Scalar Excitations Research Articles

Light scalars from a compact fifth dimension

We consider a general five-dimensional sigma-model coupled to gravity, with any number of scalars and general sigma-model metric and potential. We discuss in detail the problem of the boundary conditions for the scalar fluctuations, in the case where the fifth dimension is compact, and provide a simple (and very general) algorithmic procedure for computing the spectrum of physical scalar fluctuations of the fully back-reacted system. Focusing in particular on the conditions under which the spectrum of scalar excitations (glueballs) contains parametrically light states, we apply the formalism to some especially simple toy models, which can be thought of as the gauge/gravity duals of strongly-coupled, non-conformal four-dimensional gauge theories. Our examples are chosen both within the context of phenomenological effective field theory constructions (bottom-up approach), and within the context of consistent truncations of ten-dimensional string theories in the supergravity limit (top-down approach). In one of the examples, a light dilaton is present in the spectrum in spite of the presence of a bad naked singularity in the deep IR, near which the RG flow of the dual theory is certainly very far away from any fixed point. If this feature were to persist in a complete model in which the singularity is resolved, this would prove that a light dilaton is to be expected in at least certain walking technicolor theories. We provide here all the technical details for testing this statement, once such a complete model is identified.

Superluminality in DGP

We reconsider the issue of superluminal propagation in the DGP model of infrared modified gravity. Superluminality was argued to exist in certain otherwise physical backgrounds by using a particular, physically relevant scaling limit of the theory. In this paper, we exhibit explicit five-dimensional solutions of the full theory that are stable against small fluctuations and that indeed support superluminal excitations. The scaling limit is neither needed nor invoked in deriving the solutions or in the analysis of its small fluctuations. To be certain that the superluminality found here is physical, we analyze the retarded Green's function of the scalar excitations, finding that it is causal and stable, but has support on a widened light-cone. We propose to use absence of superluminal propagation as a method to constrain the parameters of the DGP model. As a first application of the method, we find that whenever the 4D energy density is a pure cosmological constant and a hierarchy of scales exists between the 4D and 5D Planck masses, superluminal propagation unavoidably occurs.

Possible large-N fixed points and naturalness for O(N) scalar fields

We try to use scale invariance and the large-N limit to find a non-trivial 4D O(N) scalar field model with controlled UV behavior and naturally light scalar excitations. The principle is to fix interactions by requiring the effective action for spacetime dependent background fields to be finite and scale invariant when regulators are removed. We find a line of non-trivial UV fixed points in the large-N limit, parameterized by a dimensionless coupling. They reduce to classical λϕ4 theory when ℏ → 0. For ℏ ≠ 0, neither action nor measure is scale invariant, but the effective action is. Scale invariance makes it natural to set a mass deformation to zero. The model has phases where O(N) invariance is unbroken or spontaneously broken. Masses of the lightest excitations above the unbroken vacuum are found. We derive a nonlinear equation for oscillations about the broken vacuum. The interaction potential is shown to have a locality property at large N. In 3D, our construction reduces to the line of large-N fixed points in |ϕ|6 theory.

Thermodynamics of warped AdS3 black hole in the brick wall method

The statistical entropy of a scalar field on the warped AdS3 black hole in the cosmological topologically massive gravity is calculated based on the brick-wall method, which is different from the Wald's entropy formula giving the modified area law due to the higher-derivative corrections in that the entropy still satisfies the area law. It means that the entropy for scalar excitations on this background is independent of higher-order derivative terms or the conventional brick wall method has some limitations to take into account the higher-derivative terms.

New results on the Roper resonance and the [formula omitted] partial wave

Properties of the Roper resonance, the first scalar excitation of the nucleon, are determined. Pole positions and residues of the P11 partial wave are studied in a combined analysis of pion- and photo-induced reactions. We find the Roper pole at {(1371±7)−i(92±10)} MeV and an elasticity of 0.61±0.03. The largest decay coupling is found for the Nσ (σ=(ππ)-S-wave). The analysis is based on new data on γp→pπ0π0 for photons in the energy range from the two-pion threshold to 820 MeV from TAPS at Mainz and from 0.4 to 1.3 GeV from Crystal Barrel at Bonn and includes further data from other experiments. The partial wave analysis excludes the possibility that the Roper resonance is split into two states with different partial decay widths.

