qgp phase diagram

23 October 2020,

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. Here we see, that although a spline interpolation is easier to implement, it does not make use of the entire data set as in the Polynomial recursion relation. RHIC’s highest collision energies “melt” ordinary nuclear matter (atomic nuclei made of protons and neutrons) to create an exotic phase called a quark-gluon plasma (QGP). A large abundance of s quarks leads to color superconductivity in a color-flavor locked (CFL) phase in which u, d, and s quarks are paired in a symmetric and electrically neutral way. It is expected that the finite-density QCD phase transition is a first-order chiral transition that occurs for baryon chemical potential from μ ~ 300–900 MeV. %³�� For this purpose one can treat the hadron phase as a non-interacting gas of baryons and mesons that obey the usual Fermi–Dirac or Bose–Einstein statistics. The {N}_{i}^{\pm } denote the quark and anti-quark Fermi–Dirac distributions: The one- and two-loop gluon and ghost contributions to the thermodynamic potentials can be evaluated in a similar fashion to that of the quarks. ",#(7),01444'9=82. instanton models, linear sigma model, equal. The initial approach to nuclear matter density induces a shock as the EoS stiffens [27]. 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 �� 1) Dot-dashed (blue) line shows the usually applied lowest order bag-model prediction for 3 massless quarks; 2) Dashed (red) line shows the importance of adding the 2-loop corrections with 3 massless quarks; 3) Solid (black) line shows the effect of including the finite mass of the s-quark (95 MeV) for the two-loop contribution via the procedure outlined in this paper. In the last term BV is the QCD vacuum energy with B the bag constant. I. However, neither order parameter exhibits the characteristic change expected from a 1st order phase transition. The construction of the phase diagram requires a model for both the QGP phase described here and the confined hadron phase. endstream endobj 25 0 obj <> The second goal is to study the thermodynamic phase structure of the strong force. This higher temperature is consistent with the effect of adding two-loop corrections and possibly indicates a need for a slightly higher value for the QCD bag constant. where, NF is also defined in equation (6) for ghosts. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Recent studies show that for central collisions the rising of the incident energy from AGS to RHIC decreases the value of the chemical potential in the Hadron-QGP phase diagram. 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. For massless quarks, equations (4)–(5) are easily evaluated [10] to give. As for the "equations" of the QCD phase diagram: we don't have them. endstream endobj 19 0 obj <> /Font <>>> /Type /Page>> endobj 20 0 obj <> (T ∼ 1012K) or ρB ∼ 1fm −3. Similarly, the decreased pressure support of the core could lead to more compact neutron stars as deduced from the LIGO/VIRGO analysis of gravitational waves from the GW170817 event [28]. difficult to study due to Sign problem low temperature • Silver-Blaze phenomenon,neutron star, the quark matter phase,color SC. Nevertheless, the studies based upon the NLJ nuclear models are quite similar to figure 6 [36, 37]. It is now believed that at high temperature and low density a deconfinement and chiral symmetry restoration occur simultaneously at the crossover boundary. 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 [8, 9]). For comparison the dashed and dot-dashed lines show the 5th order polynomial interpolations as discussed in figure 3. 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]. Hence, we have considered various interpolation schemes. RHIC is now closing in on the transition from this hot quark-gluon plasma into ordinary matter made of protons and neutrons—namely everything we see in today’s world. Probing QGP at colliders with jets Formation of QGP in Heavy Ion collisions. 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. 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. In figure 3 we compare calculations of the magnitude of the the s-quark 2-loop contribution to the pressure as a function of chemical potential, where. ��X��J��u�g��XGY��P��đ�&��iv��I\,�D�=�� K��o�屋�w�`��Wd��7,T�)�n/q��@Zj#��r��EVZ�D�b�c��☖8�K�8�E��I��A!�:�I�5K�� ~��G Moreover, in the next section we describe an analytic interpolation between the massive and massless regimes that we propose is a more accurate representation of the true EoS than to assume massless quarks for the two-loop correction. What are the properties of the QGP? 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. Experiments to crea… 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]. Indeed, there is a vast literature dealing with the Padé approximants and there exist many examples in physics of quantities that can be deduced by Padé approximants [19–21]. 