Khan, N.

Pawlowski, J.

Rennecke, F.

Scherer, M.

GSI Repository

The role of fluctuations in the phase diagram of two color QCD∗N. Khan1,2, J. Pawlowski1,2, F. Rennecke1,2, and M. Scherer1,21GSI, Darmstadt, Germany; 2Universita¨t Heidelberg, GermanyThe investigation of the phase diagram of QuantumChromodynamics (QCD) at finite temperature and densityis an area of very active experimental and theoretical re-search [1] due to the existence of a variety of symme-try broken phases, the transitions between them and thepresence of strong interactions. A straightforward appli-cation of lattice methods is inhibited by the property thatfor nonzero chemical potential the path integral measureof the QCD Lagrangian is complexAn instructive way toapproach the full problem and to shed light on particularaspects is the investigation of deformations of QCD [2].Generally, this can be achieved by changing e.g. mass pa-rameters, symmetries or the field content. In this work,we will choose the latter two possibilities and study a the-ory similar to real QCD, however with two colors, Nc = 2,and two quark flavors Nf = 2. An appealing feature withinthis two-color two-flavor version of QCD is that, apart fromthe chirally broken mesonic phase of quark-antiquark pairs,it allows for the formation and (Bose-Einstein-) condensa-tion of colorless diquarks, i.e. a bosonic baryon state. Thisresults in a rich phase diagram with two dynamically com-peting order parameters.In this work we employ a functional renormaliza-tion group (FRG) approach to an effective quark-meson-diquark model to study the phase diagram of two-colorQCD. The FRG method is a suitable tool for the systematicstudy of (strongly) interacting field theories allowing forthe formulation and computation of non-perturbative ap-proximation schemes.The present work systematically ex-tends the truncation scheme in Ref. [3] by taking into ac-count the scale dependence of the wave function renormal-izations as well as the renormalization of the Yukawa cou-pling between the quarks and the order parameter fields.Additional quantitative effects can be accessed systemat-ically by extensions of the truncation scheme within theFRG. Here, we can monitor the quantitative correctionsthat are induced by the additional scale dependent quanti-ties, namely the wave function renormalizations as well asthe Yukawa interaction and study their impact on the phasediagram. Due to an alternative expansion scheme for the ef-fective potential we gain direct access to the phenomenonof precondensation, a regime in the phase diagram whereorder occurs at intermediate scales but no order is foundwhen all fluctuations are integrated out. In this way, weestablish a refined picture of the FRG phase diagram forQC2D, which is shown in Fig.1.∗Work supported by Helmholtz Alliance HA216/EMMI and by ERC-AdG-290623.〈σ〉 6= 0 〈Δ〉 6= 0〈σ〉 ≈ 0 〈Δ〉 = 0BEC BCSFigure 1: The phase daigram of QC2D. μ is the baryonchemical potential in this plot.The condensates are determined by the minimum ofan order parameter potential, which is truncated to a onedimensional Taylor expansion up to six-point interactionterms. In addition, we have added a linear term in the chi-ral condensate σ, which causes chiral symmetry always tobe broken, this is rooted in the fact that quarks have a smallbut finite current mass. At small temperatures and chemi-cal potentials chiral symmetry is broken and quarks have aconstituent mass of about 300 MeV. With increasing tem-perature the system undergoes a smooth crossover wherechiral symmetry is nearly restored. The line and the shadedarea in the left part of the figure mark the crossover and itswidth. At higher μ the system undergoes a second orderphase transition at the onset of the diquark condensate Δ.At first the system is in BEC like state while at the limitof high chemical potentials the system spproaches a BCSlike state. The line where the quark mass drops below thechemical potential indicates the region of the BEC-BSCcrossover. The shaded area in the right part indicates theprecondensation phase.For the future this result is to be compared to lattice sim-ulations, in order to evaluate our methods and truncationschemes.References[1] P. Braun-Munziger and J. Wambach, Rev. Mod. Phys. 81,1031 (2009)[2] L. von Smekal, Nucl. Phys. Proc. Suppl. 228, 179 (2012)[3] N. Strodhoff, B.-J. Schaefer and L. von Smekal Phys. Rev.D85. 074007 (2012)GSI SCIENTIFIC REPORT 2013 THEORY-11doi:10.15120/GR-2014-1-THEORY-11 263

The role of fluctuations in the phase diagram of two color QCD

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The role of fluctuations in the phase diagram of two color QCD

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