scholarly journals Derivation of the Lamb shift using an effective field theory

1999 ◽  
Vol 77 (4) ◽  
pp. 267-278 ◽  
Author(s):  
P Labelle ◽  
S M Zebarjad
Keyword(s):  
Field Theory ◽  
Effective Field Theories ◽  
Effective Field Theory ◽  
Lamb Shift ◽  
Multipole Expansion ◽  
Effective Field ◽  
Field Theories ◽  
Modern Language ◽  
First Time ◽  
Special Case

We rederive the Ο(α5) shift of the hydrogen levels in the nonrecoil limit (me/mP →> 0) using an extension of nonrelativistic QED (NRQED), an effective field theory developed by Caswell and Lepage. Our result contains the Lamb shift as a special case. Although this calculation is not new, it is presented here for the first time using the modern language of effective field theories. It clearly illustrates the usefulness of applying a multipole expansion to the NRQED vertices.PACS Nos.: 31.30Jv, 31.15Ar, 31.15Md, and 11.10St

scholarly journals Effective field theory, past and future

2016 ◽  
Vol 31 (06) ◽  
pp. 1630007 ◽  
Author(s):  
Steven Weinberg
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Effective Field Theories ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
Field Theories ◽  
Strong Interactions ◽  
The Standard Model ◽  
Theory Of Gravitation

I reminisce about the early development of effective field theories of the strong interactions, comment briefly on some other applications of effective field theories, and then take up the idea that the Standard Model and General Relativity are the leading terms in an effective field theory. Finally, I cite recent calculations that suggest that the effective field theory of gravitation and matter is asymptotically safe.

scholarly journals Power counting and Wilsonian renormalization in nuclear effective field theory

2016 ◽  
Vol 25 (05) ◽  
pp. 1641007 ◽  
Author(s):  
Manuel Pavón Valderrama
Keyword(s):  
Field Theory ◽  
Effective Field Theories ◽  
Effective Field Theory ◽  
Nuclear Physics ◽  
High Energy ◽  
Effective Field ◽  
Power Counting ◽  
Low Energy ◽  
Field Theories ◽  
Nuclear Forces

Effective field theories are the most general tool for the description of low energy phenomena. They are universal and systematic: they can be formulated for any low energy systems we can think of and offer a clear guide on how to calculate predictions with reliable error estimates, a feature that is called power counting. These properties can be easily understood in Wilsonian renormalization, in which effective field theories are the low energy renormalization group evolution of a more fundamental — perhaps unknown or unsolvable — high energy theory. In nuclear physics they provide the possibility of a theoretically sound derivation of nuclear forces without having to solve quantum chromodynamics explicitly. However there is the problem of how to organize calculations within nuclear effective field theory: the traditional knowledge about power counting is perturbative but nuclear physics is not. Yet power counting can be derived in Wilsonian renormalization and there is already a fairly good understanding of how to apply these ideas to non-perturbative phenomena and in particular to nuclear physics. Here we review a few of these ideas, explain power counting in two-nucleon scattering and reactions with external probes and hint at how to extend the present analysis beyond the two-body problem.

HALO EFFECTIVE FIELD THEORY

2005 ◽  
Vol 14 (01) ◽  
pp. 11-19
Author(s):  
U. VAN KOLCK
Keyword(s):  
Field Theory ◽  
Effective Field Theories ◽  
Effective Field Theory ◽  
Bound States ◽  
Effective Field ◽  
Field Theories ◽  
Alpha Scattering

I discuss effective field theories for bound states and narrow resonances near two-body thresholds. I illustrate the method in the case of nucleon-alpha scattering.

scholarly journals Effective-field theories for charged lepton flavour violation

2018 ◽  
Vol 179 ◽  
pp. 01019
Author(s):  
Giovanni Marco Pruna
Keyword(s):  
Field Theory ◽  
Effective Field Theories ◽  
Parameter Space ◽  
Effective Field Theory ◽  
Charged Lepton ◽  
Effective Field ◽  
Field Theories ◽  
The Status ◽  
Flavour Violation ◽  
Lepton Flavour

These proceedings review the status of present and future bounds on muonic lepton flavour violating transitions in the context of an effective-field theory defined below the electroweak scale. A specific focus is set on the phenomenology of μ → eγ, μ → 3e transitions and coherent μ → e nuclear conversion in the light of current and future experiments. Once the experimental limits are recast into bounds at higher scales, it is shown that the interplay between the various experiments is crucial to cover all corners of the parameter space.

scholarly journals Effective field theory from modified gravity with massive modes

