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Reality of Diquarks Between Nuclear and Quark Matter Reality of Diquarks between Nuclear and Quark Matter Kenji Fukushima The University of Tokyo August 8, 2014 @ JPARC 1 Our belief: Nuclear Matter 2 Our belief: Squeeze Quark Matter How it happens? 3 Our belief: Squeeze Something??? Especially Between Nuclear and Quark Matter 4 Our belief: Something??? This is not theoretically clarified (surprisingly) So let’s go by experiment, some people say… 5 HIC (thermal fit) established: Densest Matter Created in Heavy-Ion Collision 8GeV/nucleon-nucleon 0.2 (~30GeV in lab.) ~ saturation density ] -3 0.15 HRG estimate based on 0.1 AGS/SPS/RHIC data 160 0.05 Baryon Density [fm Chemical 120 Freeze-out line 80 0 0 40 200 400 600 800 Temperature [MeV] Baryon Chemical Potential [MeV] 6 Thermal fit works too good: / Nuclear Physics A 00 (2010) 1–4 3 stout continuum $ 5 #$ 0.6 HRG physical # HRG physical $ $ HRG distorted stout Nt!8 $ 0.5 HRG distorted Nt!8 ! ! 4 HRG distorted asqtad Nt!8 ! !# ! ! HRG distorted Nt!12 $ !" # " stout Nt!10 ! $ # $ 0.4 " asqtad Nt!8 ! ! ! 4 ! stout Nt 8 # 2 # ! # asqtad Nt!12 T 3 ! T # $ asqtad Nt!8 $% # # " ! $ s 2 0.3 ! p4 Nt!8 $ ! 3p # p4 Nt!8 $ # Χ ! $ hisq Nt!8 # " Ε# 2 ! ! # # 0.2 $ # " ! $ # " ! $ $ $ ! ! # 0.1 1 ! $ # " !! #$ " " !!!!!!!! 0.0 0 120 140 160 180 100 120 140 160 180 T MeV T MeV Figure 2: Left panel: strange quark susceptibility as a function of the temperature. full symbols correspond to results obtained with the asqtad, p4 and hisq actions [1, 6]. Our continuum result is indicated by the gray band. The solid line is the HRG model! result" with physical masses. The dashed and dotted lines are the HRG! model" results with distorted masses corresponding to Nt = 12 and Nt = 8, which take into account the discretization e↵ects and heavier quark masses, which characterize the results of the hotQCD Collaboration. Right panel: (✏ 3p)/T 4 as a function7 − of the temperature. Open symbols are our results. Full symbols are the results for the asqtad and p4 actions at Nt = 8 [1]. Solid line: HRG model with physical masses. Dashed lines: HRG model with distorted spectrums. As it can be seen, the prediction of the HRG model with a spectrum distortion corresponding to the stout action at Nt = 8 is already quite close to the physical one. The error on the recent preliminary HISQ result [6] is larger than the di↵erence between the stout and asqtad data, that is why we do not show them here. resonances. We include all known baryons and mesons up to 2.5 GeV, as listed in the latest edition of the Particle Data Book (for an improvement of the model by including an exponential mass spectrum see [13]). We will compare the results obtained with the physical hadron masses to those obtained with the distorted hadron spectrum which takes into account lattice discretization e↵ects. Each pseudoscalar meson in the staggered formulation is split into 16 mesons with di↵erent masses, which are all included. Similarly to Ref. [9], we will also take into account the pion mass- and lattice spacing- dependence of all other hadrons and resonances. Quark number susceptibilities increase during the transition, therefore they can be used to identify this region. q T @2 ln Z They are defined as χ = 2 , (with q = u, d, s). In the left panel of Fig. 2 we show our continuum- 2 V @(µq) µi=0 extrapolated results for the strange quark number susceptibility, in comparison with the HRG results with physical spectrum. Also shown are the hotQCD collaboration data, in comparison with the HRG model results with distorted spectrum. In the right panel of Fig. 2 we show the trace anomaly (✏ 3p) divided by T 4 as a function of the − temperature. Our Nt = 8 results are taken from Ref. [14]. Notice that, for this observable, we have a check-point at Nt = 10: the results are on top of each other. Also shown are the results of the hotQCD collaboration at Nt = 8 [1] and the HRG model predictions for physical and distorted resonance spectrums. On the one hand, our results are in good agreement with the “physical” HRG model ones. It is important to note, that using our mass splittings and inserting this distorted spectrum into the HRG model gives a temperature dependence which lies essentially on the physical HRG curve (at least within our accuracy). On the other hand, a distorted spectrum based on the asqtad and p4 frameworks results in a shift of about 20 MeV to the right. In order to compare our results to those of the hotQCD collaboration, we also calculate the quantity ∆l,s = ml ml ( ¯ l,T ¯ s,T )/ ¯ l,0 ¯ s,0) (with l = u, d). We compare our results to the predictions of the HRG h i − ms h i h i − ms h i model and χPT [15]. To this purpose, we need to know the quark mass dependence of the masses of all resonances included in the partition function. We assume that all resonances behave as their fundamental states as functions of the quark mass, and take this information from Ref. [16]. They agree with the results obtained by our collaboration in [17]. 