scholarly journals The Feynman rules for the SMEFT in the background field gauge

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Tyler Corbett
Keyword(s):  
Background Field ◽  
Field Method ◽  
Effective Field ◽  
Ward Identities ◽  
The Standard Model ◽  
Gauge Fixing ◽  
Feynman Rules ◽  
Supplementary Material ◽  
Background Field Method ◽  
Mass Terms

Abstract We present a package for FeynRules which derives the Feynman rules for the Standard Model Effective Field Theory up to dimension-six using the background field method for gauge fixing. The package includes operators which shift the kinetic and mass terms of the Lagrangian up to dimension-eight and including dimension-six squared effects consistently. To the best of the author’s knowledge this is the first publicly available package to include dimension-six squared effects consistently. The package is validated in a partner publication by analyzing the Ward Identities at dimension-six and one-loop order. We also extend the partner work in this article by including the dimension-six squared effects further demonstrating the consistency of their implementation. In doing so we find that failure to consistently include field shifts to dimension-six squared causes a breakdown in the Ward identities implying concerns about many calculations in the literature which do not properly incorporate these effects.The FeynRules files, as well as Mathematica notebooks performing the relevant calculations, can be downloaded from the FeynRules website and are included as supplementary material to this publication.

scholarly journals Consistent higher order $$ \sigma \left(\mathcal{GG}\to h\right) $$, $$ \Gamma \left(h\to \mathcal{GG}\right) $$ and Γ(h → γγ) in geoSMEFT

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Tyler Corbett ◽  
Adam Martin ◽  
Michael Trott
Keyword(s):  
Background Field ◽  
Field Method ◽  
Effective Field ◽  
Leading Order ◽  
The Standard Model ◽  
Gauge Fixing ◽  
Complete Set ◽  
Background Field Method ◽  
The One ◽  
Geometric Formulation

Abstract We report consistent results for Γ(h → γγ), $$ \sigma \left(\mathcal{GG}\to h\right) $$ σ GG → h and $$ \Gamma \left(h\to \mathcal{GG}\right) $$ Γ h → GG in the Standard Model Effective Field Theory (SMEFT) perturbing the SM by corrections $$ \mathcal{O}\left({\overline{\upsilon}}_T^2/16{\pi}^2{\Lambda}^2\right) $$ O υ ¯ T 2 / 16 π 2 Λ 2 in the Background Field Method (BFM) approach to gauge fixing, and to $$ \mathcal{O}\left({\overline{\upsilon}}_T^4/{\Lambda}^4\right) $$ O υ ¯ T 4 / Λ 4 using the geometric formulation of the SMEFT. We combine and modify recent results in the literature into a complete set of consistent results, uniforming conventions, and simultaneously complete the one loop results for these processes in the BFM. We emphasize calculational scheme dependence present across these processes, and how the operator and loop expansions are not independent beyond leading order. We illustrate several cross checks of consistency in the results.

scholarly journals NONCOMMUTATIVITY AND NON-ANTICOMMUTATIVITY PERTURBATIVE QUANTUM GRAVITY

2012 ◽  
Vol 27 (13) ◽  
pp. 1250075 ◽  
Author(s):  
MIR FAIZAL
Keyword(s):  
Quantum Gravity ◽  
Lagrangian Density ◽  
Background Field ◽  
Field Method ◽  
Gauge Fixing ◽  
Perturbative Quantum ◽  
Background Field Method

In this paper, we will study perturbative quantum gravity on supermanifolds with both noncommutativity and non-anticommutativity of spacetime coordinates. We shall first analyze the BRST and the anti-BRST symmetries of this theory. Then we will also analyze the effect of shifting all the fields of this theory in background field method. We will construct a Lagrangian density which apart from being invariant under the extended BRST transformations is also invariant under on-shell extended anti-BRST transformations. This will be done by using the Batalin–Vilkovisky (BV) formalism. Finally, we will show that the sum of the gauge-fixing term and the ghost term for this theory can be elegantly written down in superspace with a two Grassmann parameter.

scholarly journals A FORMULATION OF THE YANG–MILLS THEORY AS A DEFORMATION OF A TOPOLOGICAL FIELD THEORY BASED ON THE BACKGROUND FIELD METHOD AND QUARK CONFINEMENT PROBLEM

