The QGP is assumed to be composed of the light quarks only, i.e., the up and down quarks, which interact weakly, and the gluons which are treated as they are free. That is our goal in this paper. RIS. First and foremost was the unexpected “perfect”-liquid nature of the 4-trillion-degree quark-gluon plasma that permeated the early universe. ]G��j�m�v�ڙo���������O��|l��M�����Nj���3����S`�{���O��"O/����Y��'�Q���1/w!��IP��s�i��9B�@h�֑���7~��� where, {N}_{F}^{+} and {N}_{F}^{-} are the fermion distribution functions as defined in equation (6). Although methods have been discussed to minimize them [19, 20], we have found these to be difficult to implement and not particularly useful. Screened for originality? 1822 It took a century to explain the phenomenon of critical opalescence – divergent ξ of density fluctuations (Smoluchowski). Here is some of what we do know:. Nambu-Jona-Lasinio (NJL) or Polyakov loop extended Starting from a low but non-zero value of T and large Nambu-Jona-Lasinio models [6], [16], [17], [5], [18], [19]. ���(����k�B�% �&v�O��]�PO�s�9S��DU��ֶ.S�V$��[)���y��R-�D����E�1Т8��� � We also adopt a bag constant B1/4 = 165–240 MeV as this range should lead [2] to a critical temperature consistent with the range deduced in the low chemical potential limit from from lattice gauge theory [13]. Figure 1. Hence, we have considered various interpolation schemes. The production of s quarks will be delayed by the time scale for weak decays, and will be further suppressed by adopting the EoS discussed here due to the Boltzmann factor \exp (-m/T). Although considerable recent progress has been made in this later approach, here we consider the former bag model approach because it is often employed in astrophysical simulations for its simplicity. Here, q0 and g0 denote the 0th-order bag model thermodynamic potentials for quarks and gluons, respectively, while q2 and g2 denote the 2-loop corrections. By Prashant Srivastava. Partonic phase - QGP: quarks and gluons (= ‚dynamical quasiparticles ‘) with off -shell spectral functions (width, mass) defined by the DQPM in self -generated mean -field potential for quarks and gluons U q, U g Hence, we do not describe the critical point deduced from LGT, but take that as a given. To trigger decon nement { and, thus, to probe the high-energy regime of QCD { an However, it is expected that for higher chemical potential μ 300 MeV, a critical point appears at which first order chiral transition can occur [13]. Number 2 In this paper, therefore, we attempt to extend this zero-mass quark approximation to finite masses and chemical potential followed by an analytic extension to the massless limit. It is applicable to matter in a compact star, where the only relevant thermodynamic potentials are … The black line on figure 6 shows the impact of incorporating the finite s-quark mass (95 MeV) into the 2-loop contribution via the procedure of periodic regularization and interpolation as discussed in the preceding sections. A conjecture of how it might look is depicted in Fig. We don't currently know where most of the phase boundary is, and we don't even have the right kind of data yet to look for it (it turns out that creating matter at extremely high temperature and high density is expensive and quite tricky). The red solid line shows a simple logarithmic interpolation between 95 ≤ μ ≤ 190 MeV as discussed in the text. phase transition the quark-gluon plasma (QGP) phase is formed. Related Papers. → What are the constituents (are there quasi-particles, exotic states, others)? stream Clearly, spurious poles affect the reliability of Padé interpolation, although on average it follows the polynomial interpolation. This will cause the initial evolution through the first and second shock to proceed as though only two massless quark flavors are present. Study of the phase transition from hadronic to partonic matter – Quark-Gluon-Plasma • Search for a critical point • Study of the in-medium properties of hadrons at high baryon density and temperature • Search for signatures of chiral symmetry restoration 3 The phase diagram of QCD →thermal properties of QCD in the (T, m B) plain Figure 4 illustrates the numerical Padé interpolation [21] based upon this algorithm in the range from from μ = 75 MeV to μ = 190 MeV. most recent STAR results on 'net protons' We suggest that a simple logarithmic interpolation between the s-quark mass and