Scalar Degree Of Freedom Research Articles

Formula omitted] Dirac–Yang–Mills quantum mechanics of spatially constant quark and gluon fields

The quantum mechanics of spatially constant SU(2) Yang–Mills- and Dirac-fields minimally coupled to each other is investigated as the strong coupling limit of 2-color-QCD. Using a canonical transformation of the quark and gluon fields, which Abelianises the Gauss law constraints to be implemented, the corresponding unconstrained Hamiltonian and total angular momentum are derived. In the same way as this reduces the colored spin-1 gluons to unconstrained colorless spin-0 and spin-2 gluons, it reduces the colored spin-12 quarks to unconstrained colorless spin-0 and spin-1 quarks. These however continue to satisfy anti-commutation relations and hence the Pauli-exclusion principle. The obtained unconstrained Hamiltonian is then rewritten into a form, which separates the rotational from the scalar degrees of freedom. In this form the low-energy spectrum can be obtained with high accuracy. As an illustrative example, the spin-0 energy-spectrum of the quark–gluon system is calculated for massless quarks of one flavor. It is found, that only for the case of 4 reduced quarks (half-filling) satisfying the boundary condition of particle–antiparticle C-symmetry, states with energy lower than for the pure-gluon case are obtained. These are the ground state, with an energy about 20% lower than for the pure-gluon case and the formation of a quark condensate, and the sigma–antisigma excitation with an energy about a fifth of that of the first glueball excitation.

A “composite” scalar–vector system at the LHC

In the framework of a strong dynamics for Electro-Weak Symmetry Breaking (EWSB), both vector and scalar degrees of freedom have been studied in the literature within an effective Lagrangian approach. Here we consider the case in which both a scalar, h, and a vector, V – respectively an iso-singlet and an iso-triplet under a custodial SU ( 2 ) – are relevant with a mass below the cut-off Λ ≈ 4 π v . We study the amplitudes for the processes W L W L → W L W L , h h , V L V L , V L h . Requiring unitarity for the elastic channel W L W L → W L W L we can reduce the parameter space to two free parameters for given masses of the heavy vector and the scalar. We study the numerical total cross sections for the associated productions p p → V h j j by Vector Boson Fusion (VBF) and p p → V h by Drell–Yan (DY) annihilation as functions of these free parameters. The expected rates of same-sign di-lepton and tri-lepton events from the decay of the Vh final state are also given.

THE TRACE ANOMALY AND DYNAMICAL VACUUM ENERGY IN COSMOLOGY

The trace anomaly of conformal matter implies the existence of massless scalar poles in physical amplitudes involving the stress-energy tensor. These poles may be described by a local effective action with massless scalar fields, which couple to classical sources, contribute to gravitational scattering processes, and can have long range gravitational effects at macroscopic scales. In an effective field theory approach, the effective action of the anomaly is an infrared relevant term that should be added to the Einstein-Hilbert action of classical General Relativity to take account of macroscopic quantum effects. The additional scalar degrees of freedom contained in this effective action may be understood as responsible for both the Casimir effect in flat spacetime and large quantum backreaction effects at the horizon scale of cosmological spacetimes. These effects of the trace anomaly imply that the cosmological vacuum energy is dynamical, and its value depends on macroscopic boundary conditions at the cosmological horizon scale, rather than sensitivity to the extreme ultraviolet Planck scale.

Search for Higgs bosons of the universal extra dimensions at the large Hadron collider

The Higgs sector of the Universal Extra Dimensions (UED) has a rather involved setup. With one extra space dimension, the main ingredients to the construct are the higher Kaluza-Klein (KK) excitations of the Standard Model Higgs boson and the fifth components of the gauge fields which on compactification appear as scalar degrees of freedom and can mix with the former thus leading to physical KK-Higgs states of the scenario. In this work, we explore in detail the phenomenology of such a Higgs sector of the UED with the Large Hadron Collider (LHC) in focus. We work out relevant decay branching fractions involving the KK-Higgs excitations. Possible production modes of the KK-Higgs bosons are then discussed with an emphasis on their associated production with the third generation KK-quarks and that under the cascade decays of strongly interacting UED excitations which turn out to be the only phenomenologically significant modes. It is pointed out that the collider searches of such Higgs bosons face generic hardship due to soft end-products which result from severe degeneracies in the masses of the involved excitations in the minimal version of the UED (MUED). Generic implications of either observing some or all of the KK-Higgs bosons at the LHC are discussed.

