scholarly journals ELECTROWEAK THEORY WITH A MINIMAL LENGTH

2011 ◽  
Vol 26 (24) ◽  
pp. 4251-4285 ◽  
Author(s):  
MARTIN KOBER
Keyword(s):  
Standard Model ◽  
Gauge Group ◽  
Gauge Theories ◽  
Generalized Uncertainty Principle ◽  
Z Bosons ◽  
Minimal Length ◽  
Electroweak Theory ◽  
Yang Mills ◽  
Interaction Terms ◽  
The Standard Model

According to the introduction of a minimal length to quantum field theory, which is directly related to a generalized uncertainty principle, the implementation of the gauge principle becomes much more intricated. It has been shown in another paper how gauge theories have to be extended in general, if there is assumed the existence of a minimal length. In this paper this generalization of the description of gauge theories is applied to the case of Yang–Mills theories with gauge group SU(N) to consider especially the application to the electroweak theory as it appears in the Standard Model. The modifications of the lepton-, Higgs- and gauge field sector of the extended Lagrangian of the electroweak theory maintaining local gauge invariance under SU(2)L ⊗ U(1)Y transformations are investigated. There appear additional interaction terms between the leptons or the Higgs particle respectively with the photon and the W- and Z-bosons as well as additional self-interaction terms of these gauge bosons themselves. It is remarkable that in the quark sector where the full gauge group of the Standard Model, SU(3)c ⊗ SU(2)L ⊗ U(1)Y, has to be considered there arise coupling terms between the gluons und the W- and Z-bosons which means that the electroweak theory is not separated from quantum chromodynamics anymore.

scholarly journals Progress on Proving the Mass gap for Yang Mills and Gravity (Maybe it’s already proven…)

2020 ◽  
Author(s):  
Stephane Maes
Keyword(s):  
Standard Model ◽  
Open Problem ◽  
Gauge Theories ◽  
Yang Mills ◽  
Mass Gap ◽  
Discrete Spacetime ◽  
Lattice Cell ◽  
The Standard Model ◽  
Fractional Dimensions ◽  
Real Universe

Proving and constructing viable Yang Mills Gauge is a key concern for the Standard Model and an open problem. It has only be solved on lattices. Yet, gravity is not modeled in the Standard Model. We discuss that in a multi-fold universe where gravity emerges from entanglement effects, the spacetime is discrete (fractal with fractional dimensions, noncommutative and still Lorentz invariant). For any Lorentz invariant discrete spacetime, the lattice proofs and their lattice cell size independence completes the proof of the mass gap for Yang Mills Gauge theories. Continuous spacetime may or may not have a mass gap; but it does not matter if the real universe is discrete and Lorentz invariant.

The Standard Model of Particle Physics

2015 ◽  
Vol 23 (1) ◽  
pp. 36-44 ◽  
Author(s):  
Tom W.B. Kibble
Keyword(s):  
Standard Model ◽  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Gauge Theories ◽  
Personal Perspective ◽  
Electroweak Theory ◽  
Higgs Particle ◽  
Historical Account ◽  
The Standard Model ◽  
Nuclear Interactions

This is a historical account from my personal perspective of the development over the last few decades of the standard model of particle physics. The model is based on gauge theories, of which the first was quantum electrodynamics, describing the interactions of electrons with light. This was later incorporated into the electroweak theory, describing electromagnetic and weak nuclear interactions. The standard model also includes quantum chromodynamics, the theory of the strong nuclear interactions. The final capstone of the model was the Higgs particle discovered in 2012 at CERN. But the model is very far from being the last word; there are still many gaps in our understanding.

scholarly journals Standard model from a supergravity model with a naturally small cosmological constant

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Shing Yan Li ◽  
Yu-Cheng Qiu ◽  
S.-H. Henry Tye
Keyword(s):  
String Theory ◽  
Standard Model ◽  
Cosmological Constant ◽  
Supersymmetry Breaking ◽  
Supersymmetric Standard Model ◽  
Degrees Of Freedom ◽  
Interaction Terms ◽  
Supersymmetric Version ◽  
The Standard Model ◽  
Linear Version