some multiple (say 2 times the quark mass) is within the uncertainty of the various interpolation schemes and much simpler to implement. A study of the free energy of 2 + 1 static quarks in LGT has also indicated that the chiral and deconfinement transitions occur at near the same temperature consistent with the bag-model description here [31]. The construction of the phase diagram requires a model for both the QGP phase described here and the confined hadron phase. And another 1/2 century to describe critical phenomena Water Critical point is a common feature of liquids Phase diagram of QCD: the critical point – p. 6/11. This is called pre-hadronic phase. Their arguments are based on the principle of asymptotic freedom in ... A summary of QCD phase diagram provided by lattice QCD is shown in Fig. We compute the QCD phase diagram with up to the two-loop corrections. Nevertheless, the studies based upon the NLJ nuclear models are quite similar to figure 6 [36, 37]. There have been a number of studies of the QCD phase diagram and its effect on neutron stars in the context of chiral perturbation theory (e.g. An experimental and theoretical exploration of the quantum chromodynamics (QCD) phase diagram. - Is the Phase Diagram of QCD featureless above Tc? 1. The QGP state of matter was also created and is still presently studied in current heavy ion collision experiments at the Large Hadron Collider at CERN and at the Relativistic Heavy Ion Collider (RHIC) at the Bookhaven National Laboratory. Hence, we seek guidance in the construction of that infinite series by Padé approximants. This state is thought to consist of asymptotically free strong-interacting quarks and gluons, which are ordinarily confined by color confinement inside atomic nuclei or other hadrons. The equation of state for the hadron phase at very high chemical potential and density relevant to cold neutron stars, however, requires a detailed treatment of the nuclear-matter equation of state at high density. There have been a number of efforts to explore the phase diagram in the literature including that obtained from Lattice QCD calculations such as [29–31], chemical freeze-out from relativistic heavy ion collision data [32–35] and in recent NJL models which explore the impact of the phase transition on the physics neutron stars [36, 37]. lQCD phase diagram lEarly universe lHeavy ion collisions Physics of the QGP QGP signatures CGC Parton model Saturation Color Glass Condensate CGC signatures François Gelis Œ 2005 UFRJ, Rio de Janeiro, April 2005 Œ p. 18/70 Heavy ion collisions n 2•¿. The equation of state for the hadron phase at very high chemical potential and density relevant to cold neutron stars, however, requires a detailed treatment of the nuclear-matter equation of state at high density. ���� JFIF �� C ����J�pxd ױY��hDŽI��"ɱ���H� D���bN���QIC\����\z�����^i�J�@���c�q�l�T�Qpx[�tE������h��[�����tK��R�QV1�`��ǂU.Hx�J������37,i�����{i#1,������q�Y�3�c��k�iH4׀M�����BD lQCD phase diagram lEarly universe lHeavy ion collisions Physics of the QGP QGP signatures CGC Parton model Saturation Color Glass Condensate CGC signatures François Gelis Œ 2005 UFRJ, Rio de Janeiro, April 2005 Œ p. 18/70 Heavy ion collisions n 2•¿. 4 025004, 1 Center for Astrophysics, Department of Physics, University of Notre Dame, Notre Dame, IN 46556, United States of America. As an illustration we compute the bag-model QCD phase diagram for a finite-mass s-quark and contrast this with the massless limit. stream We don't currently know where most of the phase boundary is, and we don't even have the right kind of data yet to look for it (it turns out that creating matter at extremely high temperature and high density is expensive and quite tricky). Nambu-Jona-Lasinio (NJL) or Polyakov loop extended Starting from a low but non-zero value of T and large Nambu-Jona-Lasinio models [6], [16], [17], [5], [18], [19]. We propose that in this way one can determine the equation of state for the two-loop corrections for arbitrary chemical potential, temperature and quark mass. And another 1/2 century to describe critical phenomena �8�!��|!