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)

1.) Introduction: Probing QCD Matter Bulk Properties: Equation of State, Transport Coefficients Microscopic Properties: Degrees of Freedom, Spectral Functions Phase Transitions: Condensate Structure Big Bang Compact Stellar Objects

Freeze-Out QGP A + A 1.2 Dileptons in Heavy-Ion Collisions NN coll. Emission Sources: Drell-Yan: NN→e + e  X e+e+ e-e-  Thermal radiation - Quark-Gluon Plasma: qq → e + e  - Hadron Matter     →  → e + e , … - final-state decays:  ,  →  e + e  qq Hadron Matter

 em (M,q;  B,T)  em / M 2 e + e  → hadrons 1.3 EM Spectral Function Probing the Fireball M [GeV] Thermal Dilepton Rate unique direct access to in-medium spectral function e + e   q - Hadrons:  em ~ Im D  - change in degrees of freedom? - restoration of chiral symmetry? qq Continuum:  em / M 2 ~ const (1+ O [T 2 /M 2 ]) - temperature? -

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

“Higgs” Mechanism in Strong Interactions: qq attraction  condensate fills QCD vacuum! Spontaneous Chiral Symmetry Breaking 2.1 Chiral Symmetry + QCD Vacuum 2-f lavor + chiral (left/right) invariant > > > > qLqL qRqR qLqL - qRqR - - Consequences: effective quark mass: ↔ mass generation!? near-massless Goldstone bosons  0,± “chiral partners” split:  M ≈ 0.5GeV J P =0 ± 1 ± 1/2 ±

Spectral shape matters for chiral symmetry breaking E.g. 2.2 Mass Gap + Chiral Partners Axial-/Vector Correlators pQCD cont. “Data”: lattice [Bowman et al ‘02] Theory: Instanton Model [Diakonov+Petrov; Shuryak ‘85] ● Chiral breaking: |q 2 | ≤ 2 GeV 2 Constituent Quark Mass  V,A / s

2.3 Chiral Symmetry and Dileptons [Fodor et al ’10] T [MeV] Chiral Condensate Vacuum VV AA Chiral Restoration

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  a 1 as gauge bosons into chiral  Lagrangian    |F  | 2    propagator: 3 parameters: m  (0), g,    EM formfactor  phase shift 

3.2  Meson in Hot + Dense Matter D  (M,q;  B,T) = [M 2 - m  2 -   -   B -   M ] -1 Interactions with hadrons from heat bath  In-Medium  -Propagator     [Chanfray et al, Herrmann et al, Urban et al, Weise et al, Oset et al, …] In-Medium Pion Cloud  > > R= , N(1520), a 1, K 1,... h=N, , K, …   =  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,  N→  N…)

3.2.2  -Meson Spectral Function in Medium  -meson “melts” in hot/dense matter largely driven by baryon density (  B )  B /  Hot + Dense Matter [RR+Gale ’99] Hot Meson Matter [RR+Wambach ’99]  B =330MeV

3.3 QCD + Weinberg Sum Rules √s [GeV] [Weinberg ’67, Das et al ’67]  aa T [GeV] [Weinberg ’67, Das et al ’67; Kapusta+Shuryak ‘94] accurately satisfied in vacuum In-medium input: - condensates: hadron reso. gas / lattice-QCD - in-medium  spectral function Solution for axialvector spectral function?

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  + a 1 into chiral pion lagrangian: problems with vacuum phenomenology → global gauge? Improvement - full  propagator in a 1 selfenergy - vertex corrections to preserve PCAC: enables fit to  -decay data local-gauge approach viable starting point for evaluating chiral restoration in medium [Urban et al ‘02, Rischke et al ‘10] [Hohler +RR ‘14]

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 Exponential Mass Extraction also indicates M N* (T) → M N (T) ≈ M N vac “N*(1535)” “Nucleon” [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 resonance melting  hadronic rate approaches QGP rate suggestive for deconfinement and chiral restoration robust modeling in heavy-ion collisions [qq→ee] -  em (M,q;  B,T)

4.2 EM Spectra in Heavy-Ion Collisions Space-time evolution: - lattice EoS - require fit to final hadron spectra Evolve rates over fireball: [M.He et al ’12] Au-Au (200GeV) e + e -  q q -

4.3 Precision Dileptons at SPS (17.3 GeV) Low mass: radiation from T ~ T pc  ~ 150MeV - spectrometer Intermediate mass: T ~ 200 MeV - thermometer Total yield: fireball lifetime  FB =7 ± 1fm/c - chronometer Invariant-Mass Excess Spectrum =120 [van Hees+RR ’13] See also [Dusling et al, Renk et al, Alam et al, Bratkovskaya et al, …]

4.4 Low-Mass Dileptons in Heavy-Ion Collisions Robust understanding across QCD phase diagram: QGP + hadronic radiation with melting  resonance =120

“Anomalous” low-mass enhancement [PHENIX ’08] not confirmed Now agrees with STAR data and theoretical predictions [PHENIX ‘15] 4.5 News from PHENIX

tracks fireball lifetime well! tool for critical point search? 4.6 Dilepton Excitation Functions unique temperature measurement track first order transition? Low-Mass Excess Intermediate-Mass Slope √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 - 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-v 2 J P =0 ± 1 ± 1/2 ±

