Perturbation theory, effective field theory, and oscillations in the power spectrum

Recent developments of perturbation theory at finite temperature based on effective field theory methods are reviewed. These methods allow the contributions from the different scales to be separated and the perturbative series to be reorganized. The construction of the effective field theory is shown in detail for ϕ4 theory and QCD. It is applied to the evaluation of the free energy of QCD at order g5 and the calculation of the g6 term is outlined. Implications for the application of perturbative QCD to the quark–gluon plasma are also discussed.

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Effective Field Theory of Large-Scale Structure

Effective Field Theory in Particle Physics and Cosmology ◽

10.1093/oso/9780198855743.003.0007 ◽

2020 ◽

pp. 415-478

Author(s):

Tobias Baldauf

Keyword(s):

Field Theory ◽

Perturbation Theory ◽

Effective Field Theory ◽

Random Fields ◽

Large Scale ◽

Large Scale Structure ◽

Gaussian Random Fields ◽

Effective Field ◽

Scale Structure ◽

Linear Perturbation Theory

The lectures featured in this chapter review the observables relevant to the large-scale structure (LSS) of our Universe. The chapter introduces an effective field theory (EFT) that allows us to analytically describe the growth of fluctuations into the non-linear era, with uncertainties better controlled than in classical linear perturbation theory. Topics covered in the chapter include random fields in three-dimensional space, Fourier space conventions, the shape of the matter power spectrum, Gaussian random fields, estimators and cosmic variance, dynamics in the Newtonian regime, a perturbative solution of the fluid equations, the EFT approach, the Lagrangian perturbation theory, biased tracers, and redshift space distortions.

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Role of trans-Planckian modes in cosmology

Journal of High Energy Physics ◽

10.1007/jhep08(2020)071 ◽

2020 ◽

Vol 2020 (8) ◽

Cited By ~ 2

Author(s):

Arjun Berera ◽

Suddhasattwa Brahma ◽

Jaime R. Calderón

Keyword(s):

Field Theory ◽

Power Spectrum ◽

Effective Field Theory ◽

Effective Field ◽

Inflationary Cosmology ◽

De Sitter ◽

Warm Inflation ◽

Primordial Power Spectrum ◽

Hubble Horizon

Abstract Motivated by the old trans-Planckian (TP) problem of inflationary cosmology, it has been conjectured that any consistent effective field theory should keep TP modes ‘hidden’ behind the Hubble horizon, so as to prevent them from turning classical and thereby affecting macroscopic observations. In this paper we present two arguments against the Hubble horizon being a scale of singular significance as has been put forward in the TP Censorship Conjecture (TCC). First, refinements of TCC are presented that allow for the TP modes to grow beyond the horizon while still keeping the de-Sitter conjecture valid. Second, we show that TP modes can turn classical even well within the Hubble horizon, which, as such, negates this rationale behind keeping them from crossing it. The role of TP modes is known to be less of a problem in warm inflation, because fluctuations start out usually as classical. This allows warm inflation to be more resilient to the TP problem compared to cold inflation. To understand how robust this is, we identity limits where quantum modes can affect the primordial power spectrum in one specific case.

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Chiral Perturbation Theory at NNNLO

Symmetry ◽

10.3390/sym12081262 ◽

2020 ◽

Vol 12 (8) ◽

pp. 1262

Author(s):

Nils Hermansson-Truedsson

Keyword(s):

Field Theory ◽

Perturbation Theory ◽

Effective Field Theory ◽

Chiral Perturbation Theory ◽

Pion Mass ◽

Effective Field ◽

Leading Order ◽

Chiral Perturbation ◽

Effective Lagrangian ◽

Low Energies

Chiral perturbation theory is a much successful effective field theory of quantum chromodynamics at low energies. The effective Lagrangian is constructed systematically order by order in powers of the momentum p2, and until now the leading order (LO), next-to leading order (NLO), next-to-next-to leading order (NNLO) and next-to-next-to-next-to leading order (NNNLO) have been studied. In the following review we consider the construction of the Lagrangian and in particular focus on the NNNLO case. We in addition review and discuss the pion mass and decay constant at the same order, which are fundamental quantities to study for chiral perturbation theory. Due to the large number of terms in the Lagrangian and hence low energy constants arising at NNNLO, some remarks are made about the predictivity of this effective field theory.

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Impact of bias and redshift-space modelling for the halo power spectrum: testing the effective field theory of large-scale structure

Journal of Cosmology and Astroparticle Physics ◽

10.1088/1475-7516/2020/07/011 ◽

2020 ◽

Vol 2020 (07) ◽

pp. 011-011 ◽

Cited By ~ 4

Author(s):

Lucía Fonseca de la Bella ◽

Donough Regan ◽

David Seery ◽

David Parkinson

Keyword(s):

Field Theory ◽

Power Spectrum ◽

Effective Field Theory ◽

Large Scale ◽

Large Scale Structure ◽

Effective Field ◽

Scale Structure

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SPIN POLARIZABILITY OF THE NUCLEON IN THE EFFECTIVE FIELD THEORY OF HEAVY BARYON

International Journal of Modern Physics A ◽

10.1142/s0217751x06031521 ◽

2006 ◽

Vol 21 (19n20) ◽

pp. 3947-3966

Author(s):

K. B. VIJAYA KUMAR ◽

YONG-LIANG MA ◽

YUE-LIANG WU

Keyword(s):

Field Theory ◽

Perturbation Theory ◽

Effective Field Theory ◽

Chiral Perturbation Theory ◽

Heavy Baryon ◽

Effective Field ◽

Leading Order ◽

Chiral Perturbation ◽

Spin Polarizability ◽

Large Correction

We have constructed a heavy baryon effective field theory with photon as an external field in accordance with the symmetry requirements similar to the heavy quark effective field theory. By treating the heavy baryon and antibaryon equally on the same footing in the effective field theory, we have calculated the spin polarizabilities γi, i = 1,…,4 of the nucleon at third order and at fourth-order of the spin-dependent Compton scattering. At leading order (LO), our results agree with the corresponding results of the heavy baryon chiral perturbation theory, at the next-to-leading order (NLO) the results show a large correction to the ones in the heavy baryon chiral perturbation theory due to baryon–antibaryon coupling terms. The low-energy theorem is satisfied both at LO and at NLO. The contributions arising from the heavy baryon–antibaryon vertex were found to be significant and the results of the polarizabilities obtained from our theory is much closer to the experimental data.

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