Search

One of the main goals of the cold baryonic matter (CBM) experiment at FAIR is to explore the phases of strongly interacting matter at finite temperature and baryon chemical potential μ B . The equation of state of quantum chromodynamics (QCD) at μ B > 0 is an essential input for the CBM experiment, as well as for the beam energy scan in the Relativistic Heavy Ion Collider(RHIC) experiment. Unfortunately, it is highly nontrivial to calculate the equation of state directly from QCD: numerical Monte Carlo studies on lattice are not useful at finite μ B . Using the method of Taylor expansion in chemical potential, we estimate the equation of state, namely the baryon number density and its contribution to the pressure, for two-flavor QCD at moderate μ B . We also study the quark number susceptibilities. We examine the technicalities associated with summing the Taylor series, and explore a Pade resummation. An examination of the Taylor series can be used to get an estimate of the location of the critical point in μ B , T plane.

Strongly interacting matter, which makes up the nuclei of atoms, is described by a theory called quantum chromodynamics (QCD). A critical point in the phase diagram of QCD, if established either theoretically or experimentally, would be as profound a discovery as the familiar gas–liquid critical point discovered in the nineteenth century. Due to the extremely short-lived nature of the concerned phases, novel experimental techniques are needed to search for it. The Relativistic Heavy Ion Collider (RHIC) in USA has an experimental programme which can fit the bill to do so. Theoretical techniques of Lattice QCD, which is QCD defined on a discrete space-time lattice, have provided glimpses into where the QCD critical point may be, and how to search for it in the experimental data. A brief overview of the theoretical and experimental attempts is provided.

The freeze-out curve in the QCD phase diagram embodies a substantial amount of precise experimental data in heavy ion collisions. We present our lattice QCD results along the freeze-out curve. The variance, skew and kurtosis of the event distribution of baryon number are studied at several energies of interest through Pade resummations. A smooth behaviour is predicted for three ratios of these quantities at current RHIC and future LHC energies. Any deviations from these at the RHIC energy scan would signal the presence of a nearby critical point. Our lattice results on the critical point do show such a behaviour.

We present lattice QCD results along the freezeout curve of heavy-ion collisions for the ongoing RHIC energy scan as well as the LHC heavy-ion runs planned for this year. The skew and kurtosis of the event distribution of baryon number are positive at all energies studied, We predict three ratios of non-linear susceptibilities along the freezeout curve as functions of the colliding energy, Sqrt[S_{NN}]. They have smooth behaviour except in the vicinity of a critical point; this can have multiple benefits.

I review a few selected topics in Lattice Quantum Chromo Dynamics, focusing more on the recent results. These include i) the equation of state and speed of sound, ii) J/\psi suppression, iii) flavour correlations and iv) the QCD phase diagram in the \mu-T plane., Comment: 13 Pages including figures, Plenary Talk at the 9th Workshop on High Energy Physics Phenomenology, ``WHEPP9'', Bhubaneswar, India, January 3-14, 2006, To appear in Pramana

I present our recent results on the critical end point in the \mu_B-T phase diagram of QCD with two flavours of light dynamical quarks and compare them with similar results from other groups. Implications for a possible energy scan at the RHIC are discussed. I also comment briefly on the new results of great relevance to heavy ion collisions from finite temperature lattice QCD simulations on speed of sound, specific heat and on the fate of J/\psi., Comment: Invited Plenary Talk given at 5th International Conference on Physics and Astrophysics of Quark Gluon Plasma, Kolkata, India, February 8-12, 2005; LaTeX in Journal of Physics G style; 9 pages including figures

I review some topics in lattice quantum chromodynamics, focusing more on the recent results. These include: (i) the QCD phase diagram in the μ-T plane, (ii) the quark number susceptibilities, and (iii) the screening lengths.

Results from our recent investigations of quark number susceptibilities in both quenched and 2-flavour QCD are presented as a function of valence quark mass and temperature. A strong reduction (approx. 40%) is seen in the strange quark susceptibility above T_c in both the cases. A comparison of our isospin susceptibility results with the corresponding weak coupling expansion reveals once again the non-perturbative nature of the plasma up to 3T_c. Evidence relating the susceptibility to another non-perturbative phenomena, pionic screening lengths, is presented., Talk presented at the 18th Alexander von Humboldt symposium ``100 Years Werner Heisenberg - Works and Impact'', Bamberg, Germany, September 26-30, 2001. 6 pages, LaTeX, buckow.sty needed

Results from our simulations of QCD with two light dynamical staggered flavours of mass m/Tc=0.1 are presented. Employing our earlier proposed Taylor series method for the baryonic susceptibility, we estimate the radius of convergence by using terms up to the eighth order susceptibility, χ8. Comparing with earlier results on coarser lattices, we find a very good agreement between the Nt =8 and 6 lattices for its location in the ( μB/T ,T/Tc) plane, suggesting any cut-off effects to be encouragingly small.