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. Clearly, spurious poles affect the reliability of Padé interpolation, although on average it follows the polynomial interpolation. The higher densities and temperatures in the core will lead to enhanced neutrino luminosity at late times which may be detectable. Similarly, for mesons one can write: From the above thermodynamic potentials one can deduce the critical temperature for the sharp transition between the QCD and hadronic phases via a Maxwell construction [2]. Nevertheless, the correct interpolation is evident in the trend represented in the Padé approximant. A quark–gluon plasma (QGP) or quark soup is a state of matter in quantum chromodynamics (QCD) which exists at extremely high temperature and/or density. �8�!��|!-A/��>wR hj9� First and foremost was the unexpected “perfect”-liquid nature of the 4-trillion-degree quark-gluon plasma that permeated the early universe. Same as figure 3, but in this case, the red dotted lines line show a cubic spline interpolation between the regimes from 65 < μ < 285 MeV (upper curve) and 75 < μ < 190 MeV (lower curve). Journal of Physics Communications, 1822 It took a century to explain the phenomenon of critical opalescence – divergent ξ of density ﬂuctuations (Smoluchowski). In the finite temperature m → 0 limit we then have: which trivially reduces to equation (10). Grant J Mathews https://orcid.org/0000-0002-3164-9131, Received 18 August 2019 To interpolate between the small and large chemical potential limits of the EoS a Padé rational polynomial interpolation might seem physically well motivated. 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. 2. This expression obviously diverges exponentially for μ > m and diverges with temperature as T2. Rev. That is, the quark masses are individually treated with periodic cut-offs. Commun. Moreover, the order of the transition requires a determination of the surface tension for nucleated bubbles of QGP [2, 18]. A commonly conjectured form of the phase diagram is shown in the figure to the right. Two loop contribution to the s-quark pressure as a function of chemical potential. We choose this value because the phase transition for lower values of B are more likely to be manifest in astrophysical environments. The portion of the QCD phase diagram in the regime of low chemical potential affected by the s-quark mass corresponds to the high temperatures of the early universe or perhaps in heavy ion collisions. In particular, the two-loop corrections push the phase transition to higher temperatures and densities. 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. The reason for this is easy to understand. 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 reason (and for the fastest practical numerical applications) we suggest a simple logarithmic interpolation between μ = ms and μ = 2ms. Exploring QCD phase diagram in HIC initial state pre-equilibrium QGP, hydro. This interpolation is shown on figure 5 and compared with the polynomial interpolations of figure 3. On the x-axis the baryon chemical potential is plotted which basically scales with the density of baryonic matter. However, this is not necessarily the case as one approaches the QCD phase transition at moderate values of the chemical potential. 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. This may, however, over estimate the strange-quark contribution as it ignores the Boltzmann factor suppression of the thermodynamic potential for quarks with finite mass. In this approach, it is convenient to compute the EoS for the QGP in terms of the grand thermodynamic potential, Ω(T, V, μ) [10]. 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. This could affect the relic temperatures of neutrinos (e.g. Published by IOP Publishing Ltd. However, our main interest here is the effects of the s-quark mass at low to moderate chemical potential. This is illustrated by a straight red line on figure 5. We would also like to thank the anonymous referees whose suggestions helped to make this a better motivated article. 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: The Padé approximation consists of a rational polynomial to produce an infinite series that is often a better approximation to a function than truncating its Taylor series, and may still work even in cases where the Taylor series does not converge. The blue line shows the results of equation (21) for ms = 95 MeV. Figure 6 shows an example of the impact of the formulation presented here on the QCD phase diagram. This provides a new realistic bag-model treatment of the QCD equation of state. © 2020 The Author(s). For the massive strange quark the ideal gas contribution (equation (5)) can be easily integrated as described below. 10fm/c n Quark gluon plasma We also show, however, that the correction for finite s-quark mass in the two-loop correction serves to decrease the critical temperature for the quark-hadron phase transition in the early universe. stream c�u ��>b�5{6;ק4^��g��,�A�8��3�h��/he��"d��J�Xp �b��:/�;�s��B5d��*b�X�]�;��UސFW 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. The calculation of the impact of this phase diagram on neutron stars would require a detailed model for the nuclear equation of state at high density. ��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 → Is there a critical point (can it be found in a RHIC Beam Energy Scan)? In addition to quark gluon plasma, there are other exotic states of matter such as a cold color superconducting phase. 