Chiral Order Parameter Research Articles

Empirical deduction of a medium-modified chiral order parameter from 1s π− states in heavy nuclei

We propose a model-independent procedure to deduce empirically the isovector strength b 1 of the pion–nucleus interaction, which is related to possible modification of the pion-decay constant f π , and thus of the chiral order parameter, in the nuclear medium. The first procedure is to compare the 1s binding energies of π − in two nuclei which have different ( N − Z )/ A values, such as 205 Pb and 115 Sn. The second, more direct way is to deduce b 1 from an observed isotope shift of the 1s binding energy, such as in 115 Sn and 123 Sn.

Diquark condensation at nonzero chemical potential and temperature

SU(2) lattice gauge theory with four flavors of quarks is studied at nonzero chemical potential $\mu$ and temperature $T$ by computer simulation and Effective Lagrangian techniques. Simulations are done on $8^4$, $8^3 \times 4$ and $12^3 \times 6$ lattices and the diquark condensate, chiral order parameter, Wilson line, fermion energy and number densities are measured. Simulations at a fixed, nonzero quark mass provide evidence for a tricritical point in the $\mu$-$T$ plane associated with diquark condensation. For low $T$, increasing $\mu$ takes the system through a line of second order phase transitions to a diquark condensed phase. Increasing $T$ at high $\mu$, the system passes through a line of first order transitions from the diquark phase to the quark-gluon plasma phase. Using Effective Lagrangians we estimate the position of the tricritical point and ascribe its existence to trilinear couplings that increase with $\mu$ and $T$.

Chiral fluctuations in nuclei

The near-threshold enhancement in the π+π− invariant mass distribution in nuclei, observed by CHAOS collaboration [1] and for ππ pairs by the Crystal Ball collaboration [2], offers the interesting possibility of directly observing a signal for partial restoration of chiral symmetry in a dense medium. There seems to be theoretical consensus on a strong in-medium reshaping of the s-wave isoscalar pion-pair correlations as a direct consequence of increased fluctuations of the chiral order parameter. This translates into a significant downward shift of the strength in the ππ T -matrix in the scalar-isoscalar channel as seen in Fig. 1.

Nonequilibrium transitions in fully frustrated Josephson junction arrays.

We study the effect of thermal fluctuations in a fully frustrated Josephson junction array driven by a current I larger than the apparent critical current I(c)(T). We calculate numerically the behavior of the chiral order parameter of Z2 symmetry and the transverse helicity modulus [related to the U(1) symmetry] as a function of temperature. We find that the Z2 transition occurs at a temperature T(Z2)(I) which is lower than the temperature T(U(1))(I) for the U(1) transition. Both transitions could be observed experimentally from measurements of the longitudinal and transverse voltages.

Imprinted networks as chiral pumps.

We investigate the interaction between a chirally imprinted network and a solvent of chiral molecules. We find that a liquid-crystalline polymer network is preferentially swollen by one component of a racemic solvent. This ability to separate is linked to the chiral order parameter of the network, and can be reversibly controlled via temperature or a mechanical deformation. It is maximal near the point at which the network loses its imprinted structure. One possible practical application of this effect would be a mechanical device for sorting mixed chiral molecules.

Probing chiral dynamics by charged-pion correlations

The environment generated in the midrapidity region of a high-energy nuclear collision endows the pionic degrees of freedom with a time-dependent effective mass. Its specific evolution provides a mechanism for the production of back-to-back charge-conjugate pairs of soft pions which may present an observable signal of the nonequilibrium dynamics of the chiral order parameter.

Flavour stability of the chiral vacuum and scalar meson dynamics

Previous work relating the flavour variation of the chiral order parameters $F_\pi$, $<\bar u u>$ and S-wave scattering data, based on chiral sum rules and chiral perturbation theory at order $p^4$, is extended to include $O(p^6)$ corrections. The finding of a significant decrease of these order parameters, particularly $<\bar u u>$, with the number of flavours increasing from $N_F=2$ to $N_F=3$ is confirmed, modulo an assumption on the convergence of the chiral expansion. The connection between scalar resonance physics and the phase structure of the chiral vacuum is also illustrated on the basis of the linear sigma-model. We allow for a very general symmetry breaking sector compatible with softness. The result depends strongly on the input scalar meson masses, in particular, on the presence, or not, of a light sigma.}

Phase structure of the QCD vacuum in a magnetic field at low temperature

We study the QCD phase structure in magnetic field H at low temperature T. The hadronic phase free energy in a constant homogeneous magnetic field is calculated in one-loop approximation of the chiral perturbation theory. The dependence of the quark and gluon condensates upon the temperature and field strength is found. It is shown that the chiral phase transition order parameter 〈 q ̄ q〉 remains constant provided field strength and temperature are related via H=const.· T 2.