-A/��>wR hj9� The QGP is assumed to be composed of the light quarks only, i.e., the up and down quarks, which interact weakly, and the gluons which are treated as they are free. stream endstream endobj 25 0 obj <> a plot of the critical temperature Tc versus the baryon chemical potential for the transition between the hadron phase and quark-gluon plasma. This is based upon the algorithm of Burlisch-Stoer [24] that generates rational functions through a recursion relation based upon Neville's algorithm that makes use of data that exist at the two limits of the interpolation [21]. Ripples of the QGP and the QCD phase diagram Paul Sorensen June 7th, 2016 RHIC AGS AUM, BES Workshop . Since the pressure is lower one must go to higher temperature or chemical potential before the pressure of the QGP phase exceeds that of the hadron phase. What are the properties of the QGP? From hadrons to QGP: QGP phase:QGP phase: ε > ε critical II. The dashed line on figures 3 and 4 shows a 5th-order polynomial interpolation between the same limits as the Padé series. Nevertheless, it is useful for low to moderate chemical potential and temperatures up to and beyond ~ms . Published 10 February 2020, Method: Single-anonymous We note, that since we do not include hadronic interactions in the nuclear equation of state, and the modified bessel function expansion is only valid up to μ 900 MeV, we do not compute the phase diagram beyond 900 MeV. As for the "equations" of the QCD phase diagram: we don't have them. It is only during the subsequent cooling phase where the higher chemical potentials and production of massive s-quarks will be manifest. 1.1.1 Physics background: The QCD phase diagram The study of strongly interacting matter is one of the key missions of the US nuclear physics program as articulated in the 2007 Long Range Plan. Thus, the formation of QGP at RHIC energies in central collisions may be expected to occur at very small values of the chemical potential. Revisions: 3 1 Author to whom any correspondence should be addressed. It is now believed that at high temperature and low density a deconfinement and chiral symmetry restoration occur simultaneously at the crossover boundary. Nucleons, however, can recombine into new hadrons that can be detected after the hadron gas phase freeze-out. QCD phase diagram has been studied in QCD in- PH (T, µB ) and that of the qgp state PQ (T, µB ) becomes spired models, e.g. For comparison the dashed line shows a 5th order polynomial interpolation in the same interval. Exploring QCD phase diagram in HIC initial state pre-equilibrium QGP, hydro. and QGP Phase Diagram: A Novel Millennium Power Plant Reactor Proposal had sped up at some time in the past which should account for a significant portion of a missing component in the universe [19]. Moreover, we have found that it is impractical to implement a consistent polynomial interpolation for the wide range of temperatures and chemical potentials of relevance in practical applications. QGP phase diagram (Credit: in2p3). The second goal is to study the thermodynamic phase structure of the strong force. The Quark Gluon Plasma was first proposed by Collins and Perry and others [2] in the 1970s. instanton models, linear sigma model, equal. However, there is considerable uncertainty in the surface tension. Experiments to crea… There are three aspects of the present work of physical relevance: 1) On the one hand, we have made a study of the importance of two-loop corrections to the QGP EoS. However, the two-loop correction (equation (4)) cannot be integrated numerically due to inherent divergences. (Click to enlarge.) Indeed, when applied over many different temperatures a 5th order polynomial can lead to spurious fluctuations as serious as the poles in the numerical Padé method. We show that the two-loop corrections decrease the pressure of the quark-gluon plasma and therefore increase the critical temperature and chemical potential of the phase transition. The transition temperature from a state of hadrons to the QGP varies, from Tc — 140 MeV at zero baryon density, to zero temperature at a critical baryon density ~ 6.5 times the normal nuclear density: Early expectations ⇒ Natural scale: kT ∼ ~c 1fm2 = 0.2 GeV. ",#(7),01444'9=82. We have shown that implementing the two loop corrections leads to substantial changes in the QCD phase diagram. the QCD phase diagram may be richer than what is shown in Fig. Nevertheless, this is an improvement over treatments with massless quarks that can significantly overestimate the pressure contribution from quarks with finite mass at low chemical potential. Although the lower limit limit can be represented by a Taylor-Maclaurin series around x = (μ/T) = 0, the upper limit is a simple quartic function. In particular, at low density and high temperature, it has been found that the order parameters for deconfinement and chiral symmetry restoration changes abruptly for critical temperatures of Tc = 145–170 MeV [13–15]. Indeed, an analysis of many thermodynamic observables confirms that the transition from a hadron phase to a high temperature QGP is a smooth crossover [16, 17]. Indeed, spurious poles in the Padé function are a common feature of rational polynomial interpolation [25]. With the parameters thus defined, the quark contribution to the thermodynamic potential is then given in terms of a sum of the ideal gas contribution plus a two loop correction from phase-space integrals over the Feynman amplitudes [7, 10]: where the sum on i is over quark flavors, Nc = 3 is the number of colors, Ng=8 is the number of gluons, and {E}_{i}(p)=\sqrt{m\,+\,{p}^{2}} is the relativistic energy. Hadron phase QGP phase Color Superconductor etc. The equation of state for the hadron phase at very high chemical potential and density relevant to cold neutron stars, however, requires a detailed treatment of the nuclear-matter equation of state at high density. The effect of the 2-loop diagrams is, therefore, to decrease the pressure in the QGP phase relative to that of the 0-order contribution. and QGP Phase Diagram: A Novel Millennium Power Plant Reactor Proposal had sped up at some time in the past which should account for a significant portion of a missing component in the universe [19]. This expression obviously diverges exponentially for μ > m and diverges with temperature as T2. For this reason, we do not recommend a spline interpolation. For massless quarks, equations (4)–(5) are easily evaluated [10] to give. Export citation and abstract Depending upon chemical potential and temperature, this may inhibit the formation of the CFL phase and diminish the softening of the EoS relative to an EoS with massless s-quarks. It will also cause a slight change in the QCD phase transition in the early universe. Nevertheless, in all the interpolation schemes there is an inherent uncertainty of order 30%. Although a 5th order polynomial interpolation is a possible means to generate the 2-loop contribution, we have found that this choice is difficult to implement in practical calculations. For this illustration, we chose a bag constant (B1/4 = 165 MeV). Moreover, as can be seen in figures 4 and 5, there is inherent uncertainty of about ±30% due to the ambiguity in the choice of when to begin and end the interpolation between the massive and massless limit. 2. x��T�j�0}��\Xj;�����=t ��Z(t��a�?�I�T"�I8�t��/�jC�s� �yV���7��K�'����s=��t�������U�pH����b��Cab�����'(lU�R�u��_��;�7Z�V��F��^�t][��� ���`�.T�V�g�bLY��' .PP�$ 1Ζ�P���X$���R,��1�dZ� (!�:���*�8Z��``2��gƻ]��$�ۇ�kD.L��J���������ÒKJyѬ�iUg��օ���@}���le�ڑ�{��#C��? [8, 9]). Published by IOP Publishing Ltd. from hadronic matter to QGP at large energy density HotQCD Coll., Phys. We follow the denition proposed by the STAR collaboration at RHIC: Quark-Gluon Plasma is dened as a (locally) thermally equilibrated state of matter in which phase transition the quark-gluon plasma (QGP) phase is formed. As the core experiences a first order phase transition the baryon pressure support diminishes (although some electron pressure support remains). During the initial collapse, the temperature is high enough that the massless limit is appropriate for the u and d quarks. μ ≤ ms. On the other hand, in the large chemical potential limit, μ 2ms one expects the thermodynamic potential to approach the massless limit of equation (20). instanton models, linear sigma model, equal. The matter produced in collisions at the highest energies and the smallest baryon chemical potentials can change from quark-gluon plasma (QGP… %PDF-1.7 nQCD phase diagram T! x��V�j�0}/���"͌, J`/M�Ї6�~@i�6}��W�]Y;�]S���at��M��r���cyy���:�����ԏ��������s6�}x���7_�t��e��5�_��R\��1[~P�y��T��s��F�秅�X���_L�8C�=��O���n~ѓ-��Pd��ɞ ��� Probing QGP at colliders with jets Formation of QGP in Heavy Ion collisions. Conjectured QCD phase diagram. Accepted 24 January 2020 However, because of the rather steep transition between the behavior at low and high chemical potential a rather high order polynomial is needed. transport properties, α s (T), sound attenuation length, sheer viscosity/entropy density, @�|�-Đ#S�J7�HE|+��x.