scholarly journals HIGGS MECHANISM WITH A TOPOLOGICAL TERM

2001 ◽  
Vol 16 (23) ◽  
pp. 1493-1503 ◽  
Author(s):  
ICHIRO ODA
Keyword(s):  
Degrees Of Freedom ◽  
Goldstone Boson ◽  
Higgs Mechanism ◽  
Tree Level ◽  
Gauge Fields ◽  
Massless Scalar ◽  
Time Dimension ◽  
Superstring Theory ◽  
Gauge Groups ◽  
Topological Term

In cases of both Abelian and non-Abelian gauge groups, we consider the Higgs mechanism in topologically massive gauge theories in an arbitrary space–time dimension. It is shown that the presence of a topological term makes it possible to shift mass of gauge fields in a nontrivial way compared to the conventional value at the classical tree level. We correct the previous misleading statement with respect to the counting of physical degrees of freedom, where it is shown that gauge fields become massive by "eating" the Nambu–Goldstone boson and a higher-rank tensor field, but a new massless scalar appears in the spectrum so the number of physical degrees of freedom remains unchanged before and after the spontaneous symmetry breakdown. Some related phenomenological implications and applications to superstring theory are briefly commented.

scholarly journals HIGGS MECHANISM IN THE PRESENCE OF A TOPOLOGICAL TERM

2002 ◽  
Vol 17 (01) ◽  
pp. 89-108 ◽  
Author(s):  
ICHIRO ODA
Keyword(s):  
Degrees Of Freedom ◽  
Goldstone Boson ◽  
Higgs Mechanism ◽  
Gauge Fields ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Time Dimension ◽  
Abelian Gauge ◽  
Gauge Groups ◽  
Topological Term

In cases of both Abelian and non-Abelian gauge groups, we study the Higgs mechanism in the topologically massive gauge theories in an arbitrary space–time dimension. We show that when the conventional Higgs potential coexists with a topological term, gauge fields become massive by "eating" simultaneously both the Nambu–Goldstone boson and a higher-rank tensor field and instead a new massless scalar field is "vomitted" in the physical spectrum. Because of the appearance of this new massless field, the number of the physical degrees of freedom remains unchanged before and after the spontaneous symmetry breakdown. Moreover, the fact that the new field is a physical and positive norm state is rigorously proved by performing the manifestly covariant quantization of the model in three and four dimensions. In the mechanism at hand, the presence of a topological term makes it possible to shift the mass of gauge fields in a nontrivial manner compared to the conventional value.

scholarly journals BERRY CONNECTIONS AND INDUCED GAUGE FIELDS IN QUANTUM MECHANICS ON SPHERE

2000 ◽  
Vol 15 (18) ◽  
pp. 1203-1212 ◽  
Author(s):  
HITOSHI IKEMORI ◽  
SHINSAKU KITAKADO ◽  
HIDEHARU OTSU ◽  
TOSHIRO SATO
Keyword(s):  
Quantum Mechanics ◽  
Effective Action ◽  
Degrees Of Freedom ◽  
Gauge Fields ◽  
Chern Simons ◽  
Topological Term

Quantum mechanics on sphere Sn is studied from the viewpoint that the Berry's connection has to appear as a topological term in the effective action. Furthermore we show that this term is the Chern–Simons term of gauge variables that correspond to the extra degrees of freedom of the enlarged space.

scholarly journals Gravity-assisted emergent Higgs mechanism in the post-inflationary epoch

2016 ◽  
Vol 25 (12) ◽  
pp. 1644008 ◽  
Author(s):  
Eduardo Guendelman ◽  
Emil Nissimov ◽  
Svetlana Pacheva
Keyword(s):  
Effective Potential ◽  
Degrees Of Freedom ◽  
Higgs Mechanism ◽  
Gauge Fields ◽  
Positive Mass ◽  
Nonstandard Model ◽  
Dynamical Generation ◽  
Riemannian Spacetime ◽  
Integration Measure ◽  
Volume Forms