Electronic spectrum of UO22+ and [UO2Cl4]2− calculated with time-dependent density functional theory

The electronic spectra of UO(2) (2+) and [UO(2)Cl(4)](2-) are calculated with a recently proposed relativistic time-dependent density functional theory method based on the two-component zeroth-order regular approximation for the inclusion of spin-orbit coupling and a noncollinear exchange-correlation functional. All excitations out of the bonding sigma(u) (+) orbital into the nonbonding delta(u) or phi(u) orbitals for UO(2) (2+) and the corresponding excitations for [UO(2)Cl(4)](2-) are considered. Scalar relativistic vertical excitation energies are compared to values from previous calculations with the CASPT2 method. Two-component adiabatic excitation energies, U-O equilibrium distances, and symmetric stretching frequencies are compared to CASPT2 and combined configuration-interaction and spin-orbit coupling results, as well as to experimental data. The composition of the excited states in terms of the spin-orbit free states is analyzed. The results point to a significant effect of the chlorine ligands on the electronic spectrum, thereby confirming the CASPT2 results: The excitation energies are shifted and a different luminescent state is found.

Diquarks in the color-flavor locked phase of dense quark matter

Diquark excitations of dense quark matter are considered in the framework of the Nambu\char21{}Jona-Lasinio model with three types of massless quarks in the presence of a quark number chemical potential $\ensuremath{\mu}$. We investigate the effective action of meson and diquark fields at sufficiently high values of $\ensuremath{\mu}$, where the color-flavor locked (CFL) phase is realized, and prove the existence of NG bosons in the sector of pseudoscalar diquarks. In the sector of scalar diquarks an additional NG boson is found, corresponding to the spontaneous breaking of the $\mathrm{U}(1{)}_{B}$ baryon symmetry in the CFL phase. Finally, the existence of massive scalar and pseudoscalar diquark excitations is demonstrated.

Energy Transport by Acoustic Modes of Harmonic Lattices

We study the large scale evolution of a scalar lattice excitation u which satisfies a discrete wave equation in three dimensions, $\ddot u_t(\gamma)=-\sum_{\gamma'}\alpha(\gamma-\gamma')u_t(\gamma')$, where $\gamma,\gamma'\in\mathbb{Z}^3$ are lattice sites. We assume that the dispersion relation $\omega$ associated to the elastic coupling constants $\alpha(\gamma-\gamma')$ is acoustic; i.e., it has a singularity of the type $|k|$ near the vanishing wave vector, $k= 0$. To derive equations describing the macroscopic energy transport, we employ a related multiscale Wigner transform and a scale parameter $\varepsilon>0$. The spatial and temporal scales of the Wigner transform are related to the corresponding lattice parameters via a scaling by $\varepsilon$. In the continuum limit, which is achieved by sending the parameter $\varepsilon$ to 0, the Wigner transform disintegrates into three different limit objects: the Wigner transform of a rescaled weak-$L^2$ limit, an H-measure, and a Wigner measure. The first two provide the finer resolution of the energy concentrating at $k=0$ so that a set of closed evolution equations may arise. We demonstrate that these three limit objects satisfy a set of decoupled transport equations: a wave equation for the weak limit, a geometric optics transport equation for the H-measure limit, and a dispersive transport equation for the standard limiting Wigner measure. This yields a complete characterization of macroscopic energy transport in harmonic lattices with regular acoustic dispersion relations.

