Gauge Theories and the Standard Model

We continue our research[Formula: see text] and extend the class of finite BRST–anti-BRST transformations with odd-valued parameters [Formula: see text], [Formula: see text], introduced in these works. In doing so, we evaluate the Jacobians induced by finite BRST–anti-BRST transformations linear in functionally-dependent parameters, as well as those induced by finite BRST–anti-BRST transformations with arbitrary functional parameters. The calculations cover the cases of gauge theories with a closed algebra, dynamical systems with first-class constraints, and general gauge theories. The resulting Jacobians in the case of linearized transformations are different from those in the case of polynomial dependence on the parameters. Finite BRST–anti-BRST transformations with arbitrary parameters induce an extra contribution to the quantum action, which cannot be absorbed into a change of the gauge. These transformations include an extended case of functionally-dependent parameters that implies a modified compensation equation, which admits nontrivial solutions leading to a Jacobian equal to unity. Finite BRST–anti-BRST transformations with functionally-dependent parameters are applied to the Standard Model, and an explicit form of functionally-dependent parameters [Formula: see text] is obtained, providing the equivalence of path integrals in any 3-parameter [Formula: see text]-like gauges. The Gribov–Zwanziger theory is extended to the case of the Standard Model, and a form of the Gribov horizon functional is suggested in the Landau gauge, as well as in [Formula: see text]-like gauges, in a gauge-independent way using field-dependent BRST–anti-BRST transformations, and in [Formula: see text]-like gauges using transverse-like non-Abelian gauge fields.

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Gauge Theories and the Standard Model

Astronomy and Astrophysics Library - The Early Universe ◽

10.1007/978-3-662-05267-9_5 ◽

2003 ◽

pp. 203-239

Author(s):

Gerhard Börner

Keyword(s):

Standard Model ◽

Gauge Theories ◽

The Standard Model

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DARK MATTER CANDIDATE FROM CONFORMALITY

Modern Physics Letters A ◽

10.1142/s0217732307022918 ◽

2007 ◽

Vol 22 (13) ◽

pp. 931-937 ◽

Cited By ~ 5

Author(s):

P. H. FRAMPTON

Keyword(s):

Dark Matter ◽

Standard Model ◽

Cross Section ◽

Weak Interaction ◽

Gauge Theories ◽

Dark Matter Candidate ◽

Beyond The Standard Model ◽

The Standard Model ◽

Relic Density ◽

Baryonic Dark Matter

Abelian quiver gauge theories provide candidates for the conformality approach to physics beyond the standard model which possess novel cancellation mechanisms for quadratic divergences. A Z2 symmetry ( R parity) can be imposed and leads naturally to a dark matter candidate which is the Lightest Conformality Particle (LCP), a neutral spin-1 / 2 state with weak interaction annihilation cross-section, mass in the 100 GeV region and relic density of non-baryonic dark matter Ωdm which can be consistent with the observed value Ωdm≃0.24.

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CONSTRAINTS ON UNIFIED GAUGE THEORIES FROM NONCOMMUTATIVE GEOMETRY

Modern Physics Letters A ◽

10.1142/s0217732396002575 ◽

1996 ◽

Vol 11 (32n33) ◽

pp. 2561-2572 ◽

Cited By ~ 18

Author(s):

F. LIZZI ◽

G. MANGANO ◽

G. MIELE ◽

G. SPARANO

Keyword(s):

Standard Model ◽

Noncommutative Geometry ◽

Degrees Of Freedom ◽

Gauge Theories ◽

Gauge Groups ◽

The Standard Model ◽

Number Of Particles

We analyze the possibility to extend the Connes and Lott reformulation of the standard model to larger unified gauge groups. Noncommutative geometry imposes very stringent constraints on the possible theories, and remarkably, the analysis seems to suggest that no larger gauge groups are compatible with the noncommutative structure, unless one enlarges the fermionic degrees of freedom, namely the number of particles.

