Search for Chiral Symmetry Restoration in QCD Matter Ralf Rapp Cyclotron Institute + Dept of Phys & Astro Texas A&M University College Station, USA HIC for FAIR Nuclear Physics Colloquium Institute for Theoretical Physics (Frankfurt, Germany) 22.10.15 1.) Introduction: Probing QCD Matter Big Bang Compact Stellar Objects Bulk Properties: Equation of State, Transport Coefficients Microscopic Properties: Degrees of Freedom, Spectral Functions Phase Transitions: Condensate Structure
1.2 Dileptons in Heavy-Ion Collisions e+ A+A eNN coll. QGP Hadron Matter Freeze-Out Emission Sources: Drell-Yan: NNe+eX Thermal radiation
- Quark-Gluon Plasma: qq- e+e - Hadron Matter e+e , final-state decays: , e+e qq 1.3 EM Spectral Function Probing the Fireball d N ee e2m B 3 2 f ( q 0 ,T ) em(M,q;B,T) 4 4 d xd q M Thermal Dilepton Rate
unique direct access to in-medium spectral function e+e hadrons q -q em / M2 e+ e+ e M [GeV] Hadrons: em ~ Im D - change in degrees of freedom? - restoration of chiral symmetry? qq- Continuum:
em / M2 ~ const (1+ O[T2/M2]) e Outline 1.) Introduction 2.) Spontaneous Chiral Symmetry Breaking QCD Vacuum + Excitations 3.) Axial/Vector Mesons in Medium Vacuum + Many-Body Theory QCD + Weinberg Sumrules EFT + Mechanisms of Chiral Restoration 4.) Dilepton Phenomenology From SIS to RHIC 5.) Conclusions 2.1 Chiral Symmetry + QCD Vacuum 2-flavor + chiral (left/right) invariant
Higgs Mechanism in Strong Interactions: - qq attraction condensate fills QCD vacuum! 0 | q q | 0 0 | qLqR qRqL | 0 5 fm 3 q- R Spontaneous Chiral Symmetry Breaking > qL > > qR
> mq ) q 1 Ga2 LQCD q ( i gA 4 q- L Consequences: m*q 0 | q q | 0 effective quark mass: mass generation!? near-massless Goldstone bosons 0,
chiral partners split: M 0.5GeV JP=0 1 1/2 2.2 Mass Gap + Chiral Partners Axial-/Vector Correlators Constituent Quark Mass V,A / s Data: lattice [Bowman et al 02] Theory: Instanton Model [Diakonov+Petrov; Shuryak 85]
Chiral breaking: |q2| 2 GeV2 pQCD cont. Spectral shape matters for chiral symmetry breaking 2 ds ( ) f E.g. s V A 2.3 Chiral Symmetry and Dileptons q q (T ) / q q
Chiral Condensate 0 [Fodor et al 10] Vacuum Chiral Restoration T [MeV] V ds ( A V A) mq q q Outline
1.) Introduction 2.) Spontaneous Chiral Symmetry Breaking QCD Vacuum + Excitations 3.) Axial/Vector Mesons in Medium Vacuum + Many-Body Theory QCD + Weinberg Sumrules EFT + Mechanisms of Chiral Restoration 4.) Dilepton Phenomenology From SIS to RHIC 5.) Conclusions 3.1 Meson in Vacuum Introduce a1 as gauge bosons into chiral Lagrangian 1 2 int L g ( ) g
2 3 parameters: m(0), g, |F|2 EM formfactor | F ( M ) |2 ( m ( 0 ) ) 4 | D ( M ) |2 phase shift 1 Im D ( M ) ( M ) tan Re D ( M )
D ( M ) [ M 2 ( m ( 0 ) )2 ( M )] 1 propagator: 3.2 Meson in Hot + Dense Matter Interactions with hadrons from heat bath In-Medium -Propagator
D(M,q;B,T) = [M2- m2- - B - M ]-1 [Chanfray et al, Herrmann et al, Urban et al, Weise et al, Oset et al, ] Direct -Hadron Scattering [Haglin, Friman et al, RR et al, Post et al, ] =
Theoretical Control: - symmetries (gauge, chiral) - empirical constraints (decays R+h, scattering data N/A, NN) 3.2.2-Meson Spectral Function in Medium Hot + Dense Matter Hot Meson Matter B/0 0 0.1 0.7 2.6 B =330MeV [RR+Wambach 99] [RR+Gale 99]
-meson melts in hot/dense matter largely driven by baryon density ( ) B 3.3 QCD + Weinberg Sum Rules [Weinberg 67, Das et al 67] 1 ( ) f 2 ds s V A ds ( V a A ) mq qq
2 ds s ( ) c ( q q ) s V A [Weinberg 67, Das et al 67; Kapusta+Shuryak 94] s [GeV]
accurately satisfied in vacuum In-medium input: - condensates: hadron reso. gas / lattice-QCD - in-medium spectral function Solution for axialvector spectral function? T [GeV] 3.3.2 QCD + Weinberg Sum Rules in Medium Quantitatively compatible (< 1%) with (approach to) chiral restoration Chiral mass spliting burns off