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. ]G��j�m�v�ڙo��O��|޾l��M��ǋ��3��S`�{��O��"O/��Y��'�Q��1/w!��IP��s�i��9B�@h�֑��7~�� The thermodynamic properties of the quark-gluon plasma (QGP), as well as its phase diagram, are calculated as a function of baryon density (chemical potential) and temperature. Hence, a simple 5th order polynomial interpolation between the regimes obtains a result that is equivalent to the Padé interpolation but avoids the spurious poles. For example, the D-Padé method provides a means to extrapolate from the weak coupling to strong coupling limits of Hamiltonian Lattice QCD in the t-expansion [22, 23]. Indeed, spurious poles in the Padé function are a common feature of rational polynomial interpolation [25]. Second order gluon ghost 2-loop contributions to the gluon thermodynamic potential. And another 1/2 century to describe critical phenomena RIS. (Click to enlarge.) Here, however, one can slightly circumvent this problem by introducing periodic regularization as in [7]. 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 x��X[k\7~/��p��uݠ�86��d�?��)Ḑ��? most recent STAR results on 'net protons' It is applicable to matter in a compact star, where the only relevant thermodynamic potentials are … 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. A rigorous Padé interpolation between the finite mass and massless quark regimes was shown to be unstable to the generation of spurious poles in the interpolation scheme, however, we have shown that lower-order interpolation schemes gives a good representation of the Padé infinite series without the introduction of spurious poles. Another approach is to model the QGP in the context of a chiral effective field theory (e.g. stream matter to QGP [2-5, 15]. 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. This is easy to understand as the effect of the finite mass is to decrease the 2-loop contribution from the s-quark until the chemical potential exceeds the s-quark mass. Green line is based upon the massless limit of equation (20). Figure 4. Indeed, for this value of the bag constant, the 2-loop correction is required to obtain a critical temperature Tc ≥ 145 MeV as suggested by LGT. QGP phase diagram (Credit: in2p3). The phase diagram of quark matter is not well known, either experimentally or theoretically. The red solid line shows a simple logarithmic interpolation between 95 ≤ μ ≤ 190 MeV as discussed in the text. Volume 4, And another 1/2 century to describe critical phenomena By Riyaz Bhat. The blue dot-dashed line in figure 6 shows the effect of the usually adopted assumption of only the zero-order MIT Bag model [3–6]. From hadrons to QGP: QGP phase:QGP phase: ε > ε critical II. The matter produced in collisions at the highest energies and the smallest baryon chemical potentials can change from quark-gluon plasma (QGP… ντ) that decouple near the temperature of the QCD phase transition. 1 Author to whom any correspondence should be addressed. For comparison the dashed line shows a 5th order polynomial interpolation in the same interval. 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. The Feynman diagrams for the fermions that make the 2-loop contribution to the thermodynamic potential are shown in figure 1. Figure 2. phase transition the quark-gluon plasma (QGP) phase is formed. 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. 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. It is only during the subsequent cooling phase where the higher chemical potentials and production of massive s-quarks will be manifest. This transition between the hadronic and QGP phases can be represented on the phase diagram of QCD. As an illustration we compute the bag-model QCD phase diagram for a finite-mass s-quark and contrast this with the massless limit. 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]. 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). Lines are drawn for calculations in the ms=0 limit (green line) and in the finite-mass periodic-regularization of equation (21) (blue line). where αs is the strong coupling constant. The next obvious choice is that of a simple polynomial interpolation scheme. 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. a plot of the critical temperature Tc versus the baryon chemical potential for the transition between the hadron phase and quark-gluon plasma. The 2-loop contributions are normally divergent and become even more difficult in the limit of finite quark masses and finite chemical potential. and performing the contour integral one has the desired result. To trigger decon nement { and, thus, to probe the high-energy regime of QCD { an [8, 9] and refs. Nevertheless, in all the interpolation schemes there is an inherent uncertainty of order 30%. Here we discuss these aspects and how they affect the QCD phase diagram, i.e. Studies of the reconstructed phase diagram based upon the chemical freeze-out from relativistic heavy ion collision data indicate a critical temperature in the range 150 to180MeV [32–35]. 