Supersymmetric quantum field theory (QFT): Introduction

Supersymmetry has been proposed, in particular as a principle to solve the so-called fine-tuning problem in particle physics by relating the masses of scalar particles (like Higgs fields) to those of fermions, which can be protected against ‘large’ mass renormalization by chiral symmetry. However, supersymmetry is, at best, an approximate symmetry broken at a scale beyond the reach of a large hadron collider (LHC), because the possible supersymmetric partners of known particles have not been discovered yet (2020) and thus, if they exist, must be much heavier. Exact supersymmetry would also have implied the vanishing of the vacuum energy and thus, of the cosmological constant. The discovery of dark energy has a natural interpretation as resulting from a very small cosmological constant. However, a naive model based on broken supersymmetry would still predict 60 orders of magnitude too large a value compared to 120 orders of magnitude otherwise. Gauging supersymmetry leads naturally to a unification with gravity, because the commutators of supersymmetry currents involve the energy momentum tensor. First, examples of supersymmetric theories involving scalar superfields, simple generalizations of supersymmetric quantum mechanics (QM) are described. The new feature of supersymmetry in higher dimensions is the combination of supersymmetry with spin, since fermions have spins. In four dimensions, theories with chiral scalar fields and vector fields are constructed.

DARK MATTER AND DARK ENERGY - FACT OR FANTASY?

10.1142/s0217751x04022554 ◽

2004 ◽

Vol 19 (31) ◽

pp. 5333-5333

Author(s):

PHILIP MANNHEIM

Keyword(s):

Dark Matter ◽

Dark Energy ◽

Cosmological Constant ◽

Particle Physics ◽

Einstein Gravity ◽

Fine Tuning ◽

Accelerating Universe ◽

Conformal Invariant ◽

Invariant Metric ◽

Conformal Theory

We show that the origin of the dark matter and dark energy problems originates in the assumption of standard Einstein gravity that Newton's constant is fundamental. We discuss an alternate, conformal invariant, metric theory of gravity in which Newton's constant is induced dynamically, with the global induced one which is effective for cosmology being altogether weaker than the local induced one needed for the solar system. We find that in the theory dark matter is no longer needed, and that the accelerating universe data can be fitted without fine-tuning using a cosmological constant as large as particle physics suggests. In the conformal theory then it is not the cosmological constant which is quenched but rather the amount of gravity that it produces.

ON WEYL COSMOLOGY IN FIVE DIMENSIONS AND THE COSMOLOGICAL CONSTANT

10.1142/s0217751x09044899 ◽

2009 ◽

Vol 24 (08n09) ◽

pp. 1505-1509 ◽

Cited By ~ 14

Author(s):

JOSE EDGAR MADRIZ AGUILAR ◽

CARLOS ROMERO

Keyword(s):

Cosmological Constant ◽

Energy Momentum Tensor ◽

Constant Term ◽

Momentum Tensor ◽

Five Dimensions ◽

Four Dimensions ◽

Riemannian Spacetime ◽

Matter Theory ◽

Induced Matter ◽

Weyl Scalar

In this talk notes we expose the possibility to induce the cosmological constant from extra dimensions from a geometrical framework where our four-dimensional Riemannian spacetime is embedded into a five-dimensional Weyl integrable space. In particular following the approach of the induced matter theory (IMT) we show that when we go down from five to four dimensions we may recover the induced energy momentum tensor of the IMT plus a cosmological constant term that is determined by the presence of the Weyl scalar field on the bulk.

A statistical analysis of the minimal SUSY B–L theory

10.1142/s0217732315500856 ◽

2015 ◽

Vol 30 (18) ◽

pp. 1550085 ◽

Cited By ~ 9

Author(s):

Burt A. Ovrut ◽

Austin Purves ◽

Sogee Spinner

Keyword(s):

Particle Physics ◽

Initial Conditions ◽

Initial Point ◽

Low Energy ◽

Fine Tuning ◽

Large Set ◽

Statistical Sampling ◽

Renormalization Group Equations ◽

Complete Set ◽

The structure of the B–L minimal supersymmetric Standard Model (MSSM) theory — specifically, the relevant mass scales and soft supersymmetric breaking parameters — is discussed. The space of initial soft parameters is explored at the high scale using random statistical sampling subject to a constraint on the range of dimensionful parameters. For every chosen initial point, the complete set of renormalization group equations is solved. The low energy results are then constrained to be consistent with present experimental data. It is shown that a large set of initial conditions satisfy these constraints and lead to acceptable low energy particle physics. Each such initial point has explicit predictions, such as the exact physical sparticle spectrum which is presented for two such points. There are also statistical predictions for the masses of the sparticles and the LSP species which are displayed as histograms. Finally, the fine-tuning of the μ parameter — which is always equivalent to or smaller than in the MSSM — is discussed.