Finite-volume analysis ofNf-induced chiral phase transitions

In the framework of Euclidean QCD on a torus, we study the spectrum of the Dirac operator through inverse moments of its eigenvalues, averaged over topological sets of gluonic configurations. The large-volume dependence of these sums is related to chiral order parameters. We sketch how these results may be applied to lattice simulations in order to investigate the chiral phase transitions occurring when ${N}_{f}$ increases. In particular, we demonstrate how Dirac inverse moments at different volumes could be compared to detect in a clean way the phase transition triggered by the suppression of the quark condensate and by the enhancement of the Zweig-rule violation in the vacuum channel.

Stochastic treatment of disoriented chiral condensates within a Langevin description

Applying a microscopically motivated semi-classical Langevin description of the linear sigma model we investigate for various different scenarios the stochastic evolution of a disoriented chiral condensate (DCC) in a rapidly expanding system. Some particular emphasize is put on the numerical realisation of colored noise in order to treat the underlying dissipative and nonmarkovian stochastic equations of motion. A comparison with an approximate markovian (i.e. instantaneous) treatment of dissipation and noise will be made in order to identify the possible influence of memory effects in the evolution of the chiral order parameter. Assuming a standard Rayleigh cooling term to simulate a D-dimensional scaling expansion we present the probability distribution in the low momentum pion number stemming from the relaxing zero mode component of the chiral field. The best DCC signal is expected for initial conditions centered around $<\sigma > \approx 0 $ as would be the case of effective light `pions' close to the phase transition. By choosing appropriate idealized global parameters for the expansion our findings show that an experimentally feasible DCC, if it does exist in nature, has to be a rare event with some finite probability following a nontrivial and nonpoissonian distribution on an event by event basis. DCCs might then be identified experimentally by inspecting higher order factorial cumulants $\theta_m$ ($m\ge 3$) in the sampled distribution.

Theory of chiral imprinting

We present a continuum model for a nematic elastomer network formed in a chiral environment, for instance, in the presence of a chiral solvent. When this environment is removed, the network can retain some memory of its chiral genesis. We predict the residual chiral order for a number of possible scenarios, and examine the robustness (stability) of the imprinted chirality. We show that a twist-untwist transition can take place, which determines whether the imprinting has been successful. A transition is via a coarsening of the helical director pattern and a lengthening of its pitch. Finally, the effect due to a subsequent swelling by an achiral solvent, or by a solvent of differing chirality, is considered.

Patterns of symmetry breaking in QCD at high baryon density

We study the structure of QCD at very large baryon density for an arbitrary number of flavors N f . We provide evidence that for any number of flavors larger than N f =2 chiral symmetry remains broken at asymptotically large chemical potential. For N c = N f =3, chiral symmetry breaking follows the standard pattern SU(3) L × SU(3) R → SU(3), but for N f >3 unusual patterns emerge. We study the case N f =3 in more detail and calculate the magnitude of the chiral order parameters 〈 ψ ̄ ψ〉 and 〈( ψ ̄ ψ) 2〉 in perturbative QCD. We show that, asymptotically, 〈 ψ ̄ ψ〉 1/3 is much smaller than 〈( ψ ̄ ψ) 2〉 1/6 . The result can be understood in terms of an approximate discrete symmetry.

Equation of state in finite-temperature QCD with improved Wilson quarks

We study finite-temperature phase transition and equation of state for two-flavor QCD at N t = 4 using an RG-improved gauge action and a meanfield-improved clover quark action. The pressure is computed using the integral method. The O(4) scaling of chiral order parameter is also examined.