A new model for confinement

We propose a new approach towards the understanding of confinement. Starting from an anisotropic five-dimensional pure gauge theory, we approach a second order phase transition where the system reduces dimensionally. Dimensional reduction is realized via localization of the gauge and scalar degrees of freedom on four-dimensional branes. The gauge coupling deriving from the brane Wilson loop observable runs like an asymptotically free coupling at short distance, while it exhibits clear signs of string formation at long distance. The regularization used is the lattice. We take the continuum limit by keeping the ratio of the lattice spacing in the brane over the lattice spacing along the extra dimension constant and smaller than one.

Scalar representations and minimal flavor violation

We discuss the representations that new scalar degrees of freedom (beyond those in the minimal standard model) can have if they couple to quarks in a way that is consistent with minimal flavor violation. If the new scalars are singlets under the flavor group then they must be color singlets or color octets. In this paper we discuss the allowed representations and renormalizable couplings when the new scalars also transform under the flavor group. We find that color $$ \bar 3 $$ and 6 representations are also allowed. We focus on the cases where the new scalars can have renormalizable Yukawa couplings to the quarks without factors of the quark Yukawa matrices. The renormalizable couplings in the models we introduce automatically conserve baryon number.

Modified scalar and tensor spectra in spinor driven inflation

One of the firm predictions of single-scalar field inflationarycosmology is the consistency relation between scalar and tensorperturbations. It has been argued that such a relation, ifobservationally verified, would offer strong support for the idea ofinflation. In this letter, we critically analyze the validity of theconsistency relation in the context of spinor driven inflation. The spinflaton –a condensate of the Elko field — has a single scalar degree offreedom and leads to the same acceleration equation as theinflaton. We obtain the perturbation equations for the Einstein-Elkosystem and show that the scalar perturbations are purely adiabatic andthe sound speed of the perturbations is identically one. We obtain thegeneralized Mukhanov-Sasaki equation for the spinor driven inflation and showthat, in the slow-roll limit, the scalar and tensor spectra are nearlyscale-invariant. We also show that spinor driven inflation naturally predictsrunning of spectral indices and the consistency relations for thespectra are modified.

Equivalence principle implications of modified gravity models

Theories that attempt to explain the observed cosmic acceleration by modifying general relativity all introduce a new scalar degree of freedom that is active on large scales, but is screened on small scales to match experiments. We demonstrate that if such screening occurs via the chameleon mechanism, such as in $f(R)$ theory, it is possible to have order unity violation of the equivalence principle, despite the absence of explicit violation in the microscopic action. Namely, extended objects such as galaxies or constituents thereof do not all fall at the same rate. The chameleon mechanism can screen the scalar charge for large objects but not for small ones (large/small is defined by the depth of the gravitational potential and is controlled by the scalar coupling). This leads to order one fluctuations in the ratio of the inertial mass to gravitational mass. We provide derivations in both Einstein and Jordan frames. In Jordan frame, it is no longer true that all objects move on geodesics; only unscreened ones, such as test particles, do. In contrast, if the scalar screening occurs via strong coupling, such as in the Dvali-Gabadadze-Porrati braneworld model, equivalence principle violation occurs at a much reduced level. We propose several observational tests of the chameleon mechanism: 1. small galaxies should accelerate faster than large galaxies, even in environments where dynamical friction is negligible; 2. voids defined by small galaxies would appear larger compared to standard expectations; 3. stars and diffuse gas in small galaxies should have different velocities, even if they are on the same orbits; 4. lensing and dynamical mass estimates should agree for large galaxies but disagree for small ones. We discuss possible pitfalls in some of these tests. The cleanest is the third one where the mass estimate from HI rotational velocity could exceed that from stars by 30% or more. To avoid blanket screening of all objects, the most promising place to look is in voids.

Kaluza-Klein theory in the limit of large number of extra dimensions

The Kaluza-Klein compactification in the limit of a large number of extra dimensions is studied. The starting point is the Einstein-Hilbert action plus cosmological constant in $4+\mathbf{D}$ dimensions. It is shown that in the large $\mathbf{D}$ limit the effective four-dimensional cosmological constant is of order $1/\mathbf{D}$, whereas the size of the extra dimensions remains finite. A 't Hooft-like large $\mathbf{D}$ expansion of the effective Lagrangian for the Kaluza-Klein scalar and gauge fields arising from the dimensional reduction is considered. It is shown that the propagator of the scalar field associated to the determinant of the metric of the extra dimensions is strongly suppressed. This is an interesting result as in standard Kaluza-Klein theory this scalar degree of freedom is responsible for the constraint on the gauge fields which makes it impossible to recover the usual Yang-Mills equations. Moreover in the large $\mathbf{D}$ limit it turns out that the ultraviolet divergences due to the interactions between gauge and scalar fields are softened.

