Characterizing variable for the critical point in momentum space

The possible experimentally observable signal in momentum space for the critical point, which is free from the contamination of statistical fluctuations, is discussed. It is shown that the higher order scaled moment of transverse momentum can serve as an appropriate signal for the critical point, provided the transverse momentum distribution has a sudden change when energy increases passing through this point. A 2-D percolation model with a linear temperature gradient is constructed to check this suggestion. A sudden change of third order scaled moment of transverse momentum is observed.     

Fluctuations and transverse momentum distributions in the color clustering approach

We present our results on transverse momentum fluctuations, multiplicity fluctuations and transverse momentum distributions for baryons and mesons in the framework of the clustering of color sources. We determine under what conditions the initial state configurations can lead to color connection, and more specifically, if variations of the initial state can lead to a transition from disconnected to connected color clusters, modifying the number of effective sources. We find that beyond a critical point, one has a condensate, containing interacting and hence color-connected sources. This point thus specifies the onset of color deconfinement. We show that the transverse momentum and multiplicity distributions are related to each other in a defined way. We obtain a non-monotonic dependence of the p _T and multiplicity fluctuations with the number of participants. We present our results for the fluctuations and the transverse momentum distributions at RHIC energies compared to the existing experimental data and our predictions for LHC energies.     

Finite-size behaviour of a critical related observable

Accounting for the influence of system size in relativistic heavy ion collisions, the finite-size form of a critical related observable is suggested. The fixed-point and straight line methods are proposed in exploring the QCD critical point and phase boundary in relativistic heavy ion collisions. As an application, the finitesize behaviour of the ratios of higher net-proton cumulants, dynamical electric charge fluctuations, and transverse momentum correlations in Au + Au collisions at RHIC are examined.     

Hadronization in heavy-ion collisions: recombination and fragmentation of partons

We argue that the emission of hadrons with transverse momentum up to about 5 GeV/c in central relativistic heavy ion collisions is dominated by recombination, rather than fragmentation of partons. This mechanism provides a natural explanation for the observed constant baryon-to-meson ratio of about one and the apparent lack of a nuclear suppression of the baryon yield in this momentum range. Fragmentation becomes dominant at higher transverse momentum, but the transition point is delayed by the energy loss of fast partons in dense matter.     

Critical opalescence in baryonic QCD matter

We show that critical opalescence, a clear signature of second-order phase transition in conventional matter, manifests itself as critical intermittency in QCD matter produced in experiments with nuclei. This behavior is revealed in transverse momentum spectra as a pattern of power laws in factorial moments, to all orders, associated with baryon production. This phenomenon together with a similar effect in the isoscalar sector of pions (sigma mode) provide us with a set of observables associated with the search for the QCD critical point in experiments with nuclei at high energies.     

Methods to study event-by-event fluctuations in the NA61/SHINE experiment at the CERN SPS

Theoretical calculations locate the critical point (CP) of strongly interacting matter at energies accessible at the CERN SPS. Event-by-event transverse momentum and multiplicity fluctuations are considered as one of the most important tools to search for the CP. Pilot studies of the energy dependence and the system size dependence of both p _T and multiplicity fluctuations were performed by the NA49 experiment. The NA61/SHINE ion program is a continuation of these efforts. After briefly recalling the essential NA49 results on fluctuations we will discuss the technical methods (removing Non-Target interactions) which we plan to apply for future transverse momentum and multiplicity fluctuation analyses.     

Transverse velocity dependence of the proton-antiproton ratio as a signature of the QCD critical point

The presence of a critical point in the QCD phase diagram can deform the trajectories describing the evolution of the expanding fireball in the mu_B-T phase diagram. If the average emission time of hadrons is a function of transverse velocity, as microscopic simulations of the hadronic freeze-out dynamics suggest, the deformation of the hydrodynamic trajectories will change the transverse velocity (beta_T) dependence of the proton-antiproton ratio when the fireball passes in the vicinity of the critical point. An unusual beta_T dependence of the [over]p/p ratio in a narrow beam energy window would thus signal the presence of the critical point.     