Dynamical simulation of disoriented chiral condensate formation in Bjorken rods

Using a semiclassical treatment of the linear $\ensuremath{\sigma}$ model, we simulate the dynamical evolution of an initially hot cylindrical rod endowed with a longitudinal Bjorken scaling expansion (a ``Bjorken rod''). The field equation is propagated until full decoupling has occurred and the asymptotic many-body state of free pions is then obtained by a suitable Fourier decomposition of the field and a subsequent stochastic determination of the number of quanta in each elementary mode. The resulting transverse pion spectrum exhibits visible enhancements below 200 MeV due to the parametric amplification caused by the oscillatory relaxation of the chiral order parameter. Ensembles of such final states are subjected to various event-by-event analyses. The factorial moments of the multiplicity distribution suggest that the soft pions are nonstatistical. Furthermore, their emission patterns exhibit azimuthal correlations that have a bearing on the domain size in the source. Finally, the distribution of the neutral pion fraction shows a significant broadening for the soft pions which grows steadily as the number of azimuthal segments is increased. All of these features are indicative of disoriented chiral condensates and it may be interesting to apply similar analyses to actual data from high-energy nuclear collision experiments.

First-Order Chiral Phase Transition May Naturally Lead to a “Quenched” Initial Condition and Strong Soft-Pion Fields

We propose a novel mechanism for disoriented chiral condensate (DCC) formation in a first-order chiral phase transition. In this case the effective potential for the chiral order parameter has a local minimum at $\ensuremath{\Phi}\ensuremath{\sim}0$ in which the chiral field can be ``trapped.'' If the expansion is fast, a bubble of disoriented chiral field can emerge and decouple from the rest of the fireball. The bubble may overshoot the mixed phase and supercool until the barrier disappears, when the potential resembles that at $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$. This situation corresponds to the initial condition realized in a ``quench.'' Thus, the subsequent alignment in the vacuum direction leads to strong amplification of low-momentum modes of the pion field. We propose that these DCCs could accompany the previously suggested baryon rapidity fluctuations.

Molecular surface and order parameters in liquid crystals

The surface model for solute ordering in nematics, which is based on the decomposition of the orientational potential according to the contributions of surface elements, leads to a simple procedure for the calculation of both orientational properties and the cholesteric order induced by a chiral compound. However, a realistic representation of the molecular surface accessible to the solvent is required. The rolling sphere algorithm, applied to the ensemble of atomic van der Waals spheres of a molecule, provides a natural determination of such a surface, sinceit smoothes away the smallscaledetails. Thesurfaceordering model implemented with the rolling sphere smoothing of the surface is described and applied to several molecular systems. It is shown that the orientational order parameters are substantially independent of the rolling sphere radius identified with the average curvature of the solvent molecular surface. On the contrary, a sensible dependence on such a parameter emerges for the chirality order parameter, this behaviour pointing out the role of the shape of solvent molecules in the chirality recognition of solutes. A fair agreement is obtained in the comparison with experimental data.

Studies on the Chiral Order Parameter in the Schwinger Model

Based on an analytical technique using a unitary transformation and the variational method, we study the chiral order parameter in the Schwinger model in the lattice formalism with Kogut-Susskind fermions. The fermion condensate for any coupling constant and fermion mass are calculated. Chiral symmetry is shown to be broken in the massless limit and good scaling behavior is obtained.

Lattice QED at Finite Temperature and Finite Density**The project partially supported by National Natural Science Foundation of China

In this letter, we apply the variational cumulant expansion (VCE) method to the lattice QED, which has complex action at finite density . The chiral order parameter and the number density at finite temperature are calculated.

Deconfinement at finite chemical potential

In a confining, renormalisable, Dyson-Schwinger equation model of two-flavour QCD we explore the chemical-potential dependence of the dressed-quark propagator, which provides a means of determining the behaviour of the chiral and deconfinement order parameters, and low-energy pion observables. We find coincident, first order deconfinement and chiral symmetry restoration transitions at \mu_c = 375 MeV. f_\pi is insensitive to \mu until \mu \approx \mu_0 = 0.7 mu_c when it begins to increase rapidly. m_\pi is weakly dependent on \mu, decreasing slowly with \mu and reaching a minimum 6% less than its \mu=0 value at \mu=\mu_0. In a two-flavour free-quark gas at \mu=\mu_c the baryon number density would be approximately 3 \rho_0, where \rho_0=0.16 fm^{-3}; while in such a gas at \mu_0 the density is \rho_0.

Chirality measure and chiral order parameter for a two-dimensional system

A chirality measure and a chiral order parameter are defined for two-dimensional systems based upon the transformation properties of pseudotensors. The quantities are derived by considering the polarization induced by an electric field applied normal to a system comprising a vacuum above an inhomogeneous dielectric bounded by a plane surface. The quantities are defined by analogy to the three-dimensional case which has been considered by the authors previously. The index is illustrated by a calculation of the chiral order parameter for an Archimedean spiral structure.