Correlation functions of QC 2 D at finite density Ouraman Hajizadeh, - PowerPoint PPT Presentation

Correlation functions of QC 2 D at finite density Ouraman Hajizadeh, Tamer Boz, Axel Maas, Jon-Ivar Skullerud September, 2017 Zalakaros

Overview Motivation 1 Similarities to SU ( 3 ) 2 SU ( 2 ) at finite density 3 Correlation functions 4 Finite temperature vs finite density 5 conclusion and outlook 6

Motivation Why QC 2 D? the simplest non-abelian gauge theory with fermions accessible at finite density on the lattice Insightful to the case of real QCD, based on the similarities. Informative about the behavior of non-abelian gauge theories in the different thermodynamic regimes. benchmark for other non-perturbative approaches to study QCD in different thermodynamic regimes.

Similarities to SU ( 3 ) Phase Diagram µ a 0 0.2 0.4 0.6 0.8 250 QGP <qq> <L> 200 T (MeV) 150 8 N τ 100 12 BCS? 16 Hadronic 50 24 BEC? Quarkyonic 0 0 200 400 600 800 µ q (MeV) (Tamer Boz, Seamus Cotter, Leonard Fister, Dhagash Mehta ,Jon-Ivar Skullerud, EPJ 2013 ) hadronic phase at low density and temperature QGP at high temperature and/or density quarkyonic phase at medium density and low temperature

Similarities to SU ( 3 ) Order parameters and different phases Three main distinct phases Hadronic: < qq >= 0, < L >∼ 0 low T and µ confined, chiral symmetry broken Quarkyonic: < qq >≠ 0, < L >∼ 0 medium µ , low T: quarks are bulk degrees of freedom (superfluid) but confined Quark-Gluon Plasma: at high T < qq >= 0, < L >≠ 0 ? a deconfined strongly interacting quark matter at high density and low temperature < qq >≠ 0, < L >≠ 0

Similarities to SU ( 3 ) Polyakov loop: an order parameter in unquenched QCD? Polyakov loop: order parameter of deconfinement transition of YM theory with static quarks. < L >≠ 0: deconfined phase: finite free energy for static quarks. in unquenched QCD: quarks are dynamical so we have string breaking. the free energy is always finite. what is the role of < L > in unquenched QCD, if it is always nonzero?

SU ( 2 ) at finite density Polyakov loop vs quark density 4 2.5 N τ =24 N τ =24 N τ =16 2 N τ =12 0.1 N τ =12 3 N τ = 8 N τ =8 1.5 n q /n SB 0.05 lat <L> 2 1 0 0 0.2 0.4 0.6 0.8 1 1 0.5 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.8 0.6 µ a µ a (S. Cotter, P. Giudice, S. Hands, J-I. Skullerud, Phys. Rev. D87 034507 (2013)) a dramatic increase in < L > resembling the ”deconfinement” transition in YM theory. for large T and/or µ at T = 0 for µ > µ d < L >≠ 0 for large µ and/or T: deconfined phase, static quark free energy is finite. µ d a = 0 . 7 for the lowest T. n q enters a strongly interacting region for µ > µ d , L ( µ d , T ) = L ( 0 , T d ) not compatible with the deconfinement picture at high temperatures and zero density: perturbative regime.

Correlation functions Phase diagram vs correlation functions phase diagram in terms of fundamental degrees freedom correlation functions may contain information on thermodynamic features, e.g. phase transitions phase transitions occur in medium at finite T and µ

Correlation functions finite temperature-density formalism Euclidean coordinate: no time evolution: equilibrium temperature: compactified ”time” direction density: boundary condition heat bath is at rest: its four velocity only is nonzero along time direction. finite T or µ effects: different dressing functions ( g L , g T ) for correlation functions projected along or transversal to the time direction. for p ≫ T or p ≫ µ the difference of g T and g L is getting negligible: restoration of manifest Lorentz symmetry.

Correlation functions Gluon propagator at finite density SU(2) transverse gluon propagator SU(2) longitudinal gluon propagator 7 9 (p) (p) Soft mode Soft mode L L D T=0, =0 D T= =0 µ µ -2 -2 8 T=1/8, =0 T=1/8, =0 a µ a µ 6 T=0, =0.3 T=0, =0.3 µ µ T=0, =0.4 T=0, =0.4 7 µ µ T=0, =0.5 T=0, =0.5 µ µ 5 T=0, =0.6 T=0, =0.6 µ µ 6 T=0, =0.7 µ T=0, µ =0.7 T=0, =0.75 T=0, =0.75 µ µ 4 T=0, =0.8 T=0, =0.8 5 µ µ T=0, µ =0.9 T=0, =0.9 µ 4 3 3 2 2 1 1 0 0 0.5 1 1.5 2 2.5 3 3.5 0 ap ap IR enhancement for medium chemical potentials ( µ 0 < µ < µ d ) compared to the vacuum, within this region: almost µ independence IR screening of large µ ( µ > µ d )