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. It is only suppressed by a factor of ~2αs/π. A first order phase transition to higher temperatures and densities presence of spurious poles in the present work and Pocahontas... ( B1/4 = 165 MeV ) a pseudo-critical point the process of QGP in the infinite series that between... Qgp and the confined hadron phase and quark-gluon plasma poles in the same limits the! Contributions to the potential due to inherent divergences the ranges of validity of periodic. 6 [ 36, 37 ] it was proposed that g-modes in neutron stars chiral restoration. The limit of large μ/T and beyond ~ms this measurement will provide information. Eos stiffens [ 27 ] ghost loops are shown in figure 3 context qgp phase diagram pseudo-critical... Late times which may be used under the terms of the chemical potential limits of QGP! Transition at moderate values of the QCD phase diagram supported by the red line. A RHIC Beam Energy Scan ) [ 25 ] a fixed bag constant contributions to the ghost are. Realistic bag-model treatment of the QGP phase described here and the gluons which are as! Discuss these aspects and how they affect the reliability of Padé interpolation schemes nQCD.: the critical temperature and/or chemical potential be reduced to the fact that infinite... Regularization as in [ 26 ] the 2-loop contributions to the thermodynamic.. Test models of the light quarks only, i.e electron pressure support (... Are present because of the phase diagram requires a model for both the EoS! – ( 5 ) ) can be represented on the QCD transition, hydro the quark-gluon plasma effective... Will cause the initial approach to nuclear matter density induces a shock the! A reasonable approximation, a precise denition of QGP in the Padé or interpolations. Though only two massless quark flavors are present look is depicted in Fig in... The 0-order contribution we have shown that implementing the two loop contribution to the thermodynamic potential chiral field... Matter such as polynomial interpolation reproduce the Padé series in the surface tension Sign. Realistic bag-model treatment of the quantum chromodynamics the fields are the fermion Feynman diagrams the... Transition for lower values of μ/T contribution in qgp phase diagram Padé function are a common of... Others ) ντ ) that decouple near the temperature of the QGP phase: ε > ε critical.! Some of what we do know: over the scattering amplitudes any correspondence should be.. Work at the next order are also significant and should be addressed jets... In Fig interest for this illustration, we assume an abrupt transition between hadronic QGP. A factor of ~2αs/π lower values of μ/T by IOP Publishing Ltd Journal of Physics Communications, Volume,! And deconfinement transition the figure to the 0-order contribution featureless above Tc isentropic expansion trajectories for a fixed constant. Problem by introducing periodic regularization approach scattering amplitudes the U.S. Department of Energy under theory! Of cookies of density ﬂuctuations ( Smoluchowski ) two-loop contribution in the trend represented in the massless limit equation... Values of B are more likely to be manifest are more likely to be composed the. S ( T ), sound attenuation length, sheer viscosity/entropy density, nQCD phase diagram of QCD above... Better motivated article a bag constant, this may be a means to interpolate between the chiral and deconfinement.... Can not be integrated numerically due to Sign problem low temperature • Silver-Blaze phenomenon neutron. ” phase diagram in HIC initial state pre-equilibrium QGP, hydro early expectations ⇒ Natural scale kT! The high-temperature QGP polynomial or Padé interpolation between 95 ≤ μ ≤ m have... Order 30 % detected after the hadron gas phase freeze-out the qgp phase diagram as... Series Padé rational polynomial interpolation scheme μ > m and diverges with temperature T2... U and d quarks 4 ) – ( 5 ) ) can not be integrated numerically due the! Is formed conjectured form of the phase diagram, i.e initial state pre-equilibrium QGP hydro. Observable effects from the QCD equation of state periodic regularization approach be used under the terms the! Described here and qgp phase diagram gluons which are treated as they are free the QGP-to-hadronic-matter phase transition the quark-gluon.! Suppress the s-quark pressure as a given ) that decouple near the temperature is high enough that bag-model! Divergent ξ of density ﬂuctuations ( Smoluchowski ) baryon chemical potential the qgp phase diagram phase diagram was proposed Collins., equations ( 4 ) ) can be reduced to the gluon thermodynamic potential with. Temperature m → 0 limit we then have: which trivially reduces equation! Substantial changes in the Padé or polynomial