2001 ◽  
Vol 16 (07) ◽  
pp. 1303-1346 ◽  
Author(s):  
KEI-ICHI KONDO
Keyword(s):  
Field Theory ◽  
Magnetic Monopole ◽  
Background Field ◽  
Field Method ◽  
Quark Confinement ◽  
Mass Generation ◽  
Yang Mills ◽  
Topological Quantum ◽  
Gauge Fixing ◽  
Background Field Method

By making use of the background field method, we derive a novel reformulation of the Yang–Mills theory which was proposed recently by the author to derive quark confinement in QCD. This reformulation identifies the Yang–Mills theory with a deformation of a topological quantum field theory. The relevant background is given by the topologically nontrivial field configuration, especially, the topological soliton which can be identified with the magnetic monopole current in four dimensions. We argue that the gauge fixing term becomes dynamical and that the gluon mass generation takes place by a spontaneous breakdown of the hidden supersymmetry caused by the dimensional reduction. We also propose a numerical simulation to confirm the validity of the scheme we have proposed. Finally we point out that the gauge fixing part may have a geometric meaning from the viewpoint of global topology where the magnetic monopole solution represents the critical point of a Morse function in the space of field configurations.

Convex decomposition of the gauge field and background-field quantization

1992 ◽  
Vol 70 (6) ◽  
pp. 470-474 ◽  
Author(s):  
N. C. A. Hill
Keyword(s):  
Gauge Field ◽  
Background Field ◽  
Field Method ◽  
Point Function ◽  
Yang Mills ◽  
Convex Decomposition ◽  
Perturbative Method ◽  
Gauge Fixing ◽  
The Matrix ◽  
Background Field Method

The 1PI (one-particle-irreducible) two-point function of a pure Yang–Mills gauge theory is computed. The background-field method is employed in a slightly altered form that makes use of the convexity of the space of gauge fields. It is shown how this avoids the singularity of the matrix ∂2S/∂V∂V thereby allowing the calculation of the Gaussian integral in the generating functional without having to fix the gauge. It is also shown how, when it comes to actually calculating the 1PI two-point function by a perturbative method, a singularity in a particular term, [Formula: see text] of the total matrix [Formula: see text] necessitates the introduction of a gauge-fixing term. The 1PI two-point function is shown to be identical to that of the conventional background-field method except for the presence of a new parameter, t, introduced by the convex decomposition of the gauge field.

scholarly journals SUPERGRAVITY IN 2+∊ DIMENSIONS

1994 ◽  
Vol 09 (31) ◽  
pp. 5415-5444 ◽  
Author(s):  
SHIN-ICHI KOJIMA ◽  
NORISUKE SAKAI ◽  
YOSHIAKI TANII
Keyword(s):  
Fixed Point ◽  
Dimensional Reduction ◽  
Background Field ◽  
Field Method ◽  
Three Dimensions ◽  
Supergravity Theory ◽  
Anomalous Dimensions ◽  
Gauge Fixing ◽  
Background Field Method

Supergravity theory in 2+∊ dimensions is studied. It is invariant under supertransformations in two and three dimensions. One-loop divergence is explicitly computed by the background field method and a nontrivial fixed point is found. In quantizing the supergravity, a gauge-fixing condition is devised which explicitly isolates conformal and superconformal modes. The renormalization of the gravitationally dressed operators is studied and their anomalous dimensions are computed. Problems in using the dimensional reduction are also examined.

scholarly journals GAUGE FIXING IDENTITY IN THE BACKGROUND FIELD METHOD OF QCD IN PURE GAUGE

2010 ◽  
Vol 25 (20) ◽  
pp. 3885-3898
Author(s):  
GOURANGA C. NAYAK
Keyword(s):  
Background Field ◽  
Heavy Ion ◽  
High Energy ◽  
Field Method ◽  
Coulomb Gauge ◽  
Factorization Theorem ◽  
Pure Gauge ◽  
Gauge Fixing ◽  
Covariant Gauge ◽  
Background Field Method

In this paper we derive a gauge fixing identity by varying the covariant gauge fixing term in [Formula: see text] in the background field method of QCD in pure gauge. Using this gauge fixing identity, we establish a relation between [Formula: see text] in QCD and [Formula: see text] in background field method of QCD in pure gauge. We show the validity of this gauge fixing identity, in general noncovariant and general Coulomb gauge fixings respectively. This gauge fixing identity is used to prove factorization theorem in QCD at high energy colliders and in nonequilibrium QCD at high energy heavy-ion colliders.

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