We consider a nonstandard model of gravity coupled to a neutral scalar “inflaton” as well as to [Formula: see text] iso-doublet scalar with positive mass squared and without self-interaction, and to [Formula: see text] gauge fields. The principal new ingredient is employing two alternative non-Riemannian spacetime volume-forms (covariant integration measure densities) independent of the metric. The latter have a remarkable impact — although not introducing any additional propagating degrees of freedom, their dynamics triggers a series of important features: appearance of infinitely large flat regions of the effective “inflaton” potential as well as dynamical generation of Higgs-like spontaneous symmetry breaking effective potential for the [Formula: see text] iso-doublet scalar.

scholarly journals CLASSICAL SOLUTIONS OF GHOST CONDENSATION MODELS

2008 ◽  
Vol 22 (31) ◽  
pp. 3025-3034 ◽  
Author(s):  
MASAHIRO MAENO ◽  
ICHIRO ODA
Keyword(s):  
Degrees Of Freedom ◽  
Goldstone Boson ◽  
Scalar Fields ◽  
Higgs Mechanism ◽  
Space Time ◽  
Classical Solutions ◽  
De Sitter ◽  
Symmetry Breakdown ◽  
Minkowski Space Time ◽  
Spontaneous Symmetry Breakdown

Motivated by ideas obtained from both ghost condensation and gravitational Higgs mechanism, we attempt to find classical solutions in the unitary gauge in general ghost condensation models. It is shown that depending on the form of scalar fields in an action, there are three kinds of exact solutions, which are (anti-) de Sitter space–time, polynomially expanding universes and flat Minkowski space–time. We briefly comment on gravitational Higgs mechanism in these models where we have massive gravitons of five degrees of freedom and one unitary scalar field (Nambu–Goldstone boson) after spontaneous symmetry breakdown of general coordinate reparametrization invariance. The models at hand are free from the problem associated with the non-unitary propagating mode.

scholarly journals Goldstone equivalence and high energy electroweak physics

2020 ◽  
Vol 8 (5) ◽  
Author(s):  
Gabriel Cuomo ◽  
Luca Vecchi ◽  
Andrea Wulzer
Keyword(s):  
Top Quark ◽  
Degrees Of Freedom ◽  
High Energy ◽  
Feynman Diagrams ◽  
Tree Level ◽  
Gauge Groups ◽  
Virtual Particles ◽  
Gauge Fixing ◽  
Feynman Rules ◽  
Standard Formalism

The transition between the broken and unbroken phases of massive gauge theories, namely the rearrangement of longitudinal and Goldstone degrees of freedom that occurs at high energy, is not manifestly smooth in the standard formalism. The lack of smoothness concretely shows up as an anomalous growth with energy of the longitudinal polarization vectors, as they emerge in Feynman rules both for real on-shell external particles and for virtual particles from the decomposition of the gauge field propagator. This makes the characterization of Feynman amplitudes in the high-energy limit quite cumbersome, which in turn poses peculiar challenges in the study of Electroweak processes at energies much above the Electroweak scale. We develop a Lorentz-covariant formalism where polarization vectors are well-behaved and, consequently, energy power-counting is manifest at the level of individual Feynman diagrams. This allows us to prove the validity of the Effective $W$ Approximation and, more generally, the factorization of collinear emissions and to compute the corresponding splitting functions at the tree-level order. Our formalism applies at all orders in perturbation theory, for arbitrary gauge groups and generic linear gauge-fixing functionals. It can be used to simplify Standard Model loop calculations by performing the high-energy expansion directly on the Feynman diagrams. This is illustrated by computing the radiative corrections to the decay of the top quark.