A critical point in the phase diagram of Quantum Chromodynamics (QCD), if established either theoretically or experimentally, would be as profound a discovery as the good-old gas-liquid critical point. Unlike the latter, however, first-principles based approaches are being employed to locate it theoretically. Due to the short lived nature of the concerned phases, novel experimental techniques are needed to search for it. The Relativistic Heavy Ion Collider (RHIC) in USA has an experimental program to do so. This short review is an attempt to provide a glimpse of the race between the theorists and the experimentalists as well as that of the synergy between them., 15 Pages, Invited Review for Pramana

We report the first measurements of sixth order non-linear quark number susceptibilities in continuum QCD. This extends our earlier computation of the continuum limit of non-linear quark number susceptibilities and the pressure in QCD for m/Tc=0.1. For T/Tc > 1.5, no phase transitions are observable for mu, 3 pages, 4 figures, Lattice2003(nonzero)

We present results of our simulations of QCD with two light dynamical quarks on a 32^3 X 8 lattice at a current quark mass tuned to have the Goldstone pion mass of about 230 MeV. Employing the Taylor expansion method we proposed earlier, we estimate the radius of convergence of the series for the baryonic susceptibility by using terms up to eighth order. Together with our earlier results, corresponding to the same physical parameters but on coarser lattices at respectively 1.33 times and twice the lattice cut-off (a), we were able to attempt a march towards the continuum limit., Comment: 4 pages, 4 figures, To appear in the proceedings of the 23rd International Conference on Ultrarelativistic Nucleus-Nucleus Collisions, Quark Matter 2012, August 13-18, 2012, Washington DC

We compute the quark number susceptibilities in two flavor QCD for staggered fermions by adding the chemical potential as a Lagrange multiplier for the point-split number density term. Since lesser number of quark propagators are required at any order, this method leads to faster computations. We propose a subtraction procedure to remove the inherent undesired lattice terms and check that it works well by comparing our results with the existing ones where the elimination of these terms is analytically guaranteed. We also show that the ratios of susceptibilities are robust, opening a door for better estimates of location of the QCD critical point through the computation of the tenth and twelfth order baryon number susceptibilities without significant additional computational overload., Comment: 10 pages, 12 figures

Screening correlators and masses were studied at finite temperature in QCD with two flavors of dynamical staggered quarks on a lattice. The spectrum of screening masses show a hierarchical approach to chiral symmetry restoration. Control of explicit chiral symmetry breaking through the quark mass was shown to be an important step toward understanding this phenomenon. No sign of decay was found in the finite temperature scalar mesonlike correlators in the confined phase.

The momentum diffusion coefficient for heavy quarks is studied in a deconfined gluon plasma in the static approximation by investigating a correlation function of the color electric field using Monte Carlo techniques. The diffusion coefficient is extracted from the long distance behavior of such a correlator. For temperatures Tc < T, Comment: Minor changes, version to appear in Physical Review D

We study the associated production of $ J/\psi\ + \gamma $ in fixed-target experiments with nuclear targets as well as at the relativistic heavy-ion collider (RHIC). We find that this process affords a very clean probe of $\rho_g$, the ratio of gluon density in a heavy nucleus to that of a proton. The combined $x$ range thus available can be used to discriminate between the predictions of different models of the EMC effect for $\rho_g$., Comment: 10 pages, 4 Figures (not included, available only by p-mail), LaTeX, CERN-TH.6679/92, TIFR/TH/92-59, BU-TH-92/3, Minor revision. Replaced version has the style file equation.sty appended for easy processing, which is the only change

We consider the possibility that color deconfinement and chiral symmetry restoration do not coincide in dense baryonic matter at low temperature. As a consequence, a state of massive "constituent" quarks would exist as an intermediate phase between confined nuclear matter and the plasma of deconfined massless quarks and gluons. We discuss the properties of this state and its relation to the recently proposed quarkyonic matter., 17 pages, 9 figures

We investigate medium effects on mesonic screening lengths for QCD with 2-flavours of dynamical staggered quarks on lattices with cutoff a=1/6T. Denoting the cross-over temperature by $T_c$, we vary the temperature T from 0.89$T_c$ to 1.92$T_c$, spanning both the hadronic and quark gluon plasma phases. While chiral symmetry restoration in the vector channel appears to take place near $T_c$, it is seen in the scalar channel only above 1.33 $T_c$. Varying spatial lattice sizes, we find very little volume dependence in our results at 0.94 $T_c$. We discuss the stability of the scalar meson at these temperatures., Comment: Talk presented at The XXVIII International Symposium on Lattice Field Theory, Lattice2010, June 14-19, 2010, Villasimius, Italy

