Scalar Condensate Research Articles

Quark condensates in nuclear matter in the global color symmetry model of QCD

With the global color symmetry model being extended to finite chemical potential, we study the density dependence of the local and nonlocal scalar quark condensates in nuclear matter. The calculated results indicate that the quark condensates increase smoothly with the increasing of nuclear matter density before the critical value (about 12$\rho_0$) is reached. It also manifests that the chiral symmetry is restored suddenly as the density of nuclear matter reaches its critical value. Meanwhile, the nonlocal quark condensate in nuclear matter changes nonmonotonously against the space-time distance among the quarks.

Skyrmion model and the dynamical breakdown of chiral symmetry

A scalar field, $\eta({\bf r})$, is coupled to the skyrmion. Its classical value in the vacuum ("condensate") reduces to the pion decay constant, $f_{\pi}$, being thus proportional to the chiral condensate $<\bar{q} q>$. A quadratic coupling of the scalar field to the pion kinetic Lagrangian term, reminiscent from the linear sigma model, is considered. Its mass is an additional free parameter in the model associated to the lightest scalar isoscalar meson. Solutions for the two resulting coupled differential equations are found in several cases. The nucleon, as a topological soliton, ``digs a hole'' in the vacuum making the value of the scalar condensate to be close to zero inside the skyrmion. Some of the observables, as for example the baryon masses, may have their values closer to the experimental ones. Derrick's stability analysis is applied to the model.

Inflation and Kähler stabilization of the dilaton

The problems of attempting inflationary model-building in a theory containing a dilaton are explained. In particular, I study the shape of the dilaton potential today and during inflation, based on a weakly-coupled heterotic string model where corrections to the Kahler potential are assumed to be responsible for dilaton stabilization. Although no specific model-building is attempted, if the inflationary energy density is related to the scale of gaugino condensation, then the dilaton may be stabilized close enough to today's value that there is no significant change in the GUT scale coupling. This can occur in a very wide range of models, and helps to provide some justification for the standard predictions of the spectral index. I explain how this result can ultimately be traced to the supersymmetry structure of the theory.

Phase transition from nuclear matter to color superconducting quark matter

We construct the nuclear and quark matter equations of state at zero temperature in an effective quark theory (the Nambu–Jona-Lasinio model), and discuss the phase transition between them. The nuclear matter equation of state is based on the quark–diquark description of the single nucleon, while the quark matter equation of state includes the effects of scalar diquark condensation (color superconductivity). The effect of diquark condensation on the phase transition is discussed in detail.

Quintessence Unification Models from Non-Abelian Gauge Dynamics

We show that the condensates of a non-abelian gauge group, unified with the standard model gauge groups, can parameterize the present day cosmological constant and play the role of quintessence. The models agree with SN1a and recent CMB analysis. These models have {\it no free} parameters. Even the initial energy density at the unification scale and at the condensation scale are fixed by the number of degrees of freedom of the gauge group (i.e. by $N_c, N_f$). The values of $N_c, N_f$ are determined by imposing gauge coupling unification and the number of models is quite limited. Using Affleck-Dine-Seiberg superpotential one obtains a scalar potential $V=\Lm_c^{4+n}\phi^{-n}$. Models with $2<n<4.27$ or equivalently $2\times 10^{-2} GeV < \Lm_c < 6 \times 10^3 GeV$ do not satisfy the unification constrain. In fact, there are only three models and they have an inverse power potential with $6/11 \leq n \leq 2/3$. Imposing primordial nucleosynthesis bounds the preferred model has $N_c=3, N_f=6$, with $n=2/3$, a condensation scale $\Lm_c=4.2\times 10^{-8} GeV$ and $\wpo=-0.90$ with an average value $\weff=-0.93$. Notice that the tracker solution is not a good approximation since it has $w_{tr}=-\fr{2}{n+2}=-0.75$ for $n=2/3$. We study the evolution of all fields from the unification scale and we calculate the relevant cosmological quantities. We also discuss the supersymmetry breaking mechanism which is relevant for these models.