[Hohler +RR 13] 3.4 Massive Yang-Mills Approach in Vacuum Gauge + a1 into chiral pion lagrangian: problems with vacuum phenomenology [Urban et al 02, global gauge? Rischke et al 10] Improvement - full propagator in a1 selfenergy - vertex corrections to preserve [Hohler +RR 14] PCAC:
enables fit to -decay data local-gauge approach viable starting point for evaluating chiral restoration in medium 3.4.2 Massive Yang-Mills in Hot Pion Gas Temperature progression of vector + axialvector spectral functions supports burning of chiral-mass splitting as mechanism for chiral restoration [as in sum rule analysis] [Hohler+RR 15] 3.5 Lattice-QCD Results for N(940)-N*(1535) Euclidean Correlator Ratios Nucleon Exponential Mass Extraction
N*(1535) G ( ) G ( ) R (T ) ~ d G ( ) G ( ) also indicates MN*(T) MN (T) MNvac [Aarts et al 15] Outline 1.) Introduction 2.) Spontaneous Chiral Symmetry Breaking QCD Vacuum + Excitations 3.) Axial/Vector Mesons in Medium Vacuum + Many-Body Theory QCD + Weinberg Sumrules EFT + Mechanisms of Chiral Restoration
4.) Dilepton Phenomenology From SIS to RHIC 5.) Conclusions 4.1 Dilepton Rates: Hadronic vs. Partonic d N ee e2m d 3 q B 3 2 f ( q 0 ,T ) em(M,q;B,T) 4 2 d x dM M 2q0 [qqee] resonance melting hadronic rate approaches QGP rate
suggestive for deconfinement and chiral restoration robust modeling in heavy-ion collisions 4.2 EM Spectra in Heavy-Ion Collisions Evolve rates over fireball: d N lthl erm 2 dM Space-time evolution:
- lattice EoS - require fit to final hadron spectra q q d 3 q d R lthl erm d V F B ( ) 2q0 d 4q 0 fo Au-Au (200GeV) e+ e[M.He et al 12] 4.3 Precision Dileptons at SPS (17.3 GeV)
Invariant-Mass Excess Spectrum =120 [van Hees+RR 13] Low mass: radiation from T ~ Tpc ~ 150MeV - spectrometer Intermediate mass: T ~ 200 MeV Total yield: fireball lifetime FB =7 1fm/c See also [Dusling et al, Renk et al, Alam et al, Bratkovskaya et al, ] - thermometer - chronometer 4.4 Low-Mass Dileptons in Heavy-Ion Collisions =120 Robust understanding across QCD phase diagram: QGP + hadronic radiation with melting resonance
4.5 News from PHENIX [PHENIX 15] Anomalous low-mass enhancement [PHENIX 08] not confirmed Now agrees with STAR data and theoretical predictions 4.6 Dilepton Excitation Functions Low-Mass Excess tracks fireball lifetime well! tool for critical point search? Intermediate-Mass Slope unique temperature measurement
track first order transition? s 10 GeV very promising regime for dileptons 5.) Conclusions Dilepton radiation in HICs probes in-medium vector spectral function - fate of hadrons, chiral restoration - robust theoretical understanding of data via melting resonance Mechanism of chiral restoration - mounting evidence for burning off M: QCD+Weinberg sum rules, EFT, lattice QCD
Future JP=0 1 1/2 - low-mass spec fct at B ~ 0 (RHIC/LHC) + B 400MeV (FAIR, SPS) - excitation fct. of lifetime + temperature (BES-II, FAIR, SPS, NICA) - origin of photon-/dilepton-v2 4.2.2 Evaluation of Chiral Sum Rules in Vacuum pion decay constants I 2 1 f2r2 FA 3 chiral quark condensates
I 0 2mq 0 | q q | 0 I 1 f 2 I1 c s 0 | (q q)2 | 0 vector-axialvector splitting clean observable of spontaneous chiral symmetry breaking promising starting point to search for chiral restoration 4.1.2 Sensitivity to Spectral Function In-Medium -Meson Width M[GeV] avg. (T~150MeV) ~ 370 MeV (T~Tc) 600 MeV m
driven by (anti-) baryons 3.3 Low-Mass e+e Excitation Function: 20-200 GeV [P. Huck et al. (STAR), QM14] compatible with predictions from melting meson universal source around T pc 3.2.2 Dimuon pt-Spectra + Slopes: Barometer Effective Slopes Teff slopes originally too soft
need stronger fireball acceleration, e.g. a = 0.085/fm 0.1/fm insensitive to Tc = 160-190 MeV 3.3.1 Photon Puzzle!? Spectra Elliptic Flow Teffexcess = (22025) MeV flow blue-shift: Teff ~ T (1+)/(1) , ~0.3: T ~ 220/1.35 ~ 160 MeV