We report results of the investigation of physics at finite chemical potential using the method of Taylor expansion of the free energy for staggered quarks with m π ≃ 210 MeV on N t = 6 lattices. When the spatial volume is (4/T E ) 3 we estimate that the location of the critical end point is at T E /T c ≃ 0.94(1) and μ E B /T E ≃ 1.8(1). This is to be compared to an earlier estimate of T E /T c ≃ 0.95(1) and μ E B /T E ≃ 1.3(3) made on similar spatial volumes and quark masses but with N t = 4.

Quantum Chromo Dynamics (QCD), the theory of strong interactions, predicts a transition of the usual matter to a new phase of matter, called Quark-Gluon Plasma (QGP), at sufficiently high temperatures. The non-perturbative technique of defining a theory on a space-time lattice has been used to obtain this and other predictions about the nature of QGP. Heavy ion collisions at the Large Hadron Collider in CERN can potentially test these predictions and thereby test our theoretical understanding of confinement. This brief review aims at providing a glimpse of both these aspects of QGP., Comment: 26 pages, 31 Figures, Invited article for the volume on LHC physics to celebrate the Platinum Jubilee of the Indian National Science Academy, edited by Amitava Datta, Biswarup Mukhopadhyaya and Amitava Raychaudhuri. Needs style file insa.sty (included)

We investigate the Taylor expansion of the baryon number susceptibility, and hence, pressure, in a series in the baryon chemical potential (mu_B) through a lattice simulation with light dynamical staggered quarks at a finer lattice cutoff a=1/6T. We determine the QCD cross over coupling at mu_B=0. We find the radius of convergence of the series at various temeperatures, and bound the location of the QCD critical point to be T^E/T_c = 0.94 and mu_B^E/T < 1.8. We also investigate the extrapolation of various susceptibilities and linkages to finite chemical potential., 16 pages, 12 figures

Results from our recent investigations of quark number susceptibilities in both quenched and 2-flavour QCD are presented as a function of valence quark mass and temperature. A strong reduction (~40%) is seen in the strange quark susceptibility above T c in both the cases. A comparison of our isospin susceptibility results with the corresponding weak coupling expansion reveals once again the non-perturbative nature of the plasma up to 3T c . Evidence relating the susceptibility to another non-perturbative phenomena, pionic screening lengths, is presented.

Fluctuations of conserved quantities in heavy-ion collisions have been argued to be diagnostic tools for the nature of the produced phase. These can be related to the predictions of quark number susceptibilities (QNS) from lattice QCD. Using the diagonal QNS, we extracted the Wroblewski parameter in a dynamical QCD computation. Our results on the cross correlations \chi_{BQ}, \chi_{BY}, \chi_{BS} and \chi_{QY} allow us to explore the charge and baryon number of objects that carry flavour. We present evidence that in the high temperature phase of QCD the different flavour quantum numbers are excited in linkages which are exactly the same as one expects from quarks., Comment: 9 pages, 6 Figures, Invited Talk at the International Conference on Strangeness in Quark Matter, ``SQM2006'', UCLA, Los Angeles, USA, Mar. 26-31, 2006

The Wroblewski parameter is a convenient indicator of strangeness production and can be employed to monitor a signal of quark-gluon plasma production : enhancement of strangeness production. It has been shown to be about a factor two higher in heavy ion collisions than in hadronic collisions. Using a method proposed by us earlier, we obtained lattice QCD results for the Wroblewski parameter from our simulations of QCD with two light quarks both below and above the chiral transition. Our first principles based and parameter free result compare well with the A-A data from SPS and RHIC., 5 pages, Plenary talk by R.V.G. at Hard Probes 2004, Ericeira, Portugal, Nov.4-10, 2004; Reference added

Lattice QCD predicts a phase transition to a hitherto unseen state of matter called quark-gluon plasma (QGP). A few microseconds after the big bang, our universe was most likely filled with QGP. Amazingly, attempts to produce QGP in the laboratory are currently going on in the relativistic heavy ion collider (RHIC) in the USA. In the following, we introduce the concept of QGP and then move on to its description in terms of the underlying field theory, namely quantum chromodynamics (QCD). Lattice QCD has yielded the most reliable predictions for QGP. After introducing the basics, the elementary aspects of heavy ion physics is covered with some examples of signatures of QGP.