The strange-quark chemical potential as an experimentally accessible ‘order parameter’ of the deconfinement phase transition for finite baryon density

We consider the change of the strange-quark chemical potential in the phase diagram of nuclear matter, employing the Wilson loop and scalar quark condensate order parameters, mass-scaled partition functions and enforcing flavour conservation. Assuming the region beyond the hadronic phase to be described by massive, correlated and interacting quarks, in the spirit of lattice and effective QCD calculations, we find the strange-quark chemical potential to change sign: from positive in the hadronic phase, to zero upon deconfinement, to negative in the partonic domain. We propose this change in the sign of the strange-quark chemical potential to be an experimentally accessible order parameter and a unique, concise and well-defined indication of the quark-deconfinement phase transition in nuclear matter.

Description of Nucleons, Nuclear Matter and Quark Matter in an Effective Quark Theory

Using an effective chiral quark theory for the single nucleon, we describe the equations of state (EOS) of nuclear matter (NM) and quark matter (QM), and discuss the phase transition between them. We pay special attention to the effects of the nucleon quark structure on the NM EOS, and of scalar diquark condensation (color superconductivity) on the QM EOS.

CMB anisotropy from baryogenesis by a scalar field

We study the cosmic microwave background (CMB) anisotropy in the scenario where the baryon asymmetry of the universe is generated from a condensation of a scalar field. In such a scenario, the scalar condensation may acquire fluctuation during the inflation which becomes a new source of the cosmic density perturbations. In particular, the primordial fluctuation of the scalar condensation may induce correlated mixture of the adiabatic and isocurvature fluctuations. If the scalar condensation decays before it completely dominates the universe, the CMB angular power spectrum may significantly deviate from the conventional adiabatic result. Such a deviation may be observed in the on-going MAP experiment.

Effects of chiral restoration on the behaviour of the Polyakov loop at strong coupling

We discuss the relation between the Polyakov loop and the chiral order parameter at finite temperature. For that purpose we analyse an effective model proposed by Gocksch and Ogilvie, which is constructed by the double expansion of strong coupling and large dimensionality. We make improvements in dealing with the model and then obtain plausible results for the behaviours of both the Polyakov loop and the chiral scalar condensate. The pseudo-critical temperature read from the Polyakov loop turns out to coincide exactly with that read from the chiral scalar condensate. Within the model study based on the strong coupling expansion, the coincidence of the pseudo-critical temperatures results from the fact that the jump of the Polyakov loop in the presence of dynamical quarks should signify the chiral phase transition rather than the deconfinement transition.

Acceptable inverse power potential quintessence with n=18/7

We present a particle physics quintessence model which agrees well with existing cosmological data, including the position of the acoustic peaks. This model has an inverse power law potential (IPL) with n=18/7∼2.57 and it gives weff=−0.75, an acoustic scale lA=307 and a density contrast σ8=0.95.Models with n>1 have been said to be disfavored by the analysis of the acoustic peaks. However, the results are not correct. The main reason is that the tracker approximation has been used in deriving the IPL constrains and for n<5 the scalar field has not reached its tracker value by present day.The model can be derived from particle physics, using Affleck–Dine–Seiberg “ADS” superpotential, for a non-Abelian gauge group with Nc=8, Nf=1. The advantage of having Nf=1 is that there is only one degree of freedom below the condensation scale given by the condensate (quintessence) φ2=〈QQ〉 field. The condensation scale is at 1 GeV a very interesting scale since it connects the quintessence “Q” with the standard model “SM” scale. The similarity in energy scales between Q and SM scale gives an “explanation” to the coincidence problem. The fact that only recently the universe is accelerating is a natural consequence of the Q scale and the evolution of φ.

