scholarly journals New positivity bounds from full crossing symmetry

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Andrew J. Tolley ◽  
Zi-Yue Wang ◽  
Shuang-Yong Zhou
Keyword(s):  
Field Theory ◽  
Dispersion Relation ◽  
Effective Field Theory ◽  
Scattering Amplitude ◽  
Effective Field ◽  
Field Theories ◽  
Upper And Lower Bounds ◽  
Chiral Perturbation ◽  
Partial Wave Expansion ◽  
Crossing Symmetry

Abstract Positivity bounds are powerful tools to constrain effective field theories. Utilizing the partial wave expansion in the dispersion relation and the full crossing symmetry of the scattering amplitude, we derive several sets of generically nonlinear positivity bounds for a generic scalar effective field theory: we refer to these as the P Q, Dsu, Dstu and $$ {\overline{D}}^{\mathrm{stu}} $$ D ¯ stu bounds. While the PQ bounds and Dsu bounds only make use of the s↔u dispersion relation, the Dstu and $$ {\overline{D}}^{\mathrm{stu}} $$ D ¯ stu bounds are obtained by further imposing the s↔t crossing symmetry. In contradistinction to the linear positivity for scalars, these inequalities can be applied to put upper and lower bounds on Wilson coefficients, and are much more constraining as shown in the lowest orders. In particular we are able to exclude theories with soft amplitude behaviour such as weakly broken Galileon theories from admitting a standard UV completion. We also apply these bounds to chiral perturbation theory and we find these bounds are stronger than the previous bounds in constraining its Wilson coefficients.

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 Chiral Perturbation Theory at NNNLO

Symmetry ◽  
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.

scholarly journals On the development of effective field theory

2021 ◽  
Author(s):  
Steven Weinberg
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Particle Physics ◽  
Effective Field ◽  
Early History ◽  
First Century ◽  
Field Theories ◽  
Theory Approach ◽  
Seminar Series ◽  
History Of

AbstractEditor’s note: One of the most important developments in theoretical particle physics at the end of the 20th century and beginning of the twenty-first century has been the development of effective field theories (EFTs). Pursuing an effective field theory approach is a methodology for constructing theories, where a set of core principles is agreed upon, such as Lorentz symmetry and unitarity, and all possible interactions consistent with them are then compulsory in the theory. The utility of this approach to particle physics (and beyond) is wide ranging and undisputed, as evidenced by the recent formation of the international seminar series All Things EFT (Talks in the series can be viewed at https://www.youtube.com/channel/UC1_KF6kdJFoDEcLgpcegwCQ (accessed 21 December 2020).) which brings together each week the worldwide community of EFT practitioners. The text below is a lightly edited version of the talk given by Prof. Weinberg on September 30, 2020, which inaugurated the series. The talk reviews some of the early history of EFTs from the perspective of its pioneer and concludes with a discussion of EFT implications for future discovery.

scholarly journals Operator bases in effective field theories with sterile neutrinos: d ≤ 9

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Hao-Lin Li ◽  
Zhe Ren ◽  
Ming-Lei Xiao ◽  
Jiang-Hao Yu ◽  
Yu-Hui Zheng
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Effective Field ◽  
Lepton Number ◽  
Low Energy ◽  
Field Theories ◽  
Sterile Neutrinos ◽  
Two Generations ◽  
Mass Dimension ◽  
Physical Effects

Abstract We obtain the complete and independent bases of effective operators at mass dimension 5, 6, 7, 8, 9 in both standard model effective field theory with light sterile right-handed neutrinos (νSMEFT) and low energy effective field theory with light sterile neutrinos (νLEFT). These theories provide systematical parametrizations on all possible Lorentz-invariant physical effects involving in the Majorana/Dirac neutrinos, with/without the lepton number violations. In the νSMEFT, we find that there are 2 (18), 29 (1614), 80 (4206), 323 (20400), 1358 (243944) independent operators with sterile neutrinos included at the dimension 5, 6, 7, 8, 9 for one (three) generation of fermions, while 24, 5223, 3966, 25425, 789426 independent operators in the νLEFT for two generations of up-type quarks and three generations of all other fermions.

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.

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