Correlation functions Gluon propagator vs quark density SU(2) transverse gluon propagator 7 (p) Soft mode 2.5 L D T=0, =0 µ -2 T=1/8, =0 a µ 6 T=0, =0.3 µ N τ =24 T=0, =0.4 µ 2 T=0, =0.5 N τ =12 µ 5 T=0, =0.6 µ N τ =8 T=0, =0.7 µ T=0, =0.75 µ 1.5 4 T=0, =0.8 n q /n SB µ lat T=0, =0.9 µ 3 1 2 0.5 1 0 0.2 0.4 0.6 0.8 1 0 µ a ap (Simon Hands, Seamus Cotter, Pietro Giudice and Jon-Ivar Skullerud, XQCD 2012) the screening region of chemical potential for gluon propagator corresponds to the region of strongly interacting quark matter for µ > µ d ( n q n SB > 1) the region µ d > µ > µ 0 with almost constant value for the gluon propagator covers the ”weakly” interacting region n q ∼ n SB

Finite temperature vs finite density Gluon Propagator at finite temperature YM SU(2) longitudinal gluon propagator below T SU(2) longitudinal gluon propagator above T c c 22 ] ] -2 Temperature -2 Temperature (p) [GeV (p) [GeV 25 0 20 T 0.361T c c 18 1.02T 0.440T c c L 20 0.451T L 1.04T D D c 16 c 0.549T 1.10T c c 0.603T 14 c 1.81T 0.733T c 15 c 12 2.2T 0.903T c c 0.968T 10 c 0.986T 10 c 8 T c 6 5 4 2 0 0 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 p [GeV] p [GeV] (Christian S. Fischer, Axel Maas, and Jens A. Mueller, EPJ 2010) IR limit of longitudinal propagator responds strongly to the phase transition: the drop above T c

Finite temperature vs finite density SU(2) transverse gluon propagator above T SU(2) transverse gluon propagator below T c c 4 ] ] -2 Temperature -2 Temperature (p) [GeV (p) [GeV 6 0 T 3.5 c 0.361T 1.02T c c 0.440T 5 c T 3 1.04T T D c D 0.451T c 1.10T 0.549T c c 2.5 1.81T 4 0.603T c c 0.733T 2.2T c c 2 0.903T 3 c 0.968T c 1.5 0.986T c 2 T c 1 1 0.5 0 0 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 p [GeV] p [GeV] (Christian S. Fischer, Axel Maas, and Jens A. Mueller, EPJ 2010) transverse propagator is less sensitive to the phase transition below and above T c almost temperature independent

Finite temperature vs finite density Finite density propagator SU(2) transverse gluon propagator SU(2) longitudinal gluon propagator 7 9 (p) (p) Soft mode Soft mode L L D T=0, =0 D T= =0 µ µ -2 -2 8 T=1/8, =0 T=1/8, µ =0 µ a a 6 T=0, =0.3 T=0, µ =0.3 µ T=0, =0.4 T=0, =0.4 7 µ µ T=0, =0.5 T=0, =0.5 µ µ 5 T=0, =0.6 T=0, µ =0.6 µ 6 T=0, =0.7 T=0, =0.7 µ µ T=0, =0.75 T=0, =0.75 µ µ T=0, =0.8 4 5 µ T=0, =0.8 µ T=0, =0.9 T=0, =0.9 µ µ 4 3 3 2 2 1 1 0 0 0.5 1 1.5 2 2.5 3 3.5 0 ap ap no considerable difference between longitudinal and transverse propagator around µ d . different from finite T case.

Finite temperature vs finite density Screening mass at finite temperature 1 Screening mass: M s = D ( 0 ) , D(0) is the propagator at zero momentum. √ Phase transition vicinity Phase transition vicinity in four dimensions 0.6 0.6 [GeV] [GeV] 3 4x46 3 6x48 E s E s M M 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 -0.1 -0.05 0 0.05 0.1 -0.05 0 0.05 0.1 t t SU(2) left, SU(3) right (Axel Maas, Jan M. Pawlowski, Lorenz von Smekal, Daniel Spielmann, Phys. Rev. D 85, 034037 (2012)) the 2nd order phase transition is indicated by the continuous increase of the screening mass of SU(2) gluon propagator as well as the 1st order transition by a jump in the screening mass of SU(3) gluon propagator around T c

Finite temperature vs finite density Screening mass at finite temperature Magnetic screening mass 0.7 0.65 [GeV] 0.6 E s M 0.55 0.5 -0.05 0 0.05 0.1 t (Axel Maas, Jan M. Pawlowski, Lorenz von Smekal, Daniel Spielmann, Phys. Rev. D 85, 034037 (2012)) magnetic screening mass does not indicate effects of the phase transition

Finite temperature vs finite density Screening mass at finite density Electric screening mass for SU(2) Magnetic screening mass for SU(2) 0.7 0.7 [GeV] [GeV] -1/2 -1/2 0.6 0.6 (0) (0) L L D D 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 µ µ no significant difference between electric (longitudinal) and magnetic (transverse) screening mass the effect of transition is not observed at finite density in the electric screening mass compared to finite T. the response of the magnetic screening mass to the phase transition is more observable than the electric part, in contrast to the finite T case.

Finite temperature vs finite density Ghost Dressing function no difference between finite T and µ caes. IR enhancement no obvious temperature dependence. SU(2) ghost dressing function 4.5 G(p) Matsubara frequency 1 T=0, µ =0 T=1/8, =0 µ 4 T=0, =0.3 µ T=0, µ =0.4 T=0, =0.5 µ 3.5 T=0, =0.6 µ T=0, µ =0.7 T=0, =0.75 µ 3 T=0, =0.8 µ T=0, =0.9 µ 2.5 2 1.5 1 0 0.5 1 1.5 2 2.5 3 3.5 4 ap