Photon pairs: Quantum chromodynamics continuum and the Higgs boson

A new QCD calculation is summarized for the transverse momentum distribution of photon pairs produced by QCD subprocesses, including all-orders soft-gluon resummation valid at next-to-next-to-leading logarithmic accuracy. Resummation is needed to obtain reliable predictions in the range of transverse momentum where the cross-section is the largest. Results are compared with data from the Fermilab Tevatron and predictions are made for the large hadron collider. The QCD continuum is shown to have a softer spectrum than the Higgs boson signal at the LHC.      

Forward Z-boson production and the unintegrated sea quark density

Drell–Yan production in the forward region at the Large Hadron Collider is sensitive to multiple radiation of QCD partons not collinearly ordered, emitted over large rapidity intervals. We propose a method to take account of these radiative contributions via a factorization formula which depends on the unintegrated, or transverse momentum dependent, splitting function associated with the evolution of the initial-state sea quark distribution. We analyze this formula numerically, and point out kinematic effects from the initial-state transverse momentum on the vector boson spectrum.     

Differential cross sections for Higgs boson production at tevatron collider energies

The transverse momentum Q(T) distribution is computed for inclusive Higgs boson production at sqrt[S]=1.96 TeV. We include all-orders resummation of large logarithms associated with emission of soft gluons at small Q(T). We provide results for Higgs boson and Z* masses from M(Z) to 200 GeV. The relatively hard transverse momentum distribution for Higgs boson production suggests possibilities for improvement of the signal to background ratio.     

Perturbative Correction to Transverse Ward-Takahashi Relation for the Vector Vertex

We re-derive exactly the transverse Ward-Takahashi relation for the vector vertex in momentum space.The result shows that this transverse Ward-Takahashi relation in momentum space involves a perturbative correction term. We demonstrate explicitly that this transverse Ward-Takahashi relation is satisfied indeed at one-loop order.     

Jet quenching versus jet enhancement: a quantitative study of the BDMPS-Z gluon radiation spectrum

We study the gluon radiation spectrum off a hard in-medium produced quark in the multiple soft-rescattering formalism of Baier–Dokshitzer–Mueller–Peigné–Schiff and of Zakharov (BDMPS-Z). Its dependence on the quark and gluon energy, on the gluon transverse momentum, on the in-medium pathlength and on the rescattering properties of the nuclear medium is analyzed quantitatively. The two components of gluon radiation, the hard vacuum radiation associated to the quark production vertex, and the medium-induced rescattering contribution interfere destructively. For small spatial extensions of the medium, this destructive interference overcompensates the hard vacuum radiation, and the total medium-induced radiative energy loss decreases as ΔE∝− L³. Medium-induced gluon production dominates only above a finite critical length L>L_crit which varies between 3 and more than 6 fm depending on the rescattering properties of the medium. Deviations from the BDMPS-L²-behaviour persist above L_crit. The medium-dependence of the angular gluon distribution is dominated by transverse brownian k-broadening. This results in a depletion of the low transverse momentum part of both the hard and the medium-induced contribution. As a consequence, the medium-induced energy loss outside a finite angular cone size Θ can be more than a factor two larger than the total medium-induced radiative energy loss. We discuss implications of these results for the jet quenching signal in relativistic heavy-ion collisions at RHIC and LHC.     

Transverse momentum spectra of the produced hadrons at SPS energy and a random walk model

The transverse momentum spectra of the produced hadrons have been compared to a model, which is based on the assumption that a nucleus–nucleus collision is a superposition of isotropically decaying thermal sources at a given freeze-out temperature. The freeze-out temperature in nucleus–nucleus collisions is fixed from the inverse slope of the transverse momentum spectra of hadrons in nucleon–nucleon collision. The successive collisions in thessss nuclear reactions leads to gain in transverse momentum, as the nucleons propagate in the nucleus following a random walk pattern. The average transverse rapidity shift per collision is determined from the nucleon–nucleus collision data. Using this information, we obtain parameter-free result for the transverse momentum distribution of produced hadrons in nucleus–nucleus collisions. It is observed that such a model is able to explain the transverse mass spectra of the produced pions at SPS energies. However, it fails to satisfactorily explain the transverse mass spectra of kaons and protons. This indicates the presence of collective effect which cannot be accounted for, by the initial state collision broadening of transverse momentum of produced hadrons, the basis of random walk model.     

