Quark Density Research Articles

On the Landau-gauge adjoint quark propagator

Quarks in the adjoint representation have been a subject of study for both conceptual and practical purposes. Conceptually, their differences when it comes to confining and chiral symmetry properties has long been suspected to hold important information on the relation of these two distinguished properties of QCD-like gauge theories. Practically, they have been studied as both a possibility to access finite density quark systems as well as candidate theories for technicolor in beyond-the-standard-model settings. The most elementary object describing such particles is their propagator, though it being gauge-dependent. Its properties in the minimal Landau gauge are investigated here both in the quenched and unquenched case for a range of lattice parameters using the Wilson formulation for the gauge group SU(2). It is found that the propagator shows pronounced differences to the case of fundamental quarks, especially towards the chiral limit.

The Quark Number Susceptibility of QCD at Finite Temperature and Chemical Potential

We calculate the quark number density and quark number susceptibility (QNS) of QCD at finite chemical potential μ and finite temperature T in the framework of a new nonperturbative QCD model. Analysis and discussions of the calculated results of the QNS are given. It is found that the quark number density has a singularity when μ comes close to a critical value μ0, and the QNS χ(μ,T) becomes discontinuous at some values of T. At high temperature the QNS approaches the free quark gas result, while at very low temperature the QNS equals zero. Importantly, the QNS shows a sudden increase near some temperature (T ∼ 120 MeV), which may be regarded as the signal of a crossover.

Probing nuclear parton densities (and more) from γ + Q production in p–A and A–A collisions

We present a detailed phenomenological study of the associated production of a prompt photon and a heavy-quark jet (charm or bottom) in proton-nucleus (p–A) collisions. The dominant contribution to the cross-section comes from the gluon-heavy-quark (gQ) initiated subprocess, making this process very sensitive to the gluon and the heavy quark nuclear parton densities. We show that the future p–A data to be collected at the LHC in this channel should help to disentangle the various nPDF sets currently available. In heavy-ion collisions, the photon transverse momentum can be used to gauge the initial energy of the massive parton propagating through the dense QCD medium produced in those collisions, making γ + Q production a powerful process in order to probe energy loss dynamics in the heavy-quark sector.

Scalar and Pseudo-Scalar Form Factors in Electro- and Weak-Production of Pion Near Threshold

We investigated pion production near threshold by the weak current in terms of multipole amplitudes. By exploiting the chiral Ward identity based on the QCD Lagrangian, we derived relevant multipole amplitudes in closed forms and presented their numerical results. In the amplitudes, scalar and pseudo scalar (PS) form factors, which represent the scalar and the PS quark density distributions, manifest by themselves. We applied these amplitudes to the cross sections for the weak- and electro-production near threshold. Both pion and PS form factor contributions are shown to account for the t-channel contribution in the charged pion electro-production near threshold. The asymmetry on the pion production by the neutrino and anti-neutrino is also discussed with their longitudinal and transverse cross sections.

Towards the phase diagram of dense two-color matter

We study two-color QCD with two flavors of Wilson fermion as a function of quark chemical potential $\ensuremath{\mu}$ and temperature $T$. We find evidence of a superfluid phase at intermediate $\ensuremath{\mu}$ and low $T$ where the quark number density and diquark condensate are both very well described by a Fermi sphere of nearly free quarks disrupted by a BCS condensate. Our results suggest that the quark contribution to the energy density is negative (and balanced by a positive gauge contribution), although this result is highly sensitive to details of the energy renormalization. We also find evidence that the chiral condensate in this region vanishes in the massless limit. This region gives way to a region of deconfined quark matter at higher $T$ and $\ensuremath{\mu}$, with the deconfinement temperature, determined from the renormalized Polyakov loop, decreasing only very slowly with increasing chemical potential. The quark number susceptibility ${\ensuremath{\chi}}_{q}$ does not exhibit any qualitative change at the deconfinement transition. We argue that this is because ${\ensuremath{\chi}}_{q}$ is not an appropriate measure of deconfinement for two-color QCD at high density.

Isolated prompt photon pair production at hadron colliders with k T -factorization

In the framework of the kt-factorization approach, the isolated prompt photon pair production in pp and p \bar p collisions at high energies is studied. The consideration is based on the quark-antiquark annihilation, quark-gluon scattering and gluon-gluon fusion subprocesses, where the non-zero transverse momenta of incoming partons are taken into account. The unintegrated quark and gluon densities in a proton are determined using the Kimber-Martin-Ryskin prescription. The numerical analysis covers the total and differential production cross sections and extends to specific angular correlations between the produced prompt photons. Theoretical uncertainties of our evaluations are studied and comparison with the NLO pQCD calculations is performed. The numerical predictions are compared with the recent experimental data taken by the D0, CDF, CMS and ATLAS collaborations at the Tevatron and LHC energies.

Symmetry breaking effect on determination of polarized and unpolarized parton distributions

We perform a new extraction for unpolarized and polarized parton distribution functions considering a flavor decompositions for sea quarks and applying very recent deep inelastic scattering (DIS) and semi inclusive deep inelastic scattering (SIDIS) data in the fixed flavor number scheme (FFNS) framework. In the new symmetry breaking scenario the light quark and antiquark densities are extracted separately and new parametrization forms are determined for them. The heavy flavors contribution, including charm and bottom quarks, are also taken to be account for unpolarized distributions.