We report measurements of diagonal susceptibilities for the baryon number, ${\ensuremath{\chi}}_{B}$, electrical charge, ${\ensuremath{\chi}}_{Q}$, third component of isospin, ${\ensuremath{\chi}}_{I}$, strangeness, ${\ensuremath{\chi}}_{S}$, and hypercharge, ${\ensuremath{\chi}}_{Y}$, as well as the off-diagonal ${\ensuremath{\chi}}_{BQ}$, ${\ensuremath{\chi}}_{BY}$, ${\ensuremath{\chi}}_{BS}$, etc. We show that the ratios of susceptibilities in the high-temperature phase are robust variables, independent of lattice spacing, and therefore give predictions for experiments. We also investigate strangeness production and flavor symmetry breaking matrix elements at finite temperature. Finally, we present evidence that in the high-temperature phase of QCD the different flavor quantum numbers are excited in linkages which are exactly the same as one expects from quarks. We present some investigations of these quarklike quasiparticles.

We investigate the critical end point of QCD with two flavours of light dynamical quarks at finite lattice cutoff a=1/4T using a Taylor expansion of the baryon number susceptibility. We find a strong volume dependence of the position of the critical end point. In the large volume limit we obtain T^E/T_c \~ 0.95 and mu_B^E/T^E ~ 1.1, where T_c is the cross over temperature at zero chemical potential, and T^E and mu_B^E are the temperature and the baryon chemical potential at the critical end point. The small value of mu_B^E places it in the range of observability in energy scans at the RHIC., this version contains all the figures that appear in the published journal version

Enhancement of strangeness production has since long been proposed as a promising signal of quark-gluon plasma production. A convenient indicator for it is the Wroblewski parameter which has been shown to be about a factor two higher in heavy ion collisions. Using a method proposed by us earlier, we obtained lattice QCD results for the Wroblewski parameter from our simulations of QCD with two light quarks both below and above the chiral transition. Our first principles based and parameter free result compare well with the A-A data., Comment: 5 pages, 5 figures, To appear in the proceedings of the seventeenth international conference on Ultra-Relativistic Nucleus-Nucleus Collisions (Quark Matter 2004), Oakland, USA

We investigate the quark sector of quenched QCD for $1.5l~{T/T}_{c}l~3$ in the continuum limit, using two different lattice discretizations of quarks and extrapolating from lattice spacings between $1/4T$ and $1/14T.$ At these temperatures, the flavor off-diagonal susceptibility ${\ensuremath{\chi}}_{\mathrm{ud}}{/T}^{2}$ is compatible with zero at each lattice spacing, and hence also in the continuum limit. In the continuum limit, the light quark susceptibilities are about 10% less than the ideal gas results even at the highest T, in agreement with hard thermal loop predictions but marginally below a resummed perturbative computation. For the mass range appropriate to the strange quark, the flavor diagonal susceptibility is significantly smaller. Our estimate of the Wroblewski parameter is compatible with observations at BNL RHIC and CERN SPS. The continuum limit of screening masses in all (local) quark bilinears is very close to the ideal gas results.

We report the first investigation of the QCD transition temperature, T_c, for two flavours of staggered quarks with unequal masses at lattice spacings of 1/4T. On changing the u/d quark mass ratio in such a way that m(pi_0)^2/m(pi_+)^2 changes from 1 to 0.78, thus bracketing the physical value of this ratio, we find that T_c remains unchanged in units of both m_rho and Lambda_MSbar., Comment: 12 pages, 5 figures

We studied QCD with two flavors of dynamical staggered quarks at finite temperature, with a bare sea quark mass of about 17 MeV. We report investigations of baryon, isospin, charge and strangeness susceptibilities, as well as screening masses obtained from correlators of local and one-link separated meson operators. These were studied as functions of valence quark mass at several temperatures. Our results for susceptibilities deviate significantly from ideal gas values, and even more from the weak coupling series. We also report the first measurement of off-diagonal quark number susceptibilities below the transition temperature, Tc, where they are the main contribution to charge fluctuations. We present evidence for a close connection between the susceptibilities and the screening masses., Comment: 15 pp, 4 figs

We report first results on the strange quark number susceptibility, chi_s, over a large range of temperatures, mainly in the plasma phase of QCD. Chi_s jumps across the phase transition temperature, T_c, and grows rapidly with temperature above but close to T_c. For all quark masses and susceptibilities in the entire temperature range studied, we found significant departures from ideal-gas values. We also observed a strong correlation between these quantities and the susceptibility in the scalar/pseudo-scalar channel, supporting ideas of ``dynamical confinement'' in the high temperature phase of the QCD plasma., Comment: 4 pages, 4 figures