GOLDSTONE FIELDS IN THE SUPERSTRING THEORY

2008 ◽  
Vol 17 (01) ◽  
pp. 81-94 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Cosmological Constant ◽  
Goldstone Boson ◽  
Gauge Coupling ◽  
Einstein Equations ◽  
Level Gauge ◽  
Tree Level ◽  
Internal Space ◽  
Spin Component ◽  
Additional Contribution ◽  
Superstring Theory

If global supersymmetry is broken by gaugino condensation in the hidden sector of the [Formula: see text] heterotic superstring theory after compactification, then the auxiliary field FB of the modulus B ≡ (B r , B i ) attains a finite value, while that of the dilaton A ≡ (A r , A i ) vanishes, FA = 0, the Goldstone fermion being the modulino [Formula: see text], the spin-½ component of the complex chiral supermultiplet [Formula: see text]. The Goldstone boson of the scale symmetry that is broken when the radius of the internal space is fixed at a constant value is B r , which is determined from the goldstino Lagrangian, compared term by term with the superstring Lagrangian, including higher-derivative gravitational terms [Formula: see text] and [Formula: see text], after linking the space–time curvature to the energy–momentum tensor of the goldstino via the Einstein equations. This non-linear formulation of supersymmetry, due to Volkov and Akulov, is expressed in terms of the goldstino alone, whose Lagrangian contains a negative cosmological constant, which can be cancelled by the super-Higgs mechanism of Deser and Zumino to make the gravitino massive and break supersymmetry at the level [Formula: see text] GeV, while [Formula: see text]. Here, the modulus has been scaled to the Hagedorn value for the heterotic superstring theory, [Formula: see text], and A r , identified with the inverse square of the tree-level gauge coupling, has been scaled to the calculation in the minimal supersymmetric standard model due to Weinberg, that g-2 = 1.39 at the unification mass MX = 2.2 × 1016 GeV, assuming three generations of elementary particles and two Higgs doublets. In the presence of gravitino condensation in the internal space, however, there is an arbitrary additional contribution to the cosmological constant, facilitating reduction of m s to ~ 100 TeV, say, and m3/2 to ~ 1 eV.

scholarly journals Lowering the scale of Pati-Salam breaking through seesaw mixing

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Matthew J. Dolan ◽  
Tomasz P. Dutka ◽  
Raymond R. Volkas
Keyword(s):  
Degrees Of Freedom ◽  
Tree Level ◽  
Charged Current ◽  
Meson Decay ◽  
Neutrino Masses ◽  
Down Quark ◽  
The Standard Model ◽  
Decay Widths ◽  
Left And Right ◽  
Charged Leptons

Abstract We analyse the experimental limits on the breaking scale of Pati-Salam extensions of the Standard Model. These arise from the experimental limits on rare-meson decay processes mediated at tree-level by the vector leptoquark in the model. This leptoquark ordinarily couples to both left- and right-handed SM fermions and therefore the meson decays do not experience a helicity suppression. We find that the current limits vary from $$ \mathcal{O} $$ O (80–2500) TeV depending on the choice of matrix structure appearing in the relevant three-generational charged-current interactions. We extensively analyse scenarios where additional fermionic degrees of freedom are introduced, transforming as complete Pati-Salam multiplets. These can lower the scales of Pati-Salam breaking through mass-mixing within the charged-lepton and down-quark sectors, leading to a helicity suppression of the meson decay widths which constrain Pati-Salam breaking. We find four multiplets with varying degrees of viability for this purpose: an SU(2)L/R bidoublet, a pair of SU(4) decuplets and either an SU(2)L or SU(2)R triplet all of which contain heavy exotic versions of the SM charged leptons. We find that the Pati-Salam limits can be as low as $$ \mathcal{O} $$ O (5–150) TeV with the addition of these four multiplets. We also identify an interesting possible connection between the smallness of the neutrino masses and a helicity suppression of the Pati-Salam limits for three of the four multiplets.

scholarly journals NEW SUPERSTRING ISOMETRIES AND HIDDEN DIMENSIONS

2007 ◽  
Vol 22 (29) ◽  
pp. 5301-5323 ◽  
Author(s):  
DIMITRI POLYAKOV
Keyword(s):  
Extra Dimension ◽  
Isometry Group ◽  
Space Time ◽  
Time Dimension ◽  
Superstring Theory ◽  
Symmetry Transformations ◽  
Noncritical Strings ◽  
A Chain ◽  
Symmetry Generators ◽  
Special Space