Measurement of Inclusive W and Z Production in ATLAS

A summary of five ATLAS W and Z inclusive measurements are presented, these are a mixture of analyses using the 2010 and 2011 datasets of p s = 7 TeV proton-proton collisions at the LHC. The 2010 data is used to measure the cross sections of the Z, W + and W bosons which are then used with the HERA deep inelastic scattering data to determine the strange quark density of the proton. Three analyses that use 2011 data are shown; a measurement of the forward-backward asymmetry of the Z= boson, from which the e ective weak mixing angle is extracted; a measurement of the angular correlations of Drell-Yan lepton pairs from resonant Z decays; and a measurement of the high mass Drell-Yan di erential cross section.

Measurements of vector bosons plus jets production with the ATLAS detector at the LHC

The production of jets in association with a W or Z boson in proton-proton collisions at √s = 7 TeV is measured with the ATLAS detector at the LHC. The cross sections, differential in several kinematic variables, have been measured up to high jet multiplicities and are compared to new higher-order QCD calculations. Measurements of vector bosons in association with heavy flavor, such as W+c and W+b production, have unique sensitivity to the heavy quark density of the proton. Differential cross sections are presented and compared to QCD predictions at NLO.

Understanding of radial and elliptic expansion with quark number scaling and blast wave model in 200 GeV Au+Au at RHIC-PHENIX

Abstract Measurement of azimuthal anisotropy is one of the most important study because of its relation to the initial stage. Especially, the elliptical anisotropy which is measured as the second coefficient of Fourier expansion of particle azimuthal distribution is believed to carry the information about the initial geometrical anisotropy. It seems the identified hadron v 2 depends on the number of quark contents of the hadron. The experimental result of quark number scaling of v 2 suggests quark level collectivity in the hot dense matter and quark coalescence mechanism to form hadron from quark matter via quark-gluon phase transition. The measured v 2 and p T spectra are analyzed with various assumptions based on the blast wave model in order to understand the freeze-out temperature and collective flow after the system expansion.

Sea quark densities in the effective chiral quark model with generalized harmonic oscillator potential

The solution of the Dirac equation with a generalized harmonic oscillator potential is used to extract the constituent bare parton densities. The results are firstly in spatial space which are converted to momentum space, using the Fourier transformation. The final results are presented in terms of the Bjorken x-variable. Employing the effective chiral quark model and the related convolutions, the parton densities inside the proton are obtained. Choosing an appropriate radius of proton, they indicate reasonable behavior. Although the initial framework is completely theoretical, the results for the sea and valence quark densities and also the ratio of d to u valence quarks inside the proton are in good agreement with the available experimental data and some theoretical models.

THERMODYNAMICS OF (2+1) FLAVOR QGP IN QUASIPARTICLE MODEL

Using our recently developed one parameter quasiparticle model, we analyze more recent (refined) results of (2+1)-flavor quark–gluon plasma (QGP) in lattice simulation of quantum chromodynamics (QCD) by various groups [S. Borsanyi et al., arXiv:1007.2580v2; A. Bazavov et al., Phys. Rev. D80 (2009) 014504; T. Umeda et al., arXiv:1011.2548v1; C. DeTar et al., Phys. Rev. D81 (2010) 114504]. We got a remarkable good fit to lattice thermodynamics of [S. Borsanyi et al., arXiv:1007.2580v2] and reasonable good fit to [A. Bazavov et al., Phys. Rev. D80 (2009) 014504] by adjusting single parameter of the model which may be related QCD scale parameter. The same model also fits the lattice results of [S. Borsanyi et al., arXiv:1007.2580v2] on (2+1+1)-flavor QGP. Further, we extend our model for above system with zero chemical potential to nonzero chemical potential and predict quark density without any new parameters which may be compared with future lattice data.

CHARGED PION CONDENSATION PHENOMENON OF DENSE BARYONIC MATTER INDUCED BY FINITE VOLUME: THE NJL2 MODEL CONSIDERATION

The properties of two-flavored massless Nambu–Jona-Lasinio (NJL) model in (1+1)-dimensional R1 × S1 space–time with compactified space coordinate are investigated in the presence of isospin and quark number chemical potentials μI, μ. The consideration is performed in the large Nc limit, where Nc is the number of colored quarks. It is shown that at L = ∞ (L is the length of the circumference S1) the charged pion condensation (PC) phase with zero quark number density is realized at arbitrary nonzero μI and for rather small values of μ. However, at arbitrary finite values of L the phase portrait of the model contains the charged PC phase with nonzero quark number density (in the case of periodic boundary conditions for quark fields). Hence, finite sizes of the system can serve as a factor promoting the appearance of the charged PC phase in quark matter with nonzero baryon densities. In contrast, the phase with chiral symmetry breaking may exist only at rather large values of L.

