scholarly journals A new gauge-invariant double copy for heavy-mass effective theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Andreas Brandhuber ◽  
Gang Chen ◽  
Gabriele Travaglini ◽  
Congkao Wen
Keyword(s):  
Effective Field ◽  
Field Theories ◽  
Effective Theory ◽  
Leading Order ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Crossing Symmetry ◽  
New Form ◽  
Set Up ◽  
Double Copy

Abstract We propose a new form of the colour-kinematics/double-copy duality for heavy-mass effective field theories, which we apply to construct compact expressions for tree amplitudes with heavy matter particles in Yang-Mills and in gravity to leading order in the mass. In this set-up, the new BCJ numerators are fixed uniquely and directly written in terms of field strengths, making gauge invariance manifest. Furthermore, they are local and automatically satisfy the Jacobi relations and crossing symmetry. We construct these BCJ numerators explicitly up to six particles. We also discuss relations of the BCJ numerators in the heavy-mass effective theory with those in pure Yang-Mills amplitudes.

scholarly journals Massive gravity from double copy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Arshia Momeni ◽  
Justinas Rumbutis ◽  
Andrew J. Tolley
Keyword(s):  
Sigma Model ◽  
Massive Gravity ◽  
Effective Field ◽  
Effective Theory ◽  
Nonlinear Sigma Model ◽  
Limit Theory ◽  
Four Dimensions ◽  
Yang Mills ◽  
Massive Spin ◽  
Double Copy

Abstract We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a Λ3 = (m2MPl)1/3 cutoff. We construct explicitly the Λ3 decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ3 massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.

scholarly journals Classical gravitational scattering from a gauge-invariant double copy

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Andreas Brandhuber ◽  
Gang Chen ◽  
Gabriele Travaglini ◽  
Congkao Wen
Keyword(s):  
Massive Particle ◽  
Radiation Reaction ◽  
Effective Field ◽  
Effective Theory ◽  
Tree Level ◽  
Theory Approach ◽  
Gauge Invariant ◽  
Scattering Angle ◽  
Four Dimensions ◽  
Double Copy

Abstract We propose a method to compute the scattering angle for classical black hole scattering directly from two massive particle irreducible diagrams in a heavy-mass effective field theory approach to general relativity, without the need of subtracting iteration terms. The amplitudes in this effective theory are constructed using a recently proposed novel colour-kinematic/double copy for tree-level two-scalar, multi-graviton amplitudes, where the BCJ numerators are gauge invariant and local with respect to the massless gravitons. These tree amplitudes, together with graviton tree amplitudes, enter the construction of the required D-dimensional loop integrands and allow for a direct extraction of contributions relevant for classical physics. In particular the soft/heavy-mass expansions of full integrands is circumvented, and all iterating contributions can be dropped from the get go. We use this method to compute the scattering angle up to third post-Minkowskian order in four dimensions, including radiation reaction contributions, also providing the expression of the corresponding integrand in D dimensions.

scholarly journals Predictive physics of inflation and grand unification for and from the CMB observations

2020 ◽  
Vol 35 (17) ◽  
pp. 2030008
Author(s):  
Norma G. Sanchez
Keyword(s):  
Effective Field Theories ◽  
Particle Physics ◽  
Effective Field ◽  
Energy Scale ◽  
Field Theories ◽  
Effective Theory ◽  
Grand Unification ◽  
Physical Approach ◽  
New Learning ◽  
The Future

This paper focuses on realistic and timely situations of inflation in connection with the CMB, gravitational and particle physics, adding interdisciplinarity and unification values within a strongly predictive physical approach. The formulation of inflation in the Ginsburg–Landau approach developed by de Vega and Sanchez1 and by Boyanovsky, de Vega, Sanchez and Destri[Formula: see text] clarifies and places inflation in the setting of the effective field theories of particle physics. In addition, it sets up a clean way to directly confront the inflationary predictions with the available and forthcoming CMB data and select a definitive model. All CMB[Formula: see text]+[Formula: see text]LSS data until now show how powerful is the Ginsburg–Landau effective theory of inflation in predicting observables in agreement with observations, including the inflation energy scale and the inflaton potential, and which has much more to provide in the future. It paves the way to discoveries, new learning and understanding.

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 General non-leptonic ∆F = 1 WET at the NLO in QCD

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Jason Aebischer ◽  
Christoph Bobeth ◽  
Andrzej J. Buras ◽  
Jacky Kumar ◽  
Mikołaj Misiak
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Effective Field Theory ◽  
High Energy ◽  
Effective Field ◽  
Effective Theory ◽  
Leading Order ◽  
The Standard Model ◽  
Complete Set ◽  
The One

Abstract We reconsider the complete set of four-quark operators in the Weak Effective Theory (WET) for non-leptonic ∆F = 1 decays that govern s → d and b → d, s transitions in the Standard Model (SM) and beyond, at the Next-to-Leading Order (NLO) in QCD. We discuss cases with different numbers Nf of active flavours, intermediate threshold corrections, as well as the issue of transformations between operator bases beyond leading order to facilitate the matching to high-energy completions or the Standard Model Effective Field Theory (SMEFT) at the electroweak scale. As a first step towards a SMEFT NLO analysis of K → ππ and non-leptonic B-meson decays, we calculate the relevant WET Wilson coefficients including two-loop contributions to their renormalization group running, and express them in terms of the Wilson coefficients in a particular operator basis for which the one-loop matching to SMEFT is already known.

Effective Field Theories for Heavy Quarks: Heavy Quark Effective Theory and Heavy Quark Expansion

2020 ◽  
pp. 560-615
Author(s):  
Thomas Mannel
Keyword(s):  
Heavy Quark ◽  
Particle Physics ◽  
Operator Product Expansion ◽  
Effective Field ◽  
Field Theories ◽  
Effective Theory ◽  
Tree Level ◽  
Operator Product ◽  
Heavy Quark Effective Theory ◽  
Inclusive Decays

The heavy quark effective theory (HQET) and the heavy quark expansion (HQE) have developed into the standard tools in heavy-flavour physics. The lectures in this chapter introduce the basics of the approach and illustrates the methods by discussing some of their phenomenological applications. The chapter covers construction of the HQET Lagrangian, symmetries of HQET, HQET at one loop, and HQET applications to phenomenology. It also discusses HQE inclusive decays, operator product expansion (OPE), tree-level results, HQE parameters, QCD corrections, and end-point regions. It concludes by reiterating the enormous impact that both HQET and the HQE have had on particle physics phenomenology.

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.

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.

scholarly journals QCD in a moving frame: an exploratory study

2018 ◽  
Vol 175 ◽  
pp. 14012 ◽  
Author(s):  
Mattia Dalla Brida ◽  
Leonardo Giusti ◽  
Michele Pepe
Keyword(s):  
Boundary Conditions ◽  
High Accuracy ◽  
Field Theories ◽  
Moving Frame ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Yang Mills ◽  
First Results ◽  
Set Up

The framework of shifted boundary conditions has proven to be a very powerful tool for the non-perturbative investigation of thermal quantum field theories. For instance, it has been successfully considered for the determination of the equation of state of SU(3) Yang-Mills theory with high accuracy. The set-up can be generalized to QCD and it is expected to lead to a similar breakthrough. We present first results for QCD with three flavours of non-perturbatively O(a)-improved Wilson fermions and shifted boundary conditions.

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