Scalar mode propagation in modified gravity with a scalar field

We study the propagation of the scalar modes around a Friedmann-Lema\^{\i}tre-Robertson-Walker universe for general modifications of gravity in the presence of a real scalar field. In general, there will be two propagating scalar perturbation fields, which will have in total 4 degrees of freedom. Two of these degrees will have a superluminal propagation---with $k$-dependent speed of propagation---whereas the other two will have the speed of light. Therefore, the scalar degrees of freedom do not modify the general feature of modified gravity models: the appearance of modes whose frequency depends on the second power of the modulus of the wave vector. Constraints are given and special cases are discussed.

Type II compactifications on manifolds with SU(2) × SU(2) structure

We study compactifications of type II theories on SU(2) × SU(2) structure manifolds to six, five and four spacetime dimensions. We use the framework of generalized geometry to describe the NS-NS sector of such compactifications and derive the structure of their moduli spaces. We show that in contrast to SU(3) × SU(3) structure compactifications, there is no dynamical SU(2) × SU(2) structure interpolating between an SU(2) structure and an identity structure. Furthermore, we formulate type II compactifications on SU(2) × SU(2) structures in the context of exceptional generalized geometry which makes the U-duality group manifest and naturally incorporates the scalar degrees of freedom arising in the Ramond-Ramond sector. Via this formalism we derive the structure of the moduli spaces as it is expected from N = 4 supergravity.

Newtonian limit of nonlocal cosmology

We study the consequences of the $f(R/\ensuremath{\square})$ gravity models for the Solar System and the large-scale structure of the Universe. The spherically symmetric solutions can be used to obtain bounds on the constant and the linear parts of the correction terms. The evolution of cosmological matter structures is shown to be governed by an effectively time-dependent Newton's constant. We also analyze the propagation of the perturbation modes. Tensor and vector modes are only slightly modified, but two new scalar degrees of freedom are present. Their causality and stability is demonstrated, and their formal ghost conditions are related to a singularity of the cosmological background. In general, the Newtonian limit of these models has no apparent conflicts with observations but can provide useful constraints.

MagicN= 2 supergravities from hyper-free superstrings

We show by explicit construction the existence of various four dimensional models of type II superstrings with N=2 supersymmetry, purely vector multiplet spectrum and no hypermultiplets. Among these, two are of special interest, at the field theory level they correspond to the two exceptional N=2 supergravities of the magic square that have the same massless scalar field content as pure N=6 supergravity and N=3 supergravity coupled to three extra vector multiplets. The N=2 model of the magic square that is associated to N=6 supergravity is very peculiar since not only the scalar degrees of freedom but all the bosonic massless degrees of freedom are the same in both theories. All presented hyper-free N=2 models are based on asymmetric orbifold constructions with N=(4,1) world-sheet superconformal symmetry and utilize the 2d fermionic construction techniques. The two exceptional N=2 models of the magic square are constructed via a twisting mechanism that eliminates the extra gravitini of the N=6 and N=3 extended supergravities and creates at the same time the extra spin-1/2 fermions and spin-1 gauge bosons which are necessary to balance the numbers of bosons and fermions. Theories of the magic square with the same amount of supersymmetry in three and five space-time dimensions are constructed as well, via stringy reduction and oxidation from the corresponding four-dimensional models.

Inflationary cosmology connecting dark energy and dark matter

Kination dominated quintessence models of dark energy have the intriguing feature that the relic abundance of thermal cold dark matter can be significantly enhanced compared to the predictions from standard cosmology. Previous treatments of such models do not include a realistic embedding of inflationary initial conditions. We remedy this situation by constructing a viable inflationary model in which the inflaton and quintessence field are the same scalar degree of freedom. Kination domination is achieved after inflation through a strong push or ``kick'' of the inflaton, and sufficient reheating can be achieved depending on model parameters. This allows us to explore both model-dependent and model-independent cosmological predictions of this scenario. We find that measurements of the B-mode cosmic microwave background polarization can rule out this class of scenarios almost model independently. We also discuss other experimentally accessible signatures for this class of models.