Experimental Examination of Gyrokinetics of Electron Cyclotron Maser

In this paper the linear and quasi-linear kinetic theories of the electron cyclotron maser are introduced and experimantal examination is made. It is indicated that the transverse momentum spread of the electron beam has critical value; as it grows upto the critical value in the process of the beam-wave interaction, the electron cyclotron maser runs to saturation. Comparison shows good agreement between the theories and a typical experiment.     

Spin dynamics in hole-doped two-dimensional S = 1/2 Heisenberg antiferromagnets: 63Cu NQR relaxation in La2-xSrxCuO4 for x ≤ 0.04

A cluster algorithm formulated in continuous (imaginary) time is presented for Ising models in a transverse field. It works directly with an infinite number of time-slices in the imaginary time direction, avoiding the necessity to take this limit explicitly. The algorithm is tested at the zero-temperature critical point of the pure two-dimensional (2d) transverse Ising model. Then it is applied to the 2d Ising ferromagnet with random bonds and transverse fields, for which the phase diagram is determined. Finite size scaling at the quantum critical point as well as the study of the quantum Griffiths-McCoy phase indicate that the dynamical critical exponent is infinite as in 1d. Received 6 November 1998     

A three-dimensional model for quark and gluon jets

Based on the assumption that a color force-field has a stringlike character (like a stretchedout bag_ with no excited degrees of freedom transverse to the field direction (which is strongly supported by the observed polarization of inclusively produced Λ-particles) we derive the probability to produce heavy flavor quark-antiquark pairs and pairs with transverse momentum in the field. We show how to incorporate the results into a soft hadronisation scheme for particle distributions in quark and gluon jets. We point to some non-trivial effects from the finite (longitudinal) size of the force-field which result on the one hand in important correlations between the longitudinal scaling variable and the transverse momentum and on the other hand leads to correstions to the simple iterative cascade scheme.     

Elliptic flow in Au+Au collisions at square root(S)NN = 130 GeV

Elliptic flow from nuclear collisions is a hadronic observable sensitive to the early stages of system evolution. We report first results on elliptic flow of charged particles at midrapidity in Au+Au collisions at square root(S)NN = 130 GeV using the STAR Time Projection Chamber at the Relativistic Heavy Ion Collider. The elliptic flow signal, v2, averaged over transverse momentum, reaches values of about 6% for relatively peripheral collisions and decreases for the more central collisions. This can be interpreted as the observation of a higher degree of thermalization than at lower collision energies. Pseudorapidity and transverse momentum dependence of elliptic flow are also presented.     

Signature of Critical Point in Momentum Profile of Trapped Ultracold Bose Gases

We present a new method to identify the critical point for the Bose-Einstein condensation(BEC) of a trapped Bose gas.We calculate the momentum distribution of an interacting Bose gas near the critical temperature,and find that it deviates significantly from the Gaussian profile as the temperature approaches the critical point.More importantly,the standard deviation between the calculated momentum spectrum and the Gaussian profile at the same temperature shows a turning point at the critical point,which can be used to determine the critical temperature.These predictions are aiso confirmed by our BEC experiment for magnetically trapped ~(87)Rb gases.     

A study of high transverse momentum η and π0 mesons at the CERN ISR

The production of high transverse momentum η mesons from proton-proton collisions has been studied at the CERN ISR. The decay η→γγ was identified in an array of lead-glass ?erenkov counters. The preliminary results, obtained at a total centre-of-mass energy √s=52.7 GeV, show an η signal, which amounts to approximately one half of the π⁰ cross-section for centre-of-mass transverse momenta between 3 and 5 GeV/c. The production of high transverse momentum π⁰'s was also measured and compared with previous results.