI:
- 10.1016/j.nuclphysbps.2008.09.120

[7]

Integration by parts: The algorithm to calculate $\beta$ -functions in 4 loops

K.G. Chetyrkin
(
- Moscow, INR
)
,
F.V. Tkachov
(
- Moscow, INR
)

- Nucl.Phys.B 192 (1981) 159-204,
- Nucl. Phys. B192 ( 1981) 159-204
•
DOI:
- 10.1016/0550-3213(81)90199-1

[7]

A theorem on analytical calculability of 4-loop renormalization group functions

F.V. Tkachov
(
- Moscow, INR
)

- Phys.Lett.B 100 (1981) 65-68
•
DOI:
- 10.1016/0370-2693(81)90288-4

[8]

The Three loop free energy for pure gauge QCD

- Phys.Rev.D 50 (1994) 7603-7623
•
e-Print:
- hep-ph/9408276
•
DOI:
- 10.1103/PhysRevD.50.7603

[9]

Four-loop pressure of massless O(N) scalar field theory

A. Gynther
(
- Brandon U.
)
,
M. Laine
(
- Bielefeld U.
)
,
Y. Schroder
(
- Bielefeld U.
)
,
C. Torrero
(
- Bielefeld U.
)
,
A. Vuorinen
(
- Washington U., Seattle
)

- JHEP 04 (2007) 094
•
e-Print:
- hep-ph/0703307
•
DOI:
- 10.1088/1126-6708/2007/04/094

[9]

The N(f)3 g6 term in the pressure of hot QCD

A. Gynther
(
- Vienna, Tech. U.
)
,
A. Kurkela
(
- Zurich, ETH
)
,
A. Vuorinen
(
- Vienna, Tech. U. and
- CERN
)

- Phys.Rev.D 80 (2009) 096002
•
e-Print:
- 0909.3521
•
DOI:
- 10.1103/PhysRevD.80.096002

[10]

Four-loop Screened Perturbation Theory

- Phys.Rev.D 78 (2008) 076008
•
e-Print:
- 0805.4478
•
DOI:
- 10.1103/PhysRevD.78.076008

[11]

Three-loop matching coefficients for hot QCD: Reduction and gauge independence

J. Moller
(
- Bielefeld U.
)
,
Y. Schroder
(
- Bielefeld U.
)

- JHEP 08 (2012) 025
•
e-Print:
- 1207.1309
•
DOI:
- 10.1007/JHEP08(2012)025

[12]

How to resum long distance contributions to the QCD pressure?

K. Kajantie
(
- Helsinki U.
)
,
M. Laine
(
- CERN and
- Helsinki U.
)
,
K. Rummukainen
(
- Nordita and
- Helsinki Inst. of Phys.
)
,
Y. Schroder
(
- Helsinki U.
)

- Phys.Rev.Lett. 86 (2001) 10-13
•
e-Print:
- hep-ph/0007109
•
DOI:
- 10.1103/PhysRevLett.86.10

[12]

The Pressure of hot QCD up to g6 ln(1/g)

- Phys.Rev.D 67 (2003) 105008
•
e-Print:
- hep-ph/0211321
•
DOI:
- 10.1103/PhysRevD.67.105008

[12]

The Leading non-perturbative coefficient in the weak-coupling expansion of hot QCD pressure

F. Di Renzo
(
- Parma U. and
- INFN, Parma
)
,
M. Laine
(
- Bielefeld U.
)
,
V. Miccio
(
- INFN, Milan
)
,
Y. Schroder
(
- Bielefeld U.
)
,
C. Torrero
(
- Bielefeld U.
)

- JHEP 07 (2006) 026
•
e-Print:
- hep-ph/0605042
•
DOI:
- 10.1088/1126-6708/2006/07/026

[12]

Weak-coupling expansion of the hot QCD pressure

York Schroder
(
- Bielefeld U.
)

- PoS JHW2005 (2006) 029
•
e-Print:
- hep-ph/0605057
•
DOI:
- 10.22323/1.022.0029

[13]

Open problems in hot QCD

Jan Moller
(
- Bielefeld U.
)
,
York Schroder
(
- Bielefeld U.
)

- Nucl.Phys.B Proc.Suppl. 205-206 (2010) 218-223
•
e-Print:
- 1007.1223
•
DOI:
- 10.1016/j.nuclphysbps.2010.08.046

[14]

Infrared Problem in Thermodynamics of the Yang-Mills Gas

Andrei D. Linde
(
- Lebedev Inst.
)

- Phys.Lett.B 96 (1980) 289-292
•
DOI:
- 10.1016/0370-2693(80)90769-8

[15]

First Order and Second Order Phase Transitions in Gauge Theories at Finite Temperature

Paul H. Ginsparg
(
- Saclay
)

- Nucl.Phys.B 170 (1980) 388-408
•
DOI:
- 10.1016/0550-3213(80)90418-6

[15]

High-Temperature Yang-Mills Theories and Three-Dimensional Quantum Chromodynamics

Thomas Appelquist
(
- Yale U.
)
,
Robert D. Pisarski
(
- Yale U.
)

- Phys.Rev.D 23 (1981) 2305
•
DOI:
- 10.1103/PhysRevD.23.2305

1-25 of 31
1
2
25 / page