Abstract Guided by the naturalness criterion for an exponentially small cosmological constant, we present a string theory motivated 4-dimensional $$ \mathcal{N} $$ N = 1 non-linear supergravity model (or its linear version with a nilpotent superfield) with spontaneous supersymmetry breaking. The model encompasses the minimal supersymmetric standard model, the racetrack Kähler uplift, and the KKLT anti-D3-branes, and use the nilpotent superfield to project out the undesirable interaction terms as well as the unwanted degrees of freedom to end up with the standard model (not the supersymmetric version) of strong and electroweak interactions.

scholarly journals WHAT IS A MATTER PARTICLE?

2006 ◽  
Vol 15 (01) ◽  
pp. 259-272
Author(s):  
TSAN UNG CHAN
Keyword(s):  
Standard Model ◽  
Weak Interaction ◽  
Strong Interaction ◽  
Neutral Particle ◽  
Z Bosons ◽  
Baryon Number ◽  
Lepton Number ◽  
Neutral Particles ◽  
The Standard Model ◽  
The Stability

Positive baryon numbers (A>0) and positive lepton numbers (L>0) characterize matter particles while negative baryon numbers and negative lepton numbers characterize antimatter particles. Matter particles and antimatter particles belong to two distinct classes of particles. Matter neutral particles are particles characterized by both zero baryon number and zero lepton number. This third class of particles includes mesons formed by a quark and an antiquark pair (a pair of matter particle and antimatter particle) and bosons which are messengers of known interactions (photons for electromagnetism, W and Z bosons for the weak interaction, gluons for the strong interaction). The antiparticle of a matter particle belongs to the class of antimatter particles, the antiparticle of an antimatter particle belongs to the class of matter particles. The antiparticle of a matter neutral particle belongs to the same class of matter neutral particles. A truly neutral particle is a particle identical with its antiparticle; it belongs necessarily to the class of matter neutral particles. All known interactions of the Standard Model conserve baryon number and lepton number; matter cannot be created or destroyed via a reaction governed by these interactions. Conservation of baryon and lepton number parallels conservation of atoms in chemistry; the number of atoms of a particular species in the reactants must equal the number of those atoms in the products. These laws of conservation valid for interaction involving matter particles are indeed valid for any particles (matter particles characterized by positive numbers, antimatter particles characterized by negative numbers, and matter neutral particles characterized by zero). Interactions within the framework of the Standard Model which conserve both matter and charge at the microscopic level cannot explain the observed asymmetry of our Universe. The strong interaction was introduced to explain the stability of nuclei: there must exist a powerful force to compensate the electromagnetic force which tends to cause protons to fly apart. The weak interaction with laws of conservation different from electromagnetism and the strong interaction was postulated to explain beta decay. Our observed material and neutral universe would signify the existence of another interaction that did conserve charge but did not conserve matter.

A Clifford algebra-based grand unification program of gravity and the Standard Model: a review study

2014 ◽  
Vol 92 (12) ◽  
pp. 1501-1527 ◽  
Author(s):  
Carlos Castro
Keyword(s):  
Standard Model ◽  
Geometric Probability ◽  
Coupling Constants ◽  
Grand Unified Theory ◽  
Neutrino Mixing ◽  
Yang Mills ◽  
Bounded Complex ◽  
The Standard Model ◽  
Mixing Matrix ◽  
Homogeneous Domains