Modified gravity, dark energy and modified Newtonian dynamics

We propose a class of actions for the spacetime metric that introduce corrections to theEinstein–Hilbert Lagrangian depending on the logarithm of some curvature scalars. Weshow that for some choices of these invariants the vacuum is ghost free at the perturbativelevel and Newtonian gravity is modified below a characteristic acceleration scale given bya0 = cμ, wherec is the speedof light and μ is a parameter of the model that also determines the late-time Hubble constant:H0∼μ. In these models, besides the massless spin two graviton, there is a scalar excitation of thespacetime metric whose mass depends on the background curvature. This dependence issuch that this scalar, although almost massless in vacuum, becomes massive and effectivelydecouples when one gets close to any source and we recover an acceptable weakfield limit at short distances. There is also a (classical) ‘running’ of Newton’sconstant with the distance to the sources and gravity is easily enhanced at largedistances by a large ratio. We comment on the possibility of building a model with aMOND-like Newtonian limit that could explain the rotation curves of galaxies withoutintroducing dark matter using such actions. We also explore briefly the characteristicgravitational phenomenology that these models imply: besides a long distancemodification of gravity they also predict deviations from Newton’s law at shortdistances. This short distance scale depends on the local background curvature ofspacetime, and we find that for experiments on the Earth’s surface it is of order∼0.1 mm, while this distance would be bigger in space where the local curvature is significantlylower.

Gauge-gravity duality and thermalization of a boost-invariant perfect fluid

We derive the equation for the quasinormal modes corresponding to the scalar excitation of a black hole moving away in the fifth dimension. This geometry is the AdS/CFT dual of a boost-invariant expanding perfect fluid in N=4 SUSY Yang-Mills theory at large proper-time. On the gauge-theory side, the dominant solution of the equation describes the decay back to equilibrium of a scalar excitation of the perfect fluid. Its characteristic proper-time can be interpreted as a thermalization time of the perfect fluid, which is a universal (and numerically small) constant in units of the unique scale of the problem. This may provide a new insight on the short thermalization-time puzzle encountered in heavy-ion collision phenomenology. A nontrivial scaling behavior in proper-time is obtained which can be interpreted in terms of a slowly varying adiabatic approximation.

An analog of bulk-brane duality in field theory

We consider ($3+1$)-dimensional $\mathcal{N}=2$ supersymmetric QED with two flavors of fundamental hypermultiplets. This theory supports $1/2$-Bogomol'nyi-Prasad-Sommerfield (BPS) domain walls and flux tubes (strings), as well as their $1/4$-BPS junctions. The effective ($2+1$)-dimensional theory on the domain wall is known to be a U(1) gauge theory. Previously, the wall-string junctions were shown to play the role of massive charges in this theory. However, the field theory of the junctions on the wall (for semi-infinite strings) appears to be inconsistent due to infrared problems. All these problems can be eliminated by compactifying one spatial dimension orthogonal to the wall and considering a wall-antiwall system ($W\overline{W}$) on a cylinder. We argue that for certain values of parameters this setup provides a controllable analog of bulk-brane duality in field theory. Dynamics of the 4D bulk are mapped onto 3D boundary theory: 3D $\mathcal{N}=2$ supersymmetric quantum electrodynamics (SQED) with two matter superfields and a weak-strong coupling constant relation in 4D and 3D, respectively. The cylinder radius is seen as a ``real mass'' in 3D $\mathcal{N}=2$ SQED. We work out (at weak coupling) the quantum version of the world-volume theory on the walls. Integrating out massive matter (strings in the bulk theory) one generates a Chern-Simons term on the wall world volume and an interaction between the wall and antiwall that scales as a power of distance. Vector and scalar (classically) massless excitations on the walls develop a mass gap at the quantum level; the long-range interactions disappear. The above duality implies that the wall and its antiwall partner (at strong coupling in the bulk theory) are stabilized at the opposite sides of the cylinder.

Accuracy improvement in nonlinear magnetostatic field computations with integral equation methods and indirect total scalar potential formulations

PurposeThe paper seeks to solve nonlinear magnetostatic field problems with the integral equation method and different indirect formulations.Design/methodology/approachTo avoid large cancellation errors in cases where the demagnetizing field is high a difference field concept is used. This requires the computation of sources of the scalar potential of the excitation field.FindingsA new formulation to compute these sources is presented. The improved computational accuracy is demonstrated with numerical examples.Originality/valueThe paper develops a novel formulation for the computation of sources of scalar excitation potential.

What is the dual of a dipole?