A subset solution to the sign problem in random matrix simulations

We present a solution to the sign problem in dynamical random matrix simulations of a two-matrix model at nonzero chemical potential. The sign problem, caused by the complex fermion determinants, is solved by gathering the matrices into subsets, whose sums of determinants are real and positive even though their cardinality only grows linearly with the matrix size. A detailed proof of this positivity theorem is given for an arbitrary number of fermion flavors. We performed importance sampling Monte Carlo simulations to compute the chiral condensate and the quark number density for varying chemical potential and volume. The statistical errors on the results only show a mild dependence on the matrix size and chemical potential, which confirms the absence of sign problem in the subset method. This strongly contrasts with the exponential growth of the statistical error in standard reweighting methods, which was also analyzed quantitatively using the subset method. Finally, we show how the method elegantly resolves the Silver Blaze puzzle in the microscopic limit of the matrix model, where it is equivalent to QCD.

Twist analysis of the nucleon spin in QCD

The decomposition of the nucleon spin into that of quarks and gluons is related to twist-two GPDs according to Ji sum rule. Further decomposition into the helicity and the orbital angular momentum inevitably requires twist-three GPDs. In this paper we derive exact relations between twist-three GPDs and the canonical orbital angular momentum density of quarks and gluons, and check their consistency with the longitudinal spin sum rule. Our work demonstrates that the complete decomposition of the nucleon spin fits well with the framework of perturbative QCD.

Helicity parton distributions at a future electron-ion collider: A quantitative appraisal

We present a quantitative assessment of the impact a future electron-ion collider will have on determinations of helicity quark and gluon densities and their contributions to the proton spin. Our results are obtained by performing a series of global QCD analyses at next-to-leading order accuracy based on realistic sets of pseudo-data for the inclusive and semi-inclusive deep-inelastic scattering of longitudinally polarized electrons and protons at different, conceivable center-of-mass system energies.

(ANTI-)STRANGE DENSITY AND CONTRIBUTION OF HEAVY FLAVOR, $F_2^c$, TO THE NUCLEON STRUCTURE FUNCTION IN THE CHIRAL QUARK MODEL

A new approach is employed to provide the required expressions for the bare constituent quark densities in the proton. In this approach, we assume the bare quark densities take a Gaussian form in four-momentum space, which fulfill more properly the desired constrains of parton densities inside the proton. Using the modified chiral quark model and the related convolutions, the parton densities inside the proton are obtained. By evolving the gluon density to high energy scale, the contribution of charm quark to the proton structure function can be extracted and it is found in good agreement with the available experimental data. Sea quark ((anti-)strange) densities are calculated and compared with the ones from some phenomenological and experimental groups in which consistent results are obtained. What makes the results more valuable is that the initial framework is completely theoretical and we do not need to resort to any parametrizations in our calculations.

Electrical conductivity of quark matter at finiteTunder external magnetic field

We investigate the electrical conductivity (sigma) of quark matter via the Kubo formula at finite temperature and zero quark density (T>0, mu=0) in the presence of an external strong magnetic field. For this purpose, we employ the dilute instanton-liquid model, taking into account its temperature modification with the trivial-holonomy caloron distribution. By doing that, the momentum and temperature dependences for the effective quark mass and model renormalization scale are carefully evaluated. From the numerical results, it turns out that sigma\approx(0.02 ~ 0.15)/fm for T=(0 ~ 400) MeV with the relaxation time tau=(0.3 ~ 0.9) fm. In addition, we also parameterize the electrical conductivity as sigma/T ~ (0.46,0.77,1.08,1.39)C_EM for tau=(0.3,0.5,0.7,0.9) fm, respectively. These results are well compatible with other theoretical estimations, including those from the lattice QCD simulations. It also turns out that the external magnetic field plays only a minor role for sigma even for the very strong one B_0 ~ m^2_pi*10 and becomes relatively effective for T\lesssim200 MeV. Moreover, we compute the soft photon emission rate from the quark-gluon plasma, using the electrical conductivity calculated.

Anisotropic Optical Response of Dense Quark Matter under Rotation: Compact Stars as Cosmic Polarizers

Quantum vortices in the color-flavor locked phase of QCD have bosonic degrees of freedom, called the orientational zero modes, localized on them. We show that the orientational zero modes are electromagnetically charged. As a result, a vortex in the color-flavor locked phase nontrivially interacts with photons. We show that a lattice of vortices acts as a polarizer of photons with wavelengths larger than some critical length.

Temperature and quark density effects on the chiral condensate: an AdS/QCD study

We investigate the dependence of the chiral condensate $<\bar qq>$ on the temperature and quark density using the soft-wall holographic model of QCD, adopting geometries with black holes at finite temperature and quark chemical potential $\mu$. We find that, for $\mu$ below a critical value, increasing the temperature the condensate decreases and vanishes at a temperature $\tilde T\simeq 210$ MeV (at $\mu=0$). An analogous behaviour is observed increasing the chemical potential at fixed temperature. These results agree with the findings obtained by other methods. We also comment on the robustness of the results if geometries not involving black holes are adopted at low temperature, and an Hawking-Page transition is implemented.