Using weak coupling methods McLerran and Venugopalan~\cite{LV1} expressed the parton distributions in large nuclei as correlation functions of a two dimensional Euclidean field theory. The theory has the dimensionful coupling $g^2 ��$, where $��^2\sim A^{1/3}$ is the valence quark color charge squared per unit area. We use a lattice regularization to investigate these correlation functions both analytically and numerically for the simplified case of $SU(2)$ gauge theory. In weak coupling ($g^2��L<< 5$), where $L$ is the transverse size of the nucleus, the numerical results agree with the {\it analytic} lattice weak coupling results. For $g^2��L>> 5$, no solutions exist at O($a^4$) where $a$ is the lattice spacing. This suggests an ill-defined infrared behavior for the two dimensional theory. A recent proposal of McLerran et al.~\cite{Kovner} for an {\it analytic} solution of the classical problem is discussed briefly., 21 pages in LaTex+six figures

A systematic study of the inclusive single heavy quark and heavy-quark pair production cross sections in pp collisions is presented for RHIC and LHC energies. We compare with existing data when possible. The dependence of the rates on the renormalization and factorization scales is discussed. Predictions of the cross sections are given for two different sets of parton distribution functions., Comment: 28 pages, 10 tables, 30 figures

We compute the J/ψ production in leading order of QCD perturbation theory in the central region of pp and AA collisions at CERN (√ s =20 GeV / N ) energy. The parton distribution functions which we use for nuclei take the EMC effect into account, albeit in a model-dependent way. We find a large suppression of J/ψ in O 16 -U collisions at √ s =20 GeV / N relative to pp collisions depending on the model.

Using a Langevin algorithm to incorporate low-mass dynamical quarks, we simulate QCD with three light flavors on an 8 3 × 4 lattice. We find clear metastabilities in lattice measurables at a quark mass of 0.025 in lattice units, whereas earlier analyses at 4 times the mass above did not prove their presence. Our results suggest a first-order chiral phase transition in three-flavor QCD. We also confirm the presence of a stronger first-order transition with four flavors and indicate the possibility of a weaker first-order transition with two flavors.

We analyse large p T J ψ production in the central rapidity region of nucleus-nucleus (AA) and proton-proton (pp) collisions, in the framework of perturbative QCD. The nuclear effects are assumed to come entirely from the structure functions. We find qualitative similarities with the expected signature of a quark-gluon plasma. The cross section for J ψ production in AA collisions relative to that in pp collisions is suppressed more at small pT than at large pT. The Drell-Yan production of muon pairs, on the other hand, shows very little pT dependence.

We present first results for the masses of the 0 ++ and 2 ++ glueballs obtained from a simulation of lattice QCD on a 4 3 ·24 lattice with the effects of dynamical fermions included using the pseudo-fermion method. The masses are determined from the exponential falloff of adjoint line correlation functions. We find that M 2 ++ M 0 ++ , extending an earlier result by Berg, Billoire and Vohwinkel for the pure gauge case to the full theory.

Quark number susceptibility on the lattice, obtained by merely adding a $\mu N$ term with $\mu$ as the chemical potential and $N$ as the conserved quark number, has a quadratic divergence in the cut-off $a$. We show that such a divergence already exist for free fermions with a cut-off regulator. While one can eliminate it in the free lattice theory by suitably modifying the action, as is popularly done, it can simply be subtracted off as well. Computations of higher order susceptibilities, needed for estimating the location of the QCD critical point, then need a lot fewer number of quark propagators at any order. We show that this method of divergence removal works in the interacting theory., Comment: Published version, with added discussion of the results and the appendix removed

On mesure, en utilisant des fermions en quiconce, la susceptibilite du nombre de quark de la chromodynamique quantique trempee dans une simulation de Monte Carlo sur un reseau 8 3 ×4. Aux basses temperatures, elles est compatible avec zero et s'eleve subitement a des valeurs non nulles a travers la transition de phase de deconfinement connue. On etudie les implications pour l'interpretation de cette susceptibilite comme indicateur de la presence des modes baryoniques legers dans le plasma

A systematic analysis of the L-dependence of the J/psi-suppression in the data of the CERN NA38 and NA50 experiments shows that the anomalous suppression in the 1995 Pb-Pb data is at best a 4$\sigma$ effect at any of the L-values for the Pb-Pb data, where L is the geometrical mean path length of the J/psi in the colliding nuclei. Possible implications for the 1996 data are discussed., Comment: 7 pages, Latex with epsfig, 2 figures (PS-files)