Cosmic density perturbations from late-decaying scalar condensations

We study the cosmic density perturbations induced from fluctuation of the amplitude of late-decaying scalar condensations (called \phi) in the scenario where the scalar field \phi once dominates the universe. In such a scenario, the cosmic microwave background (CMB) radiation originates to decay products of the scalar condensation and hence its anisotropy is affected by the fluctuation of \phi. It is shown that the present cosmic density perturbations can be dominantly induced from the primordial fluctuation of \phi, not from the fluctuation of the inflaton field. This scenario may change constraints on the source of the density perturbations, like inflation. In addition, a correlated mixture of adiabatic and isocurvature perturbations may arise in such a scenario; possible signals in the CMB power spectrum are discussed. We also show that the simplest scenario of generating the cosmic density perturbations only from the primordial fluctuation of \phi (i.e., so-called ``curvaton'' scenario) is severely constrained by the current measurements of the CMB angular power spectrum if correlated mixture of the adiabatic and isocurvature perturbations are generated.

An analytic torsion for graded D-branes

I consider the semiclassical approximation of the graded Chern-Simons field theories describing certain systems of topological A type branes in the large radius limit of Calabi-Yau compactifications. I show that the semiclassical partition function can be expressed in terms of a certain (differential) numerical invariant which is a version of the analytic torsion of Ray and Singer, but associated with flat graded superbundles. I also discuss a `twisted' version of the Ray-Singer norm, and show its independence of metric data. As illustration, I consider graded D-brane pairs of unit relative grade with a scalar condensate in the boundary condition changing sector. For the particularly simple case when the reference flat connections are trivial, I show that the generalized torsion reduces to a power of the classical Ray-Singer invariant of the base 3-manifold.

Transient domain walls and lepton asymmetry in the left-right symmetric model

It is shown that the dynamics of domain walls in left-right symmetric models, separating respective regions of unbroken ${\mathrm{SU}(2)}_{L}$ and ${\mathrm{SU}(2)}_{R}$ in the early universe, can give rise to baryogenesis via leptogenesis. Neutrinos have a spatially varying complex mass matrix due to CP-violating scalar condensates in the domain wall. The motion of the wall through the plasma generates a flux of lepton number across the wall which is converted to a lepton asymmetry by helicity-flipping scatterings. Subsequent processing of the lepton excess by sphalerons results in the observed baryon asymmetry, for a range of parameters in left-right symmetric models.

Erratum: Expectation values of four-quark operators in pions [Phys. Rev. D65,074015 (2002)

The values of four-quark operators averaged over pions are expressed through those averaged over vacuum. The specific values are obtained in the framework of the factorization assumption. For the condensates of the light quarks of the same flavour \bar q\Gamma q\bar q\Gamma q the scalar condensate is shown to be an order of magnitude larger than the other ones. The condensates containing the strange quarks \bar q q\bar s s appear to be only about twice smaller than those of the light quarks. The degeneracy of the ground state in the Nambu--Jona--Lasinio model is shown explicitly.

Lattice measurements of nonlocal quark condensates, vacuum correlation length, and pion distribution amplitude in QCD

Recent data of lattice measurements of the gauge-invariant nonlocal scalar quark condensates are analyzed to extract the short--distance correlation length, 1/\lambda_q, and to construct an admissible Ansatz for the condensate behaviour in a coordinate space. The correlation length values for both the quenched and full-QCD cases appear in a good agreement with the well-known QCD SR estimates of the mixed quark-gluon condensate, 2 \lambda_q^2 = <\bar{q}(ig\sigma^{\mu\nu}G_{\mu\nu})q>/<\bar{q}q> = 0.8 - 1.1 GeV^2. We test two different Ansatzes for a nonlocal quark condensate and trace their influence on the twist-2 pion distribution amplitude by means of QCD SRs. The main features of the pion distribution amplitude are confirmed by the CLEO experimental results.