Non-linear resonance in bouncing braneworld universes and initial conditions forinflation

We examine the phase space dynamics of closed Friedmann–Robertson–Walker universeswith a massive inflaton field, where the Friedmann equations contain additional termsarising from high energy corrections to cosmological scenarios. The model is basedupon a Randall–Sundrum type of action, with an extra timelike dimension, andthe corrections implement non-singular bounces in the early evolution of theuniverse. In narrow windows of the parameter space of the models non-linearresonance phenomena of Kolmogorov–Arnold–Moser tori are shown to occur, leadingto the destruction of tori that trap the inflaton. As a consequence the escapeinto inflation takes place. These resonance windows are labeled with an integern≥2,where n is related to the ratio of the frequencies in the scale factor to those in the scalar field degrees offreedom. We examine the constraints imposed by non-linear resonance in the physicaldomain of parameters of the model so that inflation may be realized. The larger the ordern of the resonance, the stronger the gravitational interaction in the braneworld universeinflated from initial conditions connected with the resonance considered. We also discussthe structural stability of the resonance pattern, the complex dynamics arising inthis pre-inflationary phase and some of its possible imprints in the physics ofinflation.

Greybody factors for brane scalar fields in a rotating black hole background

We study the evaporation of ($4+n$)-dimensional rotating black holes into scalar degrees of freedom on the brane. We calculate the corresponding absorption probabilities and cross sections obtaining analytic solutions in the low-energy regime and compare the derived analytic expressions to numerical results, with very good agreement. We then consider the high-energy regime, construct an analytic high-energy solution to the scalar-field equation by employing a new method, and calculate the absorption probability and cross section for this energy regime, finding again a very good agreement with the exact numerical results. We also determine the high-energy asymptotic value of the total cross section and compare it to the analytic results derived from the application of the geometrical optics limit.

Cosmological dark energy: prospects for a dynamical theory

We present an approach to the problem of vacuum energy in cosmology, based on dynamical screening of Λ on the horizon scale. We review first the physical basis of vacuum energy as a phenomenon connected with macroscopic boundary conditions, and the origin of the idea of its screening by particle creation and vacuum polarization effects. We next discuss the relevance of the quantum trace anomaly to this issue. The trace anomaly implies additional terms in the low-energy effective theory of gravity, which amounts to a non-trivial modification of the classical Einstein theory, fully consistent with the Equivalence Principle. We show that the new dynamical degrees of freedom the anomaly contains provide a natural mechanism for relaxing Λ to zero on cosmological scales. We consider possible signatures of the restoration of conformal invariance predicted by the fluctuations of these new scalar degrees of freedom on the spectrum and statistics of the cosmic microwave background radiation (CMB), in light of the latest bounds from WMAP. Finally we assess the prospects for a new cosmological model in which the dark energy adjusts itself dynamically to the cosmological horizon boundary, and therefore remains naturally of order H2 at all times without fine tuning.

Neutrino dark energy and moduli stabilization in a BPS braneworld scenario

A braneworld model for neutrino Dark Energy (DE) is presented. We consider a five dimensional two-branes set up with a bulk scalar field motivated by supergravity. Its low-energy effective theory is derived with a moduli space approximation (MSA). The position of the two branes are parametrized by two scalar degrees of freedom (moduli). After detuning the brane tensions a classical potential for the moduli is generated. This potential is unstable for dS branes and we suggest to consider as a stabilizing contribution the Casimir energy of bulk fields. In particular we add a massive spinor (neutrino) field in the bulk and then evaluate the Casimir contribution of the bulk neutrino with the help of zeta function regularization techniques. We construct an explicit form of the 4D neutrino mass as function of the two moduli. To recover the correct DE scale for the moduli potential the usual cosmological constant fine-tuning is necessary, but, once accepted, this model suggests a stronger connection between DE and neutrino physics.

Moduli-space approximation for BPS brane worlds

We develop the moduli-space approximation for the low energy regime of Bogomolnyi-Prasad-Sommerfield (BPS) branes with a bulk scalar field to obtain an effective four-dimensional action describing the system. An arbitrary BPS potential is used and account is taken of the presence of matter in the branes and small supersymmetry breaking terms. The resulting effective theory is a bi-scalar tensor theory of gravity. In this theory, the scalar degrees of freedom can be stabilized naturally without the introduction of additional mechanisms other than the appropriate BPS potential. We place observational constraints on the shape of the potential and the global configuration of branes.

The radionactive universe

In a large class of extra-dimensional models, a scalardegree of freedom known as the radion is long-lived, or evenstable, on cosmological scales. In this paper we investigate theimpact of radionactivity on the evolution of the universe. Wedemonstrate that whether the radion overcloses the universe,constitutes the dark matter, is the inflaton, the curvaton, or doesnot play any role in cosmology, depends crucially on the ratio betweenthe energy densities stored in the radion and in the inflaton at thetime of inflation. We discuss the general difficulties in reconcilingmodels with low compactification scale (i.e., TeV scale) withthe simple picture of inflation.