The Discovery of a Higgs Particle at the Large Hadron Collider

European Review ◽

10.1017/s1062798714000544 ◽

2015 ◽

Vol 23 (1) ◽

pp. 57-70

Author(s):

Aleandro Nisati

Keyword(s):

Higgs Boson ◽

Large Hadron Collider ◽

Standard Model ◽

Particle Physics ◽

Hadron Collider ◽

Scientific Programme ◽

Fundamental Particle ◽

The Standard Model ◽

8 Tev ◽

The Large Hadron Collider (LHC) at CERN is the highest energy machine for particle physics research ever built. In the years 2010–2012 this accelerator has collided protons to a centre-mass-energy up to 8 TeV (note that 1 TeV corresponds to the energy of about 1000 protons at rest; the mass of one proton is about 1.67×10–24 g). The events delivered by the LHC have been collected and analysed by four apparatuses placed alongside this machine. The search for the Higgs boson predicted by the Standard Model and the search for new particles and fields beyond this theory represent the most important points of the scientific programme of the LHC. In July 2012, the international collaborations ATLAS and CMS, consisting of more than 3000 physicists, announced the discovery of a new neutral particle with a mass of about 125 GeV, whose physics properties are compatible, within present experimental and theoretical uncertainties, to the Higgs boson predicted by the Standard Model. This discovery represents a major milestone for particle physics, since it indicates that the hypothesized Higgs mechanism seems to be responsible for the masses of elementary particles, in particular W± and Z0 bosons, as well as fermions (leptons and quarks). The 2013 Physics Nobel Prize has been assigned to F. Englert and P. Higgs, ‘for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which recently was confirmed through the discovery of the predicted fundamental particle, by the ATLAS and CMS experiments at CERN's Large Hadron Collider’.

Brief history for the search and discovery of the Higgs particle — A personal perspective

10.1142/s0217751x14300622 ◽

2014 ◽

Vol 29 (27) ◽

pp. 1430062 ◽

Cited By ~ 1

Author(s):

Sau Lan Wu

Keyword(s):

Higgs Boson ◽

Large Hadron Collider ◽

Physics Education ◽

Particle Physics ◽

Hadron Collider ◽

Personal Perspective ◽

Atlas Collaboration ◽

Higgs Particle ◽

History Of ◽

In 1964, a new particle was proposed by several groups to answer the question of where the masses of elementary particles come from; this particle is usually referred to as the Higgs particle or the Higgs boson. In July 2012, this Higgs particle was finally found experimentally, a feat accomplished by the ATLAS Collaboration and the CMS Collaboration using the Large Hadron Collider at CERN. It is the purpose of this review to give my personal perspective on a brief history of the experimental search for this particle since the '80s and finally its discovery in 2012. Besides the early searches, those at the LEP collider at CERN, the Tevatron Collider at Fermilab, and the Large Hadron Collider at CERN are described in some detail. This experimental discovery of the Higgs boson is often considered to be one of the most important advances in particle physics in the last half a century, and some of the possible implications are briefly discussed. This review is based on a talk presented by the author at the conference "OCPA8 International Conference on Physics Education and Frontier Physics," the 8th Joint Meeting of Chinese Physicists Worldwide, Nanyang Technological University, Singapore, June 23–27, 2014.

Brief history for the search and discovery of the Higgs particle – A personal perspective

10.1142/s0217732313300279 ◽

2014 ◽

Vol 29 (09) ◽

pp. 1330027 ◽

Cited By ~ 5

Author(s):

Sau Lan Wu

Keyword(s):

Higgs Boson ◽

Large Hadron Collider ◽

Particle Physics ◽

Hadron Collider ◽

Personal Perspective ◽

Atlas Collaboration ◽

Higgs Particle ◽

History Of ◽

Quo Vadis ◽

In 1964, a new particle was proposed by several groups to answer the question of where the masses of elementary particles come from; this particle is usually referred to as the Higgs particle or the Higgs boson. In July 2012, this Higgs particle was finally found experimentally, a feat accomplished by the ATLAS Collaboration and the CMS Collaboration using the Large Hadron Collider at CERN. It is the purpose of this review to give my personal perspective on a brief history of the experimental search for this particle since the '80s and finally its discovery in 2012. Besides the early searches, those at the LEP collider at CERN, the Tevatron Collider at Fermilab, and the Large Hadron Collider at CERN are described in some detail. This experimental discovery of the Higgs boson is often considered to be the most important advance in particle physics in the last half a century, and some of the possible implications are briefly discussed. This review is partially based on a talk presented by the author at the conference "Higgs Quo Vadis," Aspen Center for Physics, Aspen, CO, USA, March 10–15, 2013.