Space-time evolution and Hanbury Brown–Twiss analysis of relativistic heavy ion collisions in a chiralSU(3)×SU(3)model

The space-time dynamics and pion--Hanbury Brown--Twiss (HBT) radii in central heavy ion collisions at CERN-SPS and BNL-RHIC are investigated within a hydrodynamic simulation. The dependence of the dynamics and the HBT parameters on the equation of state (EOS) is studied with different parametrizations of a chiral SU(3) $\ensuremath{\sigma}\ensuremath{-}\ensuremath{\omega}$ model. The self-consistent collective expansion includes the effects of effective hadron masses, generated by the nonstrange and strange scalar condensates. Different chiral EOS show different types of phase transitions and even a crossover. The influence of the order of the phase transition and of the latent heat on the space-time dynamics and pion-HBT radii is studied. A small latent heat, i.e., a weak first-order chiral phase transition, or a smooth crossover lead to distinctly different HBT predictions than a strong first order phase transition. A quantitative description of the data, both at SPS energies as well as at RHIC energies, appears difficult to achieve within the ideal hydrodynamic approach using the SU(3) chiral EOS. A strong first-order quasiadiabatic chiral phase transition seems to be disfavored by the pion-HBT data from CERN-SPS and BNL-RHIC.

Quintessence restrictions on negative power and condensate potentials

We study the cosmological evolution of scalar fields that arise from a phase transition at some energy scale ${\ensuremath{\Lambda}}_{c}.$ We focus on negative power potentials given by $V=c{\ensuremath{\Lambda}}_{c}^{4+n}{\ensuremath{\varphi}}^{\ensuremath{-}n}$ and restrict the cosmologically viable values of ${\ensuremath{\Lambda}}_{c}$ and n. We make a complete analysis of V and impose SN1a conditions on the different cosmological parameters. The cosmological observations ruled out models where the scalar field has reached its attractor solution. For models where this is not the case, the analytic approximated solutions are not good enough to determine whether a specific model is phenomenologically viable or not and the full differential equations must be solved numerically. The results are not fine-tuned since a change of $45%$ in the initial conditions does not spoil the final results. We also determine the values of ${N}_{c}$ and ${N}_{f}$ that give a condensation scale ${\ensuremath{\Lambda}}_{c}$ consistent with gauge coupling unification, leaving only four models that satisfy unification and SN1a constraints.

Expectation values of four-quark operators in pions

The values of four-quark operators averaged over pions are expressed through those averaged over vacuum. The specific values are obtained in the framework of the factorization assumption. For the condensates of the light quarks of the same flavor $\overline{q}\ensuremath{\Gamma}q\overline{q}\ensuremath{\Gamma}q$ the scalar condensate is shown to be an order of magnitude larger than the other ones. The condensates containing the strange quarks $\overline{q}q\overline{s}s$ appear to be only about twice as small as those of the light quarks. The degeneracy of the ground state in the Nambu--Jona-Lasinio model is shown explicitly.

Scalar condensate and light quark masses from overlap fermions

We have studied pseudoscalar correlation functions computed using the overlap operator. Within the accuracy of our calculation we find that the quark mass dependence agrees with the prediction of lowest-order Chiral Perturbation Theory χPT for quark masses in the range of m ∼ m s/2 – 2 m s. We present the results of an analysis which assumes lowest-order χPT to be valid to extract the low-energy constants Σ and f P, as well as the strange quark mass. Non-perturbative renormalization is implemented via a matching procedure with data obtained using Wilson fermions in the Schrödinger functional set-up. We find that the scalar condensate computed here agrees with the one obtained previously through a finite-size scaling analysis.

Dynamics of the scalar condensate in thermal 4D self-interacting scalar field theory on the lattice

We simulate a four dimensional self-interacting scalar field theory on the lattice at finite temperature. By varying temperature, the system undergoes a phase transition from broken phase to symmetric phase. Our data show that the zero-momentum field renormalization increases by approaching critical temperature. On the other hand, finite-momentum wave-function renormalization remains remarkably constant.