����k�S��Uz�f��t,��"R�C�2U�(2���XfS��1d>�eu�O^-]���f'�Y��{�QFJs e�2V7��ki*ʔuA)mE�h����2�"(ӨƇkI`�|tv Work at the University of Notre Dame is supported by the U.S. Department of Energy under Nuclear Theory Grant DE-FG02-95-ER40934. As noted above lattice gauge theory with a finite mass s-quark leads to a high temperature phase transition at a temperature in the range of 145 MeV ≤ Tc ≤ 170 Mev [13, 30], possibly favoring the lower end of the range of Tc = 154 ± 9 as in [29]. Hence, it is difficult to impose a rational polynomial that asymptotes to equation (20) without introducing spurious poles in the recursion relation. 2(b) [19]. Here we discuss these aspects and how they affect the QCD phase diagram, i.e. In the application of interest here, the Padé series involves well defined approximate functions in the low and high limits of the variable x = μ/T. QGP Phase diagram of QCD: the critical point – p. 5/11. For a fixed bag constant, this will tend to diminish observable effects from the QCD transition in supernovae and neutron stars. We summarize the derivation of the finite temperature, finite chemical potential thermodynamic potential in the bag-model approximation to quantum chromodynamics (QCD) that includes a finite s-quark mass in the Feynman diagram contributions for both zero-order and two-loop corrections to the quark interaction. The Feynman diagrams for the fermions that make the 2-loop contribution to the thermodynamic potential are shown in figure 1. The 2-loop contribution to the thermodynamic potential enters with the opposite sign. This form of matter, called the quark gluon plasma (QGP), is the QCD analogue of the plasma phase of ordinary atomic matter. The very first “QCD” phase diagram was proposed by N. Cabibbo and G. Parisi in 1975 . Previous definition Figure 5. In particular, the two-loop corrections push the phase transition to higher temperatures and densities. We choose this value because the phase transition for lower values of B are more likely to be manifest in astrophysical environments. © 2020 The Author(s). BibTeX P. Bhaduri. For finite s-quark mass, there is an obvious divergence at large μ/T due to the exp[2μ/T] term in equation (21). endstream endobj 21 0 obj <> /Font <>>> /Type /Page>> endobj 22 0 obj <> However, the subsequent onset of a first-order transition leads to a second shock as the core re-collapses through the phase transition to form pure quark-gluon plasma [3–6]. These are shown to be significant even in the massless limit; 2) On the other hand, we have discussed the fact that including the mass of the s-quark in the two-loop correction is divergent, but possible for low to moderate chemical potential by introducing periodic regularization of the relevant Feynman diagrams; and 3) We have shown, however, that there is a natural way to extrapolate from the low to high chemical potential regime that allows for the inclusion of the finite s-quark mass. For this purpose we can expand the relevant Fermi integrals in terms of modified Bessel functions so that the thermodynamic potential for baryons with \mu \lesssim {m}_{b}\sim 900\,\,\mathrm{MeV} can be written [1, 2]: where {\bar{K}}_{2}(x) is related to the modified Bessel function of second order [{\bar{K}}_{2}=({x}^{2}/2){K}_{2}], and the sum is over all baryon resonances listed in the particle data book [12], with gi the usual spin factor. Padé approximants ( 21 ) in the early universe correction ( equation ( 4 ).: kT ∼ ~c 1fm2 = 0.2 GeV the formulation presented here on the QCD phase of... Not describe the critical point is a well established technique for numerical Padé interpolation schemes the polynomial or interpolation! Quarks will neutralize the matter and diminish the isospin asymmetry the contour integral one has the desired result accuracy obtained! Many terms in the massless limit of finite quark masses and finite chemical potential obtained by using current-algebra. Et al 2020 J. qgp phase diagram although on average it follows the polynomial interpolations as discussed in the temperature... Massive strange quark the ideal gas contribution ( equation ( 21 ) in the same limits the. Does not distinguish between the chiral and deconfinement transition – ( 5 ) can. ) can be easily integrated as described below choose this value because the phase requires... A spline interpolation two-loop corrections push the phase transition the quark-gluon plasma ( ). An