We study gravitational solutions that admit a dual CFT description and carry non-zero dipole charge. We focus on the black ring solution in AdS 3 × S 3 and extract from it the one-point functions of all CFT operators dual to scalar excitations of the six-dimensional metric. In the case of small black rings, characterized by the level N, angular momentum J and dipole charge q 3 , we show how the large N and J dependence of the one-point functions can be reproduced, under certain assumptions, directly from a suitable ensemble in the dual CFT. Finally we present a simple toy model that describes the thermodynamics of the small black ring for arbitrary values of the dipole charge.

Structure of the breathing mode of the nucleon from high-energyp−pscattering

Spectra of $p\text{\ensuremath{-}}p$ and $\ensuremath{\pi}\text{\ensuremath{-}}p$ scattering at beam momenta between 6 and 30 GeV/c have been reanalyzed. These show strong excitation of ${N}^{*}$ resonances, the strongest one corresponding to the ``scalar'' ${P}_{11}$ excitation (breathing mode) at ${m}_{0}=1400\ifmmode\pm\else\textpm\fi{}10\phantom{\rule{0.3em}{0ex}}\text{MeV}$ with $\ensuremath{\Gamma}=200\ifmmode\pm\else\textpm\fi{}20\phantom{\rule{0.3em}{0ex}}\text{MeV}$. The result of a strong scalar excitation is supported by a large longitudinal amplitude ${S}_{1/2}$ extracted from $e\text{\ensuremath{-}}p$ scattering. From exclusive data on $p+p\ensuremath{\rightarrow}\mathit{pp}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, a large $2\ensuremath{\pi}\text{\ensuremath{-}}N$ decay branch for the ${P}_{11}$ resonance of ${B}_{2\ensuremath{\pi}}=75\ifmmode\pm\else\textpm\fi{}20$% has been extracted.The differential cross sections were described in a double-folding approach, assuming multigluon exchange as the dominant part of the effective interaction between the constituents of projectile and target. First, the parameters of the interaction were fitted to elastic scattering; then, with this interaction, the inelastic cross sections were described in the distorted wave Born approximation (DWBA). A good description of the data requires a surface peaked transition density, quite different from that of a pure radial mode. In contrast, the electron scattering amplitude ${S}_{1/2}$ is quite well described by a breathing mode transition density with radial node. This large difference between charge and matter transition densities suggests that in $p\text{\ensuremath{-}}p$ scattering the coupling to the multigluon field is much more important than the coupling to the valence quarks. A multigluon (or sea-quark) transition density is derived, which also shows breathing, indicating a rather complex multiquark structure of N and ${N}^{*}$ including additional multigluon (or ${q}^{2n}{\overline{q}}^{2n}$) creation out of the ground state vacuum.

Ghost Condensation and a Consistent IR Modification of Gravity

We propose a theoretically consistent modification of gravity in the infrared, which is compatible with all current experimental observations. This is an analog of Higgs mechanism in general relativity, and can be thought of as arising from ghost condensation--a background where a scalar field \phi has a constant velocity, <\dot\phi> = M^2. The ghost condensate is a new kind of fluid that can fill the universe, which has the same equation of state, \rho = -p, as a cosmological constant, and can hence drive de Sitter expansion of the universe. However, unlike a cosmological constant, it is a physical fluid with a physical scalar excitation, which can be described by a systematic effective field theory at low energies. The excitation has an unusual low-energy dispersion relation \omega^2 \sim k^4 / M^2. If coupled to matter directly, it gives rise to small Lorentz-violating effects and a new long-range 1/r^2 spin dependent force. In the ghost condensate, the energy that gravitates is not the same as the particle physics energy, leading to the possibility of both sources that can gravitate and antigravitate. The Newtonian potential is modified with an oscillatory behavior starting at the distance scale M_{Pl}/M^2 and the time scale M_{Pl}^2/M^3. This theory opens up a number of new avenues for attacking cosmological problems, including inflation, dark matter and dark energy.

Multigravity from a discrete extra dimension

Multigravity theories are constructed from the discretization of the extra dimension of five-dimensional gravity. Using an ADM decomposition, the discretization is performed while maintaining the four-dimensional diffeomorphism invariance on each site. We relate the Goldstone bosons used to realize nonlinearly general covariance in discretized gravity to the shift fields of the higher-dimensional metric. We investigate the scalar excitations of the resulting theory and show the absence of ghosts and massive modes; this is due to a local symmetry inherited from the reparametrization invariance along the fifth dimension.