A Clifford Cl(5, C) unified gauge field theory formulation of conformal gravity and U(4) × U(4) × U(4) Yang–Mills in 4D, is reviewed along with its implications for the Pati–Salam (PS) group SU(4) × SU(2)L × SU(2)R, and trinification grand unified theory models of three fermion generations based on the group SU(3)C × SU(3)L × SU(3)R. We proceed with a brief review of a unification program of 4D gravity and SU(3) × SU(2) × U(1) Yang–Mills emerging from 8D pure quaternionic gravity. A realization of E8 in terms of the Cl(16) = Cl(8) ⊗ Cl(8) generators follows, as a preamble to F. Smith’s E8 and Cl(16) = Cl(8) ⊗ Cl(8) unification model in 8D. The study of chiral fermions and instanton backgrounds in CP2 and CP3 related to the problem of obtaining three fermion generations is thoroughly studied. We continue with the evaluation of the coupling constants and particle masses based on the geometry of bounded complex homogeneous domains and geometric probability theory. An analysis of neutrino masses, Cabbibo–Kobayashi–Maskawa quark-mixing matrix parameters, and neutrino-mixing matrix parameters follows. We finalize with some concluding remarks about other proposals for the unification of gravity and the Standard Model, like string, M, and F theories and noncommutative and nonassociative geometry.

scholarly journals The Standard Model vs. Physical Facts

2020 ◽  
pp. 1-12
Author(s):  
E. Comay
Keyword(s):  
Standard Model ◽  
Quantum Chromodynamics ◽  
Particle Physics ◽  
Scientific Theory ◽  
Electroweak Theory ◽  
Relevant Theory ◽  
The Standard Model ◽  
Physics Literature ◽  
Fundamental Physical ◽  
Physical Principles

Dynamical sectors of the Standard Model of particle physics are critically analyzed. It is proved thatquantum electrodynamics, quantum chromodynamics, and the electroweak theory are inconsistentwith fundamental physical principles. More than two examples apply to each of these theories, andany of these examples substantiate the unacceptable status of the relevant theory. Unfortunately,the mainstream particle physics literature ignores this situation and glorifies the Standard Modelas an excellent scientific theory.

scholarly journals Zeros of amplitude in the associated production of photon and leptoquark at $$\varvec{e}$$-$$\varvec{p}$$ collider

2021 ◽  
Vol 81 (4) ◽  
Author(s):  
Priyotosh Bandyopadhyay ◽  
Saunak Dutta ◽  
Anirban Karan
Keyword(s):  
Standard Model ◽  
Gauge Group ◽  
Single Photon ◽  
Tree Level ◽  
Associated Production ◽  
The Standard Model ◽  
Radiation Amplitude ◽  
Complementary Set

AbstractThough various extensions of the Standard Model with higher gauge group predict the existence of leptoquarks, none of them has been observed yet at any of the colliders. In this paper, we study the prospect of several past and future $$e$$ e -$$p$$ p colliders like HERA, LHeC and FCC-he to detect them through radiation amplitude zero. We find that the leptoquarks showing zeros in the tree-level single-photon amplitudes at $$e$$ e -$$p$$ p collider lie within the complementary set of those exhibiting zeros at e-$$\gamma $$ γ collider. We present a PYTHIA-based analysis for HERA, LHeC and FCC-he (run II) to detect the leptoquarks with masses 70 GeV, 900 GeV and 1.5 TeV (2.0 TeV) respectively through radiation amplitude zero.

Complexification of the Exceptional Jordan Algebra and Its Application to Particle Physics

2021 ◽  
Vol 61 ◽  
pp. 1-16
Author(s):  
Daniele Corradetti ◽  
Keyword(s):  
Standard Model ◽  
Gauge Group ◽  
Jordan Algebra ◽  
Particle Physics ◽  
Compact Form ◽  
Symmetric Extension ◽  
Grand Unified Theories ◽  
The Standard Model ◽  
Unified Theories ◽  
Standard Model Gauge Group

Recent papers contributed revitalizing the study of the exceptional Jordan algebra $\mathfrak{h}_{3}(\mathbb{O})$ in its relations with the true Standard Model gauge group $\mathrm{G}_{SM}$. The absence of complex representations of $\mathrm{F}_{4}$ does not allow $\Aut\left(\mathfrak{h}_{3}(\mathbb{O})\right)$ to be a candidate for any Grand Unified Theories, but the automorphisms of the complexification of this algebra, i.e., $\mathfrak{h}_{3}^{\mathbb{C}}(\mathbb{O})$, are isomorphic to the compact form of $\mathrm{E}_{6}$ and similar constructions lead to the gauge group of the minimal left-right symmetric extension of the Standard Model.

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