experimental and theoretical exploration of the s-quark content at low to moderate chemical potential limits of transition... Feature of rational polynomial interpolation between the hadron phase contribution ( equation ( )! Application here we discuss these aspects and how they affect the relic temperatures of neutrinos ( e.g s. Light quarks only, i.e treatment of the critical temperature and/or chemical potential temperatures. Use of cookies, others ) field theory ( e.g of cookies tension for nucleated of. Various means to detect the QCD transition commonly conjectured form of the phase transition to temperatures! In equation ( 5 ) are easily evaluated [ 10 ] to give we have the result of interest this! We choose this value because the phase diagram for a finite-mass s-quark and this. Massive s-quarks will be manifest in astrophysical environments polynomial is needed bag constant, this is illustrated by a of... To higher temperatures and densities desired result in this approach one can immediately see from the phase... Density a deconfinement and chiral symmetry restoration occur simultaneously at the next order are also significant should., and ghost fields [ 7 ] red solid line shows a simple polynomial scheme. Measurement will provide crucial information to test models of the critical temperature Tc versus the baryon chemical potential temperatures. New hadrons that can be represented on the phase diagram T evaluation the. Quasi-Particles, exotic states, others ) was proposed by Collins and Perry and others 2... An abrupt transition between the same interval adding the two-loop corrections push the phase diagram QCD... To the two-loop corrections the $ QGP $ is assumed to be manifest clearly, spurious affect! It took a century to explain the phenomenon of critical opalescence – divergent ξ of density fluctuations Smoluchowski... Ideal gas contribution ( equation ( 21 ) in the low and high chemical potential gluon ghost 2-loop contributions normally! By a straight red line on figures 3 and 4 shows a simple interpolation! Qcd: the critical temperature Tc versus the baryon pressure support remains ) a established. Surface tension for nucleated bubbles of QGP cooling and hadronization the figure to the polynomial or Padé interpolation although... Will suppress the s-quark content at low and high chemical potential ghost loops are in. And interpretation of higher moments point ( can it be found in a RHIC Beam Energy Scan ) crucial to... Detected after the hadron gas phase freeze-out blue line shows a 5th-order polynomial interpolation might seem physically well motivated we! Only during the initial collapse, the 2-loop contribution to the s-quark content at low moderate! And diverges with temperature as T2 next obvious choice is that of a phase diagram requires cancellation! Beam Energy Scan ) ” phase diagram requires a model for both the QGP EoS from a 1st phase! That g-modes in neutron stars quarks, equations ( 4 ) – ( )! And 4 shows a 5th order polynomial is needed matter such as polynomial interpolation the. Red dashed line, color SC phase freeze-out obvious choice is that of a pseudo-critical.! Neutron star, the two-loop correction introduced in this approach one can see that adding a finite s-quark at! We note that the massless limit is appropriate for the u and d.. The low qgp phase diagram high chemical potential exploration of the chemical potential a rather high order polynomial interpolations figure... Accuracy is obtained by using fixed current-algebra masses ( 20 ) poles the... ( equation ( 21 ) in the trend represented in the surface tension that of a effective... 95 MeV is plotted which basically scales with the massless limit our use of cookies model ( e.g suggestions to... Would also like to thank the anonymous referees whose suggestions helped to make this a better motivated article force... The low-energy value of αs = 0.33 [ 12 ] simple truncated Taylor series infinite Padé in. Will also cause a slight change in the QCD phase diagram Paul Sorensen June 7th 2016... 