4.2.2 Evaluation of Chiral Sum Rules in Vacuum vector-axialvector splitting clean observable of spontaneous chiral symmetry breaking promising starting point to search for chiral restoration pion decay constants chiral quark condensates

M  [GeV] Sensitivity to Spectral Function avg.   (T~150MeV) ~ 370 MeV    (T~T c ) ≈ 600 MeV → m  driven by (anti-) baryons In-Medium  -Meson Width

compatible with predictions from melting  meson “universal” source around T pc [P. Huck et al. (STAR), QM14] 3.3 Low-Mass e + e  Excitation Function: GeV

3.2.2 Dimuon p t -Spectra + Slopes: Barometer slopes originally too soft need stronger fireball acceleration, e.g. a ┴ = 0.085/fm → 0.1/fm insensitive to T c = MeV Effective Slopes T eff

3.3.1 Photon Puzzle!? T eff excess = (220±25) MeV flow blue-shift: T eff ~ T √(1+  )/(1  ),  ~0.3: T ~ 220/1.35 ~ 160 MeV small slope + large v 2 suggest main emission around T pc similar indications at LHC [ALICE] Spectra Elliptic Flow

4.2 Low-Mass Dileptons: Chronometer first “explicit” measurement of interacting-fireball lifetime:  FB ≈ (7±1) fm/c In-In N ch >30

Thermal rates folded over coarse-grained UrQMD medium evolution consistent with baryon-driven medium effects at SPS+RHIC [Endres,van Hees, Weil+Bleicher, in prep] 3.4 Low-Mass e + e  at HADES (2.6 GeV) See also [Bratkovskaya et al, Kämpfer et al, Weil et al,…]

3.2.3 Transverse-Momentum Spectra: Baro-meter SPS Effective Slope Parameters qualitative change from SPS to RHIC: flowing QGP true temperature “shines” at large m T RHIC [Deng,Wang, Xu+Zhuang ‘11] QGP HG

2.2 Chiral Condensate +  -Meson Broadening  qq  /  qq  0 - effective hadronic theory  h = m q  h|qq|h  > 0 contains quark core + pion cloud =  h core +  h cloud ~ + + matches spectral medium effects: resonances + pion cloud resonances + chiral mixing drive  -SF toward chiral restoration   > > - 

3.2 Vector Correlator in Thermal Lattice QCD Analyticity: Spectral Function Euclidean Correlator Ratio correlator enhancement comparable to lattice QCD indicates transition from hadronic to partonic degrees of freedom [Ding et al ‘10] [RR ‘02]

rather different spectral shapes compatible with data QGP contribution? 4.1 Prospects I: Spectral Shape at  B ~ 0 STAR Excess Dileptons [STAR ‘14]

2.2 Transverse-Momentum Dependence p T -Sliced Mass Spectra m T -Slopes x 100 spectral shape as function of pair-p T entangled with transverse flow (barometer)

Thermal rates folded over coarse-grained UrQMD medium evolution good description in (M,q t ) data well beyond kinematic limit (0.75GeV)! [Endres,van Hees+Bleicher, in prep] 2.4 Low-Mass e + e  at HADES (2.63 GeV)

3.3.2 Effective Slopes of Thermal Photons thermal slope can only arise from T ≤ T c (constrained by closely confirmed by hydro hadron data) exotic mechanisms: glasma BE? Magnetic fields+ U A (1)? [van Hees,Gale+RR ’11] [Liao at al ’12, Skokov et al ’12, F. Liu ’13,…] [S.Chen et al ‘13] Thermal Fireball Viscous Hydro

3.3.3 Direct Photons at LHC similar to RHIC results non-perturbative photon emission rates around T pc ? Spectra Elliptic Flow ● ALICE [van Hees et al in prep]

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= MeV) enrich with (low-) p t cuts

4.4 Elliptic Flow of Dileptons at RHIC maximum structure due to late  decays [Chatterjee et al ‘07, Zhuang et al ‘09] [He et al ‘12]

3.3.2 Fireball vs. Viscous Hydro Evolution very similar! [van Hees, Gale+RR ’11] [S.Chen et al ‘13]

2.3 Dilepton Rates vs. Exp.: NA60 “Spectrometer” invariant-mass spectrum directly reflects thermal emission rate! M  [GeV] Evolve rates over fireball expansion: [van Hees+RR ’08] In-In(17.3GeV) [NA60 ‘09] Acc.-corrected  +   Excess Spectra

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 multi-strange hadrons at “T c ” v 2 bulk fully built up at hadronization chemical potentials for , K, … Hadron - QGP continuity! conservative estimates… Emission Rates Fireball Evolution [van Hees et al ’11] [Turbide et al ’04]

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 [CLAS+GiBUU ‘08] E  ≈1.5-3 GeV  e+ee+e  extracted “in-med”  -width   ≈ 220 MeV Microscopic Approach: Fe - Ti  N  product. amplitude in-med.  spectral fct. + M [GeV] [Riek et al ’08, ‘10] full calculation fix density 0.4  0  -broadening reduced at high 3-momentum; need low momentum cut!