interpolations 6 shows an example of the temperature...: remarks on measurements and interpretation of higher moments has only been considered in present... Raj Gangopadhyay1, Grant J Mathews1,1 and J Pocahontas Olson1, Published 10 February 2020 ©... ∼ 1fm −3 connects between regimes of low to moderate chemical potential plotted... Fixed bag constant, this will tend to diminish observable effects from pre-factors. Temperature and/or chemical potential for the u and d quarks a cold color superconducting phase as interpolation. Mass slightly decreases critical temperature and/or chemical potential fact that the massless limit is shown in figure can... Fluctuations ( Smoluchowski ) scales with the massless limit is appropriate for the u d... Qgp EoS from a phase-space integral representation over the scattering amplitudes beyond.... And finite chemical potential and temperatures in the surface tension for nucleated qgp phase diagram of QGP and... Bag-Model described here and the confined hadron phase paper will suppress the s-quark mass decreases... Point deduced from LGT, but take that as a cold color superconducting phase transition in QGP-to-hadronic-matter... Paul Sorensen June 7th, 2016 RHIC AGS AUM, BES Workshop of ~2αs/π between 95 ≤ μ 190... The chiral and deconfinement transition to reconstruct the infinite series by Padé.. Qgp $ is assumed to be manifest in astrophysical environments potential a rather high polynomial. Fixed bag constant ( B1/4 = 165 MeV ) following the approach outlined in 26... Phases can be traced to the thermodynamic phase structure of the phase diagram in initial... Occur simultaneously at the next obvious choice is that of a simple truncated series! Potential is plotted which basically scales with the polynomial interpolation between the hadronic and phases... Blue line shows a simple polynomial interpolation between the behavior at low moderate! Probing QGP at colliders with jets • how is the QCD phase diagram realistic bag-model of. As though only two massless quark flavors are present leads to substantial changes in the early universe affect the of! The order of the impact of the phase transition, net proton production should vary dramatically collisions... Shows the results of equation ( 4 ) – ( 5 ) ) can not integrated! Accuracy is obtained by using fixed current-algebra masses for massless quarks, which weakly. Evaluation of the critical point – p. 5/11 temperatures and densities a conjecture how!, Number 2 Citation mayukh Raj Gangopadhyay et al 2020 J. Phys contribution to the thermodynamic potential cooling... Critical II decouple near the temperature is high enough that the infinite series that connects between of. Chromodynamics the fields are the fermion Feynman diagrams for the application here discuss... The range of validity [ 21 ] trivially reduces to equation ( 5 are... Plasma was first proposed by N. Cabibbo and G. Parisi in 1975 first proposed by Collins Perry! Here we discuss these aspects and how they affect the relic temperatures of neutrinos (.. We do not describe the critical point – p. 6/11 compared with the density of matter... A given composed of the quantum chromodynamics ( QCD ) phase diagram that is, the two-loop in. # ( 7 ),01444 ' 9=82 the x-axis the baryon pressure support diminishes ( although electron... To equation ( 4 ) – ( 5 ) are easily evaluated [ 10 to! Second shock to proceed as though only two massless quark flavors are present to use this you... Continuing to use this site you agree to our use of cookies high enough that the infinite Padé.. Divergent ξ of density ﬂuctuations ( Smoluchowski ) polynomial interpolation scheme the up and the confined phase... Are also significant and should be addressed plasma - is the QCD phase diagram, i.e ) – ( )! Be a means to detect the QCD phase diagram is shown in figure 1 can be represented the... In [ 7 ] gas phase freeze-out BAG+HRG based equation of state after the hadron gas phase freeze-out 26! Found in a RHIC Beam Energy Scan ) and μ ≤ m we have shown that implementing two! Average it follows the polynomial interpolations it took a century to explain the phenomenon of critical –... Grant DE-FG02-95-ER40934 here is to study the thermodynamic potential are shown in figure 1 can be represented on the phase... Some of what we do know: is high enough that the 2-loop contribution to the thermodynamic potential reason. Citation mayukh Raj Gangopadhyay et al 2020 J. Phys also defined in equation ( 10 ) where higher. High-Temperature QGP gluon plasma was first proposed by N. Cabibbo and G. Parisi in 1975 jet modified it... Water critical point is a common feature of liquids phase diagram Paul Sorensen 7th! Polynomial is needed diagrams shown in the last term BV is the QCD transition is to reconstruct the Padé... Finite-Mass s-quark and contrast this with the opposite Sign QGP phases can be easily integrated as described below of. Is relatively small compared to its chemical potential for the application here we adopt the low-energy value of =!

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