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Lattice studies of quantum chromodynamics-like theories with many fermionic degrees of freedom

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2010.0380 ◽

2011 ◽

Vol 369 (1946) ◽

pp. 2701-2717 ◽

Cited By ~ 6

Author(s):

Thomas DeGrand

Keyword(s):

Fixed Point ◽

Standard Model ◽

Quantum Chromodynamics ◽

Degrees Of Freedom ◽

Gauge Theories ◽

Gauge Coupling ◽

Higgs Sector ◽

Intrinsic Interest ◽

The Standard Model

I give an elementary introduction to the study of gauge theories coupled to fermions with many degrees of freedom. Besides their intrinsic interest, these theories are candidates for non-perturbative extensions of the Higgs sector of the standard model. While related to quantum chromodynamics, these systems can exhibit very different behaviour from it: they can possess a running gauge coupling with an infrared-attractive fixed point. I briefly survey recent lattice work in this area.

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Dark QCD matters

Journal of High Energy Physics ◽

10.1007/jhep12(2021)139 ◽

2021 ◽

Vol 2021 (12) ◽

Author(s):

Raghuveer Garani ◽

Michele Redi ◽

Andrea Tesi

Keyword(s):

Dark Matter ◽

Standard Model ◽

Structure Formation ◽

Gauge Theories ◽

Initial Temperature ◽

Pion Mass ◽

Dark Sector ◽

Abelian Gauge ◽

The Standard Model

Abstract We investigate the nightmare scenario of dark sectors that are made of non-abelian gauge theories with fermions, gravitationally coupled to the Standard Model (SM). While testing these scenarios is experimentally challenging, they are strongly motivated by the accidental stability of dark baryons and pions, that explain the cosmological stability of dark matter (DM). We study the production of these sectors which are minimally populated through gravitational freeze-in, leading to a dark sector temperature much lower than the SM, or through inflaton decay, or renormalizable interactions producing warmer DM. Despite having only gravitational couplings with the SM these scenarios turn out to be rather predictive depending roughly on three parameters: the dark sector temperature, the confinement scale and the dark pion mass. In particular, when the initial temperature is comparable to the SM one these scenarios are very constrained by structure formation, ∆Neff and limits on DM self-interactions. Dark sectors with same temperature or warmer than SM are typically excluded.

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Gauge Theories and the Standard Model

Particle Physics Reference Library ◽

10.1007/978-3-030-38207-0_2 ◽

2020 ◽

pp. 7-33

Author(s):

Guido Altarelli ◽

Stefano Forte

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Standard Model ◽

Gauge Theories ◽

Quantum Field ◽

Link Type ◽

The Standard Model ◽

Strong Sector ◽

Introductory Textbooks ◽

Symmetry Structure

AbstractThis chapter, Chaps. 10.1007/978-3-030-38207-0_3 and 10.1007/978-3-030-38207-0_4 present a self-contained introduction to the Standard Model of fundamental interactions, which describes in the unified framework of gauge quantum field theories all of the fundamental forces of nature but gravity: the strong, weak, and electromagnetic interactions. This set of chapters thus provides both an introduction to the Standard Model, and to quantum field theory at an intermediate level. The union of the three chapters can be taken as a masters’ level course reference, and it requires as a prerequisite an elementary knowledge of quantum field theory, at the level of many introductory textbooks, such as Vol. 1 of Aitchison-Hey, or, at a somewhat more advanced level, Maggiore. The treatment is subdivided into three parts, each corresponding to an individual chapter, with more advanced field theory topics introduced along the way as needed. Specifically, this chapter presents the general structure of the Standard Model, its field content, and symmetry structure. This involves an introduction to non-abelian gauge theories both at the classical and quantum level. Also, it involves a discussion of spontaneous symmetry breaking and the Higgs mechanism, that play a crucial role in the architecture of the Standard Model, and their interplay with the quantization of gauge theories. Chapter 10.1007/978-3-030-38207-0_3 then presents the electroweak sector of the Standard Model. This requires introducing the concepts of CP violation and mixing, and of radiative corrections. Finally, Chap. 10.1007/978-3-030-38207-0_4 presents the strong sector of the theory, which requires a more detailed treatment of renormalization and the renormalization group.

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