GRAVITY, COSMOLOGY AND PARTICLE PHYSICS WITHOUT THE COSMOLOGICAL CONSTANT PROBLEM

10.1142/s0217732398001662 ◽

1998 ◽

Vol 13 (19) ◽

pp. 1583-1586 ◽

Cited By ~ 18

Author(s):

E. I. GUENDELMAN ◽

A. B. KAGANOVICH

Keyword(s):

Cosmological Constant ◽

Particle Physics ◽

Vacuum Energy ◽

Vacuum State ◽

Scalar Fields ◽

Fine Tuning ◽

Gauge Fields ◽

Hierarchy Problem ◽

Cosmological Constant Problem ◽

First Order

This letter elucidates recent achievements of the "nongravitating vacuum energy (NGVE) theory" which has the feature that a shift of the Lagrangian density by a constant does not affect dynamics. In the first-order formalism, a constraint appears that enforces the vanishing of the cosmological constant Λ. Standard dynamics of gauge unified theories (including fermions) and their SSB appear if a four-index field strength condensate is present. At the vacuum state, there is exact balance (to zero) of the gauge fields condensate and the original scalar fields potential. As a result it is possible to combine the solution of the Λ problem with inflation and transition to a Λ=0 phase without fine tuning after a reheating period. The model opens new possibilities for a solution of the hierarchy problem.

AN ATTEMPT TO EXPLAIN THE SMALLNESS OF THE COSMOLOGICAL CONSTANT

10.1142/s0217751x88000692 ◽

1988 ◽

Vol 03 (07) ◽

pp. 1593-1602 ◽

Cited By ~ 13

Author(s):

T.P. SINGH ◽

T. PADMANABHAN

Keyword(s):

Scalar Field ◽

Cosmological Constant ◽

Initial Conditions ◽

Momentum Tensor ◽

Fine Tuning ◽

Field Equations ◽

A Value ◽

Effective Cosmological Constant ◽

Age Of The Universe ◽

The Universe

Fields which couple directly to the cosmological constant (Λ) may provide a scenario for explaining the smallness of Λ at the present epoch. In this paper we postulate the existence of a scalar field which couples universally to the trace of energy—momentum tensor of matter. Various possibilities for the explicit form of the coupling function are considered. The field equations in such a theory are derived, and the cosmological models with such a scalar field are analyzed. The proposed coupling makes the effective cosmological constant a dynamically evolving quantity, which can be driven to zero by allowing the scalar field to grow to sufficiently large values. For the case of linear coupling, however, it does not seem to be possible to attain sufficient growth during the age of the universe (~1017 s ). A quadratic coupling to the trace can evolve Λ to a value consistent with today’s observations, but the universe is dominated by the scalar field, rather than by radiation, at late times. The evolution is singular for couplings through a higher power law, in that the scalar field blows up at a finite time. The model is not very sensitive to initial conditions and the problems encountered can be avoided only by a severe fine-tuning of the parameters in the basic theory.

QUANTIZATION OF THE FREEDMAN–TOWNSEND MODEL OF MASSIVE VECTOR MESONS

10.1142/s0217732391003870 ◽

1991 ◽

Vol 06 (36) ◽

pp. 3359-3363 ◽

Cited By ~ 5

Author(s):

M. LEBLANC ◽

D. G. C. McKEON ◽

A. REBHAN ◽

T. N. SHERRY

Keyword(s):

Vector Fields ◽

Symmetric Tensor ◽

Vector Mesons ◽

Tensor Fields ◽

Gauge Invariant ◽

Massive Vector ◽

Four Dimensions ◽

Vector Gauge ◽

Invariant Coupling ◽

We examine a model for massive vector mesons in four dimensions proposed by Freedman and Townsend, where the masses for non-Abelian vector gauge fields are generated without symmetry breaking through a gauge invariant coupling to anti-symmetric tensor fields. The model is quantized using the formalism of Batalin and Vilkovisky. While the Abelian version immediately gives a renormalizable model for massive vector fields, it is shown that in the non-Abelian case the addition of an extra gauge invariant term in the initial Lagrangian leads to an ultraviolet behavior consistent with power-counting renormalizability.

Constraining the Swiss-Cheese IR-Fixed Point Cosmology with Cosmic Expansion

Universe ◽

10.3390/universe7080263 ◽

2021 ◽

Vol 7 (8) ◽

pp. 263

Author(s):

Ayan Mitra ◽

Vasilios Zarikas ◽

Alfio Bonanno ◽

Michael Good ◽

Ertan Güdekli

Keyword(s):

Fixed Point ◽

Cosmological Constant ◽

Cosmic Acceleration ◽

Fine Tuning ◽

Clusters Of Galaxies ◽

Swiss Cheese ◽

Coincidence Problem ◽

Cosmological Expansion ◽

Cosmic Evolution ◽

Previous Assumption

A recent work proposed that the recent cosmic passage to a cosmic acceleration era is the result of the existence of small anti-gravity sources in each galaxy and clusters of galaxies. In particular, a Swiss-cheese cosmology model, which relativistically integrates the contribution of all these anti-gravity sources on a galactic scale has been constructed assuming the presence of an infrared fixed point for a scale dependent cosmological constant. The derived cosmological expansion provides an explanation for both the fine tuning and the coincidence problem. The present work relaxes the previous assumption on the running of the cosmological constant and allows for a generic scaling around the infrared fixed point. Our analysis reveals that, in order to produce a cosmic evolution consistent with the best ΛCDM model, the IR-running of the cosmological constant is consistent with the presence of an IR-fixed point.