We study the hierarchy of hidden space–time symmetries of noncritical strings in RNS formalism, realized nonlinearly. Under these symmetry transformations the variation of the matter part of the RNS action is canceled by that of the ghost part. These symmetries, referred to as the α-symmetries, are induced by special space–time generators, violating the equivalence of ghost pictures. We classify the α-symmetry generators in terms of superconformal ghost cohomologies Hn ~ H-n-2(n≥0) and associate these generators with a chain of hidden space–time dimensions, with each ghost cohomology Hn ~ H-n-2 "contributing" an extra dimension. Namely, we show that each ghost cohomology Hn ~ H-n-2 of noncritical superstring theory in d-dimensions contains d+n+1 α-symmetry generators and the generators from Hk ~ H-k-2, 1≤k ≤n, combined together, extend the space–time isometry group from the naive SO (d, 2) to SO (d+n, 2). In the simplest case of n = 1 the α-generators are identified with the extra symmetries of the 2T-physics formalism, also known to originate from a hidden space–time dimension.

WHY IS THE HIDDEN SECTOR INVISIBLE?

2000 ◽  
Vol 15 (35) ◽  
pp. 2131-2137 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Degrees Of Freedom ◽  
Coupling Parameter ◽  
Vacuum State ◽  
Fine Tuning ◽  
Gauge Mediation ◽  
Superstring Theory ◽  
Thermodynamical Equilibrium ◽  
Hidden Sector ◽  
Axion Field ◽  
Model Independent

The hidden sector of the E8×E′8 heterotic superstring theory of Gross et al. can in principle contain additional "shadow" matter, interacting only gravitationally with the real world in which we live. The SU (3)′ C × SU (2)′ L × U (1)′ Y shadow configuration symmetric to the standard model has been ruled out by Kolb et al. from nucleosynthesis arguments, combined with the existence of three light neutrinos. In the absence of inflation and of entropy enhancement by the out-of-equilibrium decay of an unstable particle, the same exclusion applies to the unbroken E′8 hidden gauge group, assuming thermodynamical equilibrium with the observable sector E6 group, and consequently all breaking chains E′8→ G1×G2×⋯, since they can only reduce the effective number of four-dimensional degrees of freedom g eff . The hidden sector would then appear to be in its vacuum state, which implies the absence of all condensates as well, if their potentials are positive semi-definite. In this case, and if there is no anomalous U(1) symmetry in the observable sector, the QCD axion is the model-independent axion, whose decay constant [Formula: see text] (where [Formula: see text] is the strong-interaction coupling parameter) requires a fine-tuning of the initial value of this axion field to ai/fa≲3×10-3, in order not to overclose the Universe today, supersymmetry being broken by gauge mediation. Vice versa, if ai/fa~1, then hidden-sector gaugino condensation is necessary for there to be a sufficiently massive gravitino, whose decay can increase the entropy. Astronomical microlensing observations may help to discriminate between these two cases.

Spontaneously Broken Symmetries

2021 ◽  
pp. 287-303
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Phase Transitions ◽  
Vector Field ◽  
Quantum Physics ◽  
Goldstone Boson ◽  
Internal Symmetry ◽  
Higgs Mechanism ◽  
Broken Symmetry ◽  
Massive Vector ◽  
Broken Symmetries ◽  
Gauge Symmetries

The phenomenon of spontaneous symmetry breaking is a common feature of phase transitions in both classical and quantum physics. In a first part we study this phenomenon for the case of a global internal symmetry and give a simple proof of Goldstone’s theorem. We show that a massless excitation appears, corresponding to every generator of a spontaneously broken symmetry. In a second part we extend these ideas to the case of gauge symmetries and derive the Brout–Englert–Higgs mechanism. We show that the gauge boson associated with the spontaneously broken generator acquires a mass and the corresponding field, which would have been the Goldstone boson, decouples and disappears. Its degree of freedom is used to allow the transition from a massless to a massive vector field.

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