arXiv subjects
Publications and source records attributed to Wojciech Broniowski.
Chiral quark models offer a practical and simple tool to describe covariantly both low and high energy phenomenology in combination with QCD evolution. This can be done in full harmony with chiral symmetry and electromagnetic gauge invariance. We review the recently proposed spectral quark model where all these constraints are implemented.
We analyze the impact-parameter dependent diagonal non-singlet generalized parton distribution of the pion in two distinct chiral quark models: the Spectral Quark Model and the Nambu-Jona-Lasinio model. Leading-order perturbative QCD evolution from the low quark-model scale to higher scales is carried out with the help of the inverse Mellin transform. The model agrees very reasonably with the recent results from transverse-lattice calculations, while the forward parton distribution agrees with the experimental data.
We compute the off-forward diagonal non-singlet generalized parton distribution of the pion in two distinct chiral quark models: the Nambu-Jona-Lasinio model with the Pauli-Villars regulator and the Spectral Quark Model. The analysis is carried out in the impact-parameter space. Leading-order perturbative QCD evolution is carried out via the inverse Mellin transform in the index space. The model predictions agree very reasonably with the recent results from transverse-lattice calculations, reproducing qualitatively both the Bjorken-x and the impact-parameter dependence of the data.
Production of resonances is considered in the framework of the single-freeze-out model of ultra-relativistic heavy ion collisions. The formalism involves the virial expansion, where the probability to form a resonance in a two-body channel is proportional to the derivative of the phase-shift with respect to the invariant mass. The thermal model incorporates longitudinal and transverse flow, as well as kinematic cuts of the STAR experiment at RHIC. We find that the shape of the pi+ pi- spectral line qualitatively reproduces the preliminary experimental data when the position of the rho peak is lowered. This confirms the need to include the medium effects in the description of the RHIC data. We also analyze the transverse-momentum spectra of rho, K*(892), and f_0(980), and find that the slopes agree with the observed values. Predictions are made for eta, eta', omega, phi, Lambda(1520), and Sigma(1385).
The unintegrated quark and gluon distributions in the pion and nucleon are analysed using the CCFM equations in the single-loop approximation. We utilise the transverse-coordinate (or impact-parameter) representation which diagonalises the equations and study in detail the dependence on the transverse coordinate induced by the CCFM evolution. We find considerable broadening of the transverse-momentum distributions with an increasing magnitude of the hard scale, Q. For instance, at the Bjorken x=0.1 the root mean squared transverse momentum of the gluons is enhanced by about 1 GeV when evolved from the the initial low scale to Q^2=10 GeV^2, and by about 2 GeV when evolved up to Q^2=100 GeV^2. The broadening effect is enhanced with decreasing Bjorken x, and is stronger for the gluons than for the quarks. Analytic solution for the average transverse momentum corresponding to the x-moments of the distributions is obtained. The parton luminosities are also discussed.
We propose a spectral quark model which can be applied to low energy hadronic physics. The approach is based on a generalization of the Lehmann representation of the quark propagator. We work at the one-quark-loop level. Electromagnetic and chiral invariance are ensured with help of the gauge technique which provides particular solutions to the Ward-Takahashi identities. General conditions on the quark spectral function follow from natural physical requirements. In particular, the function is normalized, its all positive moments must vanish, while the physical observables depend on negative moments and the so-called log-moments. As a consequence, the model is made finite, dispersion relations hold, chiral anomalies are preserved, and the twist expansion is free from logarithmic scaling violations, as requested of a low-energy model. We study a variety of processes and show that the framework is very simple and practical. Finally, incorporating the idea of vector-meson dominance, we present an explicit construction of the quark spectral function which satisfies all the requirements. The corresponding momentum representation of the resulting quark propagator exhibits only cuts on the physical axis, with no poles present anywhere in the complex momentum space. The momentum-dependent quark mass compares very well to recent lattice calculations. A large number of predictions and relations can be deduced from our approach for such quantities as the pion light-cone wave function, non-local quark condensate, pion transition form factor, pion valence parton distribution function, etc.
A simple thermal model with single freeze-out and flow is used to analyze the ratios of hadron yields and the hadron transverse-mass spectra measured in 130 GeV Au+Au collisions at RHIC. An overall very good agreement between the model predictions and the data is achieved for all measured hadron species, including hyperons.
We continue the analysis of the preceding talk with a discussion of the elliptic flow and the HBT pion correlation radii. It is shown that the thermal model can be extended to describe these phenomena. The description of the elliptic flow involves an appropriate deformation of the freeze-out hypersurface and flow velocity. The obtained results agree reasonably with the data for soft (< 2 GeV) transverse momenta. For the pionic HBT correlation radii the experimental feature that R_out/R_side ~ 1 is naturally obtained. The reproduction of individual R_side and R_out can be achieved with the inclusion of the excluded volume corrections, which effectively increase the radii by \~30%.