Dynamical symmetry breaking and the Nambu–Goldstone theorem in the Gaussian wave functional approximation

We analyze the group-theoretical ramifications of the Nambu–Goldstone (NG) theorem in the self-consistent relativistic variational Gaussian wave functional approximation to spinless field theories. In an illustrative example we show how the Nambu–Goldstone theorem would work in the O(N) symmetric φ4 scalar field theory, if the residual symmetry of the vacuum were lesser than O(N−1), e.g., if the vacuum were O(N−2), or O(N−3),… symmetric. (This does not imply that any of the “lesser” vacua is actually the absolute energy minimum: stability analysis has not been done.) The requisite number of NG bosons would be (2N−3), or (3N−6),…, respectively, which may exceed N, the number of elementary fields in the Lagrangian. We show how the requisite new NG bosons would appear even in channels that do not carry the same quantum numbers as one of N “elementary particles” [scalar field quanta, or Castillejo–Dalitz–Dyson (CDD) poles] in the Lagrangian, i.e., in those “flavor” channels that have no CDD poles. The corresponding Nambu–Goldstone bosons are composites (bound states) of pairs of massive elementary (CDD) scalar fields excitations. As a nontrivial example of this method we apply it to the physically more interesting ’t Hooft σ model (an extended Nf=2 bosonic linear σ model with four scalar and four pseudoscalar fields), with spontaneously and explicitly broken chiral O(4)×O(2)≃SUR(2)×SUL(2)×UA(1) symmetry.

The Vector Manifestation and Effective Degrees of Freedom at Chiral Restoration

The role of effective degrees of freedom on the vector and axial-vector susceptibilities and the pion velocity at chiral restoration is analyzed. We consider two possible scenarios, one in which pions are considered to be the only low-lying degrees of freedom -- that we shall refer to as "standard" -- and the other in which pions, vector mesons and constituent quarks (or quasiquarks in short) are the relevant low-lying degrees of freedom -- that we shall refer to as "vector manifestation (VM)." We show at one-loop order in chiral perturbation theory with hidden local symmetry Lagrangian that while in the standard scenario, the pion velocity vanishes at the chiral transition, it instead approaches unity in the VM scenario. If the VM is realized in nature, the chiral phase structure of hadronic matter can be much richer than that in the standard one and the phase transition will be a smooth crossover: Sharp vector and scalar excitations are expected in the vicinity of the critical point. Some indirect indications that lend support to the VM scenario, and in consequence to BR scaling, are discussed.

Excitations in hot non-commutative theories

We study the dispersion relation for scalar excitations in supersymmetric, non-commutative theories at finite temperature. In N=4 Yang-Mills the low momenta modes have superluminous group velocity. In the massless Wess-Zumino model the minimum of the dispersion relation is at non zero momentum for temperatures above T_0 ~ (g \theta)^(-1\2). We briefly comment on N=2 Yang-Mills at finite density.

Generalized mesons in dense QCD

QCD superconductors in the color–flavor-locked (CFL) phase support excitations (generalized mesons) that can be described as pairs of particles or holes (rather than particle–hole) around a gapped Fermi surface. In weak coupling and to leading logarithm accuracy the scalar and pseudoscalar excitations are massless and the vector and axial-vector excitations are massive and degenerate. The massless scalar excitations are combined with the longitudinal gluons leading to the Meissner effect in the CFL phase. The mass of the composite vector excitations is close to twice the gap in weak coupling, but goes asymptotically to zero with increasing coupling thereby realizing Georgi's vector limit in cold and dense matter. We discuss the possible mixing of the composite scalar and vector excitations with the gluons, their possible coupling to the modified photons and their decay into light pseudoscalars in the CFL phase. The issue of hidden gauge-symmetry in the QCD superconductor is critically examined. The physical implications of our results on soft dilepton and neutrino emission in cold and dense matter are briefly discussed.