small slope + large v2 suggest main emission around Tpc similar indications at LHC [ALICE] 4.2 Low-Mass Dileptons: Chronometer In-In Nch>30 first explicit measurement of interacting-fireball lifetime: FB (71) fm/c 3.4 Low-Mass e+e at HADES (2.6 GeV) [Endres,van Hees, Weil+Bleicher, in prep]
Thermal rates folded over coarse-grained UrQMD medium evolution consistent with baryon-driven medium effects at SPS+RHIC See also [Bratkovskaya et al , Kmpfer et al, Weil et al,] 3.2.3 Transverse-Momentum Spectra: Baro-meter Effective Slope Parameters RHIC SPS QGP HG [Deng,Wang, Xu+Zhuang 11] qualitative change from SPS to RHIC: flowing QGP true temperature shines at large m T
> + matches spectral medium effects: resonances + pion cloud 3.2 Vector Correlator in Thermal Lattice QCD Analyticity:
em ii ( dq c o s h [ q 0 ( 1 / 2 T )] , q ; T ) 0 ieim ( q 0 , q ; T ) 2 s inh [ q 0 / 2 T ] 0 Euclidean Correlator Ratio Spectral Function [Ding et al 10] [RR 02] GV ( ,T )
GVfre e ( ,T ) correlator enhancement comparable to lattice QCD indicates transition from hadronic to partonic degrees of freedom 4.1 Prospects I: Spectral Shape at B ~ 0 STAR Excess Dileptons [STAR 14] rather different spectral shapes compatible with data QGP contribution? 2.2 Transverse-Momentum Dependence pT -Sliced Mass Spectra mT -Slopes x 100
spectral shape as function of pair-pT entangled with transverse flow (barometer) 2.4 Low-Mass e+e at HADES (2.63 GeV) [Endres,van Hees+Bleicher, in prep] Thermal rates folded over coarse-grained UrQMD medium evolution good description in (M,q ) t data well beyond kinematic limit (0.75GeV)! 3.3.2 Effective Slopes of Thermal Photons Thermal Fireball Viscous Hydro
[van Hees,Gale+RR 11] [S.Chen et al 13] thermal slope can only arise from T Tc (constrained by closely confirmed by hydro hadron data) exotic mechanisms: glasma BE? Magnetic fields+ U (1)? A [Liao at al 12, Skokov et al 12, F. Liu 13,] 3.3.3 Direct Photons at LHC Spectra Elliptic Flow ALICE
[van Hees et al in prep] similar to RHIC results non-perturbative photon emission rates around T ? pc 5.2 Chiral Restoration Window at LHC low-mass spectral shape in chiral restoration window: ~60% of thermal low-mass yield in chiral transition region (T=125-180MeV) enrich with (low-) pt cuts 4.4 Elliptic Flow of Dileptons at RHIC
maximum structure due to late decays [He et al 12] [Chatterjee et al 07, Zhuang et al 09] 3.3.2 Fireball vs. Viscous Hydro Evolution [van Hees, Gale+RR 11] [S.Chen et al 13] very similar! 2.3 Dilepton Rates vs. Exp.: NA60 Spectrometer
Evolve rates over fireball expansion: th erm fo dN therm M d 3 q dR d V F B ( ) 4 dM q0 d q 0 Acc.-corrected + Excess Spectra In-In(17.3GeV) [NA60 09] [van Hees+RR 08]
M[GeV] invariant-mass spectrum directly reflects thermal emission rate! 4.2 Low-Mass e+e at RHIC: PHENIX vs. STAR PHENIX enhancement (central!) not accounted for by theory STAR data ok with theory (charm?!) 4.3.2 Revisit Ingredients Emission Rates Hadron - QGP continuity! conservative estimates Fireball Evolution
multi-strange hadrons at Tc v2bulk fully built up at hadronization chemical potentials for , K, [Turbide et al 04] [van Hees et al 11] 4.7.2 Light Vector Mesons at RHIC + LHC baryon effects important even at B,tot= 0 : sensitive to Btot= + B (-N and -N interactions identical)
also melts, more robust OZI 4.1 Nuclear Photoproduction: Meson in Cold Matter + A e+e X e+ E1.5-3 GeV e extracted
in-med -width 220 MeV [CLAS+GiBUU 08] Microscopic Approach: product. amplitude + in-med. spectral fct. Fe - Ti full calculation fix density 0.40
N [Riek et al 08, 10] M [GeV] -broadening reduced at high 3-momentum; need low momentum cut!
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