# Four-loop lattice-regularized vacuum energy density of the three-dimensional SU(3) + adjoint Higgs theory

Di Renzo F, Laine M, Schroeder Y, Torrero C (2008)

JHEP 2008(09).

*Journal Article*|

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*English*

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Abstract

The pressure of QCD admits at high temperatures a factorization into purely perturbative contributions from "hard" thermal momenta, and slowly convergent as well as non-perturbative contributions from "soft" thermal momenta. The latter can be related to various effective gluon condensates in a dimensionally reduced effective field theory, and measured there through lattice simulations. Practical measurements of one of the relevant condensates have suffered, however, from difficulties in extrapolating convincingly to the continuum limit. In order to gain insight on this problem, we employ Numerical Stochastic Perturbation Theory to estimate the problematic condensate up to 4-loop order in lattice perturbation theory. Our results seem to confirm the presence of "large" discretization effects, going like $a\ln(1/a)$, where $a$ is the lattice spacing. For definite conclusions, however, it would be helpful to repeat the corresponding part of our study with standard lattice perturbation theory techniques.

Keywords

perturbation theory: stochastic
;
perturbation theory: higher-order
;
Higgs model
;
gluon: condensation
;
lattice field theory
;
quantum chromodynamics
;
gauge field theory: SU(3)
;
factorization
;
effective field theory
;
dimension: 3
;
dimensional reduction
;
numerical calculations
;
energy: density

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### Cite this

Di Renzo F, Laine M, Schroeder Y, Torrero C. Four-loop lattice-regularized vacuum energy density of the three-dimensional SU(3) + adjoint Higgs theory.

*JHEP*. 2008;2008(09).Di Renzo, F., Laine, M., Schroeder, Y., & Torrero, C. (2008). Four-loop lattice-regularized vacuum energy density of the three-dimensional SU(3) + adjoint Higgs theory.

*JHEP*,*2008*(09).Di Renzo, F., Laine, M., Schroeder, Y., and Torrero, C. (2008). Four-loop lattice-regularized vacuum energy density of the three-dimensional SU(3) + adjoint Higgs theory.

*JHEP*2008.Di Renzo, F., et al., 2008. Four-loop lattice-regularized vacuum energy density of the three-dimensional SU(3) + adjoint Higgs theory.

*JHEP*, 2008(09).F. Di Renzo, et al., “Four-loop lattice-regularized vacuum energy density of the three-dimensional SU(3) + adjoint Higgs theory”,

*JHEP*, vol. 2008, 2008.Di Renzo, F., Laine, M., Schroeder, Y., Torrero, C.: Four-loop lattice-regularized vacuum energy density of the three-dimensional SU(3) + adjoint Higgs theory. JHEP. 2008, (2008).

Di Renzo, F., Laine, Mikko, Schroeder, York, and Torrero, C. “Four-loop lattice-regularized vacuum energy density of the three-dimensional SU(3) + adjoint Higgs theory”.

*JHEP*2008.09 (2008).
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