4. Conclusions We have presented our latest results for the QCD transition temperature. The quantities that we have studied are the strange quark number susceptibility, the chiral condensate and the trace anomaly. We have given the complete temperature dependence of these quantities, which provide more information than the characteristic temperature val- Theorists may say: Our understanding of dense matter is so poor because of the sign problem in lattice-QCD So far, no reliable lattice results at µ =0,T=0 B 6 8 Theorists may say: Our understanding of dense matter is so poor because of the sign problem in lattice-QCD So far, no reliable lattice results at µ =0,T=0 B 6 Is this really so? Isn’t it just a lame excuse of theorist? (Lattice is not a unique theory tool) 9 BI-TP 2009/30 CERN-PH-TH-2009-229 INT-PUB-09-060 This O(g4) calculation appearedTUW-09-19 in 2009 Cold Quark Matter Aleksi Kurkela,1 Paul Romatschke,2 and Aleksi Vuorinen3, 4, 5 1Institute for Theoretical Physics, ETH Zurich, CH-8093 Zurich, Switzerland 2Institute for Nuclear Theory, University of Washington, Box 351550, Seattle, WA, 98195 3Faculty of Physics, University of Bielefeld, D-33501 Bielefeld, Germany 4CERN, Physics Department, TH Unit, CH-1211 Geneva 23, Switzerland 5ITP, TU Vienna, Wiedner Hauptstr. 8-10, A-1040 Vienna, Austria We p erform an (α2)perturbativecalculationoftheequationofstateofcoldbut O s dense QCD matter with two massless and one massive quark flavor, finding that perturbation theory converges reasonably well for quark chemical potentials above 1GeV.Usingarunningcouplingconstantandstrangequarkmass, and allowing for further non-perturbative effects, our results point to a narrow range where absolutely stable strange quark matter may exist. Absent stable strangequarkmatter,our findings suggest that quark matter in compact star cores becomes confined to hadrons only slightly above the density of atomic nuclei. Finally, weshowthatequations of state including quark matter lead to hybrid star masses up to M 2M ,in ∼ ⊙ agreement with current observations. For strange stars, we find maximal masses of M 2.75M and conclude that confirmed observations of compact stars with ∼ ⊙ M>2M would strongly favor the existence of stable strange quark matter. ⊙ 10 arXiv:0912.1856v2 [hep-ph] 29 Jan 2010 3 I. INTRODUCTION The properties of cold nuclear matter at densities above that of atomic nuclei, in par- ticular its equation of state (EoS) and the location of the phase transition to deconfined quark matter, remain poorly known to this day. The difficulty in performing first principles calculations in such systems can be traced back to the complicated non-linear and non- perturbative nature of Quantum Chromodynamics (QCD). These properties have precluded an analytic solution describing confinement, while non-perturbative numerical techniques, such as lattice QCD, are inapplicable at large baryon densities and small temperatures due to the so-called sign problem. This should be contrasted with the situation at small baryon density and large temperatures, where close to the deconfinement transition region lattice QCD has provided controlled results for the EoS as well as the nature of the transition [1, 2], while at temperatures much above the transition, the system is well described by analytic results from resummed perturbation theory [3–6]. Experimentally, the high temperature / low baryon density regime of QCD can be studied in relativistic heavy-ion collisions at the Relativistic Heavy Ion Collider (RHIC) [7–10] and in the future at the Large Hadron Collider (LHC) [11]. Collisions at lowerenergy,e.g. at the Alternating Gradient Synchrotron (AGS) and Super Proton Synchrotron (SPS) [12, 13], as well as those planned at the Facility for Antiproton and Ion Research (FAIR) and RHIC [14, 15], study QCD matter at somewhat higher baryon density, and may give some insight into the EoS of cold nuclear matter. However, at truly low temperatures and supra- nuclear densities, QCD matter exists only in somewhat inconveniently located ’laboratories’: Compact stars. In the cores of compact stars, nuclear matter is expected to reach densities several times 3 that of atomic nuclei nsat 0.16 fm− , so that astrophysical observations may be able to provide critical information∼ about the EoS of strongly interacting matter in a regime inac- cessible to terrestrial experiments. Theoretically, the bulk properties of nuclear matter at or close to nsat have been studied using microscopic calculations [16] as well as phenomeno- logical mean-field theory [17].
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