We study the approximation of chiral quark models with simpler models, obtained via gradient expansion. The resulting Lagrangian of the type of the linear sigma-model contains, at the lowest level, an additional term with two derivatives. We investigate the dynamical consequences of this term and its relevance to the phenomenology of the soliton models of the nucleon. It is found that the inclusion of the new term allows for a more efficient approximation of the underlying quark theory, especially in those cases where dynamics allows for a large deviation of the chiral fields from the chiral circle, such as in quark models with non-local regulators.
Applications of a simple thermal model to ultra-relativistic heavy-ion collisions are presented. We compute abundances of various hadrons, including particles with strange quarks, the pT-spectra, and the HBT radii for the pion. Surprising agreement is found, showing that the thermal approach can be used successfully to understand and describe the RHIC data.
We compute the pion light-cone wave function and the pion quark distribution amplitude in the Nambu-Jona-Lasinio model. We use the Pauli-Villars regularization method and as a result the distribution amplitude satisfies proper normalization and crossing properties. In the chiral limit we obtain the simple results, namely phi_pi(x)=1 for the pion distribution amplitude, and = -M / f_pi^2 for the second moment of the pion light-cone wave function, where M is the constituent quark mass and f_pi is the pion decay constant. After the QCD Gegenbauer evolution of the pion distribution amplitude good end-point behavior is recovered, and a satisfactory agreement with the analysis of the experimental data from CLEO is achieved. This allows us to determine the momentum scale corresponding to our model calculation, which is close to the value Q_0 = 313 MeV obtained earlier from the analogous analysis of the pion parton distribution function. The value of is, after the QCD evolution, around (400 MeV)^2. In addition, the model predicts a linear integral relation between the pion distribution amplitude and the parton distribution function of the pion, which holds at the leading-order QCD evolution.
We show that the transverse-momentum spectra of all hadrons measured at RHIC, including hyperons, are described very well in a thermal model assuming the simultaneous chemical and thermal freeze-outs. The model calculation takes into account all hadronic resonances and uses a simple parametrization of the freeze-out hypersurface.
We show, by means of a simple compilation of the available experimental results, that the pT-spectra obtained at RHIC and SPS are strikingly similar up to pT ~ 1.5-2 GeV. In fact, the discrepancies between various experimental groups working at the same experiment are of the same size as the differences between RHIC and SPS. Our observation is complementary to the well known fact of the equality of the measured R_side and R_out HBT radii at RHIC and SPS. In essence, it points out that the transverse size of the firecylinder and the strength of the transverse flow are not significantly changed between SPS and RHIC. This suggests that a saturation mechanism is effective already at SPS. We also point out that the dominance of protons over pi^+ at large pT can be seen not only in the RHIC data, but already in the SPS data.
Strange particle ratios and pT-spectra are calculated in a thermal model with single freeze-out, previously used successfully to describe non-strange particle production at RHIC. The model and the recently released data for phi, Lambda, anti-Lambda, and K*(892) are in very satisfactory agreement, showing that the thermal approach can be used to describe the strangeness production at RHIC.
The pt-spectra of hadrons measured at RHIC are very well described in a model which assumes that the chemical and thermal freeze-outs occur simultaneously. The model calculation includes all hadronic resonances and uses a simple parametrization of the freeze-out hypersurface.
Medium modifications of the pion-omega-rho vertex are analyzed in context of the omega -> pi gamma* and rho -> pi gamma* decays in nuclear matter. A relativistic hadronic model with mesons, nucleons, and Delta(1232)isobars is applied. A substantial increase of the widths for the decays omega -> pi gamma* and rho -> pi gamma* is found for photon virtualities in the range 0.3-0.6 GeV. This enhancement has a direct importance for the description of dilepton yields obtained in relativistic heavy-ion collisions.
The assumption of simultaneous chemical and thermal freeze-outs of the hadron gas leads to a surprisingly accurate, albeit entirely conventional, explanation of the recently-measured RHIC pT spectra. The original thermal spectra are supplied with secondaries from decays of all resonances, and subsequently folded with a suitably parameterized expansion involving longitudinal and transverse flow. The predictions of this thermal approach, with various parametrizations for the expansion, are in a striking quantitative agreement with the data in the whole available range of 0 < pT < 3.5GeV.
Predictions of the single-freeze-out model for the particle spectra at RHIC are presented. The model assumes that the chemical and thermal freeze-outs occur simultaneously, and incorporates in simple terms the longitudinal and transverse flow. All resonance decays are included. The model predictions and the data are in striking agreement in the whole available range of momenta.