scholarly journals Multi-spin soft bootstrap and scalar-vector Galileon

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Karol Kampf ◽  
Jiří Novotný ◽  
Filip Přeučil ◽  
Jaroslav Trnka
Keyword(s):  
Effective Field Theories ◽  
Sigma Model ◽  
Bootstrap Method ◽  
Effective Field ◽  
Power Counting ◽  
Field Theories ◽  
Linear Sigma Model ◽  
Higher Derivative ◽  
Soft Limit ◽  
General Power

Abstract We use the amplitude soft bootstrap method to explore the space of effective field theories (EFT) of massless vectors and scalars. It is known that demanding vanishing soft limits fixes uniquely a special class of EFTs: non-linear sigma model, scalar Galileon and Born-Infeld theories. Based on the amplitudes analysis, we conjecture no-go theorems for higher-derivative vector theories and theories with coupled vectors and scalars. We then allow for more general soft theorems where the non-trivial part of the soft limit of the (n+1)-pt amplitude is equal to a linear combination of n-pt amplitudes. We derive the form of these soft theorems for general power-counting and spins of particles and use it as an input into the soft bootstrap method in the case of Galileon power-counting and coupled scalar-vector theories. We show that this unifies the description of existing Galileon theories and leads us to the discovery of a new exceptional theory: Special scalar-vector Galileon.

scholarly journals On the power counting in effective field theories

2014 ◽  
Vol 731 ◽  
pp. 80-86 ◽  
Author(s):  
Gerhard Buchalla ◽  
Oscar Catà ◽  
Claudius Krause
Keyword(s):  
Effective Field Theories ◽  
Effective Field ◽  
Power Counting ◽  
Field Theories

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.

scholarly journals Bound states and power counting in effective field theories

1997 ◽  
Vol 55 (7) ◽  
pp. 4129-4140 ◽  
Author(s):  
Michael Luke ◽  
Aneesh V. Manohar
Keyword(s):  
Effective Field Theories ◽  
Bound States ◽  
Effective Field ◽  
Power Counting ◽  
Field Theories

Introduction to Effective Field Theories and Inflation

2020 ◽  
pp. 220-306
Author(s):  
C. P. Burgess
Keyword(s):  
Effective Field Theories ◽  
Big Bang ◽  
Effective Field ◽  
Power Counting ◽  
Field Theories ◽  
Effective Theory ◽  
Inflationary Cosmology ◽  
Big Bang Theory ◽  
The Universe ◽  
Inflationary Models

The lecture notes presented in this chapter provide an introduction to inflationary cosmology with an emphasis on some of the ways effective field theories (EFTs) are used in its analysis. Topics covered in the chapter include introduction to cosmological backgrounds and fluctuations, including a brief discussion of inflationary models; general relativity as an effective theory; new issues raised by cosmology for EFTs, such as time-dependent backgrounds; and power-counting in cosmological EFTs. It also discusses issues surrounding the existence in the universe of both dark matter and dark energy, and the broader controversial question of their existence. It touches on the Hot Big Bang theory of cosmology, and the various types of particles believed to be 'elementary' at the temperatures of interest.

scholarly journals S-matrix bootstrap for effective field theories: massless pions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Andrea L. Guerrieri ◽  
João Penedones ◽  
Pedro Vieira
Keyword(s):  
Effective Field Theories ◽  
Bootstrap Method ◽  
Effective Field ◽  
Low Energy ◽  
Field Theories ◽  
Proof Of Concept ◽  
Energy Dynamics ◽  
S Matrix ◽  
Energy Constants ◽  
Chiral Lagrangian

Abstract We use the numerical S-matrix bootstrap method to obtain bounds on the two leading Wilson coefficients (or low energy constants) of the chiral lagrangian controlling the low-energy dynamics of massless pions. This provides a proof of concept that the numerical S-matrix bootstrap can be used to derive non-perturbative bounds on massless EFTs in more than two spacetime dimensions.

scholarly journals Exceptional nonrelativistic effective field theories with enhanced symmetries

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Tomáš Brauner
Keyword(s):  
Effective Field Theories ◽  
Explicit Construction ◽  
Effective Field ◽  
Field Theories ◽  
Relativistic Case ◽  
Starting Point ◽  
Higher Power ◽  
Mere Presence ◽  
Spatial Rotations

Abstract We initiate the classification of nonrelativistic effective field theories (EFTs) for Nambu-Goldstone (NG) bosons, possessing a set of redundant, coordinate-dependent symmetries. Similarly to the relativistic case, such EFTs are natural candidates for “exceptional” theories, whose scattering amplitudes feature an enhanced soft limit, that is, scale with a higher power of momentum at long wavelengths than expected based on the mere presence of Adler’s zero. The starting point of our framework is the assumption of invariance under spacetime translations and spatial rotations. The setup is nevertheless general enough to accommodate a variety of nontrivial kinematical algebras, including the Poincaré, Galilei (or Bargmann) and Carroll algebras. Our main result is an explicit construction of the nonrelativistic versions of two infinite classes of exceptional theories: the multi-Galileon and the multi-flavor Dirac-Born-Infeld (DBI) theories. In both cases, we uncover novel Wess-Zumino terms, not present in their relativistic counterparts, realizing nontrivially the shift symmetries acting on the NG fields. We demonstrate how the symmetries of the Galileon and DBI theories can be made compatible with a nonrelativistic, quadratic dispersion relation of (some of) the NG modes.

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