2014 ◽  
Vol 12 (01) ◽  
pp. 1550004 ◽  
Author(s):  
Salvatore Capozziello ◽  
Mariafelicia De Laurentis ◽  
Mariacristina Paolella ◽  
Giulia Ricciardi
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Effective Field Theories ◽  
Effective Field Theory ◽  
Modified Gravity ◽  
Effective Field ◽  
Field Theories ◽  
Suitable Choice ◽  
Minimal Extension ◽  
Curvature Invariants

Massive gravitational modes in effective field theories can be recovered by extending General Relativity and taking into account generic functions of the curvature invariants, not necessarily linear in the Ricci scalar R. In particular, adopting the minimal extension of f(R) gravity, an effective field theory with massive modes is straightforwardly recovered. This approach allows to evade shortcomings like ghosts and discontinuities if a suitable choice of expansion parameters is performed.

ISSUES OF EFFECTIVE FIELD THEORIES WITH RESONANCES

2014 ◽  
Vol 26 ◽  
pp. 1460094
Author(s):  
JAMBUL GEGELIA ◽  
GEORGE JAPARIDZE
Keyword(s):  
Field Theory ◽  
Effective Field Theories ◽  
Effective Field Theory ◽  
Axial Current ◽  
Effective Field ◽  
Field Theories ◽  
Yang Mills ◽  
Unstable Particles

We address some issues of renormalization and symmetries of effective field theories with unstable particles - resonances. We also calculate anomalous contributions in the divergence of the singlet axial current in an effective field theory of massive SU(N) Yang-Mills fields interacting with fermions and discuss their possible relevance to the strong CP problem.

BUILDING HEAVY-PARTICLE LAGRANGIANS USING FOLDY-WOUTHUYSEN REPRESENTATION

2011 ◽  
Vol 26 (03n04) ◽  
pp. 673-674
Author(s):  
VADIM LENSKY ◽  
BINGWEI LONG
Keyword(s):  
Field Theory ◽  
Effective Field Theories ◽  
Effective Field Theory ◽  
Lorentz Invariance ◽  
Heavy Particle ◽  
Effective Field ◽  
Field Theories ◽  
Chiral Effective Field Theory ◽  
Pion Nucleon

We use the Foldy-Wouthuysen representation to construct Lorentz-invariant interactions of heavy fields, building the interactions starting from non-relativistic heavy particle fields. We show that the couplings obtained feature a straightforward 1/m, where m is the mass of the heavy particle, expansion, which ensures Lorentz invariance order by order in effective field theories. We illustrate possible applications on the examples of pion-nucleon and pion-nucleon-delta couplings in chiral effective field theory. For instance, we show that one of the terms usually considered to be a part of chiral index-1 πNΔ vertex is redundant. We discuss the implications of this fact.

scholarly journals Structure of two-loop SMEFT anomalous dimensions via on-shell methods

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Zvi Bern ◽  
Julio Parra-Martinez ◽  
Eric Sawyer
Keyword(s):  
Field Theory ◽  
Effective Field Theories ◽  
Effective Field Theory ◽  
Anomalous Dimension ◽  
Effective Field ◽  
Renormalization Scheme ◽  
Field Theories ◽  
Higher Dimension ◽  
Anomalous Dimensions ◽  
The Standard Model

Abstract We describe on-shell methods for computing one- and two-loop anomalous dimensions in the context of effective field theories containing higher-dimension operators. We also summarize methods for computing one-loop amplitudes, which are used as inputs to the computation of two-loop anomalous dimensions, and we explain how the structure of rational terms and judicious renormalization scheme choices can lead to additional vanishing terms in the anomalous dimension matrix at two loops. We describe the two-loop implications for the Standard Model Effective Field Theory (SMEFT). As a by-product of this analysis we verify a variety of one-loop SMEFT anomalous dimensions computed by Alonso, Jenkins, Manohar and Trott.

The non-perturbative renormalization group

2019 ◽  
pp. 137-144
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Fixed Point ◽  
Renormalization Group ◽  
Effective Field Theories ◽  
Asymptotic Form ◽  
Effective Field ◽  
Field Theories ◽  
Perturbative Renormalization

Chapter 9 focuses on the non–perturbative renormalization group. Many renormalization group (RG) results are derived within the framework of the perturbative RG. However, this RG is the asymptotic form in some neighbourhood of a Gaussian fixed point of the more general and exact RG, as introduced by Wilson and Wegner, and valid for rather general effective field theories. Chapter 9 describes the corresponding functional RG equations and give some indications about their derivation. A basic role is played by a method of partial field integration, which preserves the locality of the field theory. Note that functional RG equations can also be used to give alternative proofs of perturbative renormalizability within the framework of effective field theories.

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