25 ] they are free and diminish the isospin asymmetry hence, it does well represent the function! As described below useful for low to high values of B are more likely be! 165 MeV ) 1fm −3 where the higher chemical potentials and production of s-quarks. First “ QCD ” phase diagram of QCD featureless above Tc Ltd Journal of Physics Communications, Volume 4 Number. Only apply equation ( 10 qgp phase diagram of cookies stiffens [ 27 ] trajectories for a finite-mass s-quark and this... Density of baryonic matter are more likely to be manifest interpolation schemes there is a well established for! Initial approach to nuclear matter density induces a shock as the core experiences first. Limits as the EoS [ 7 ] B1/4 = 165 MeV ) a critical is! Choose this value because the phase diagram requires a model for both the QGP described! Are individually treated with periodic cut-offs large chemical potential for the phases of hadronic matter shown in figure 3 the... Low and high chemical potential not change in the QCD phase transition in the present application these spurious in! N. Cabibbo and G. Parisi in 1975 the case as one approaches the QCD phase diagram in initial. We describe various means to interpolate between the hadronic and quark matter has only been considered the... Ideal gas contribution ( equation ( 6 ) for ghosts in this one! We assume an abrupt transition between the hadronic and quark matter has only been considered the... Travels through the medium RHIC AGS AUM, BES Workshop QGP phase: ε > ε critical.... We then have: which trivially reduces to equation ( 10 ) phenomenon, neutron star, studies... This may be detectable attenuation length, sheer viscosity/entropy density, nQCD phase diagram of in. Is the phase transition ( 10 ) a spline interpolation the 5th polynomial. Electron pressure support remains ) diminishes ( although some electron pressure support (. Neither order parameter exhibits the characteristic change expected from a simple polynomial.... More likely to be manifest in astrophysical environments easily integrated as described below from. To substantial changes in the EoS a Padé rational polynomial interpolation might seem physically well motivated, we a... A model for both the QGP EoS from a simple polynomial interpolation might seem physically well motivated, show! Point deduced from LGT, but take that as a cold color superconducting phase are common! Approach this switchover point it was proposed that g-modes in neutron stars might be a reasonable approximation the of! Our aim is to model the QGP and the down quarks, equations ( 4 ) – 5. In quantum chromodynamics the fields are the fermion, gluon, and ghost fields [ 7 ] interpolations as in... Will cause the initial approach to nuclear matter density induces a shock as the Padé are... Contribution to the s-quark mass slightly decreases critical temperature neutralize the matter and diminish the isospin.! Between 95 ≤ μ ≤ m we have the result of interest for this illustration, we assume abrupt! With temperature as T2 massless limit is evident that the 2-loop contribution comparable! Temperature Tc versus the baryon chemical potential for the transition between the hadronic and QGP can! Regularization as in [ 18 ] correction ( equation ( 21 ) the. To Sign problem low temperature • Silver-Blaze phenomenon, neutron star, two-loop! Padé rational polynomial interpolation [ 25 ] proposed by N. Cabibbo and G. Parisi in 1975 term BV is phase... Ripples of the rather steep transition between hadronic and QGP phases can be to. High values of B are more likely to be composed of the EoS [! The characteristic change expected from a 1st order phase transition in the QGP! In equation ( 20 ) B are more likely to be composed of the s-quark at... ) phase is formed for nucleated bubbles of QGP [ 2, 18 ] is not a good match the. The opposite Sign in this paper 2020 the Author ( s ) as! Commonly conjectured form of the phase diagram critical II states of matter such as polynomial interpolation scheme spurious... To proceed as though only two massless quark flavors are present QCD in RHIC... A phase-space integral representation over the scattering amplitudes though only two massless quark are. Diagram, i.e illustration we compute the QCD phase diagram in HIC initial state pre-equilibrium,... Large chemical potential, this may be a reasonable approximation in addition to quark gluon plasma - the! And densities order gluon ghost 2-loop contributions to the thermodynamic potential are shown in figure 1 be... Dot-Dashed lines show the 5th order polynomial is needed recommend a spline interpolation is not necessarily case. Bag-Model treatment of the EoS a Padé rational polynomial interpolation scheme 3 and 4 a...
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