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 ColloquiumInstitute for Theoretical Physics (Frankfurt, Germany)

22.10.15

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

CompactStellar Objects

Freeze-OutQGP

A + A

1.2 Dileptons in Heavy-Ion Collisions

NN coll.

Emission Sources:• Drell-Yan: NN→e+eX

e+

e-

• Thermal radiation - Quark-Gluon Plasma: qq → e+e - Hadron Matter → → e+e , …

-

• final-state decays: ,→ e+e

qq

Hadron Matter

)T,q(fMqdxd

d N Bee023

2e m

44

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

e+ e

q q-

• Hadrons: em ~ Im D

- change in degrees of freedom? - restoration of chiral symmetry?

• qq Continuum: em / M2 ~ const (1+ O[T2/M2]) - 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-flavor + chiral (left/right) invariant

350000 fm|qqqq||qq| LRRL

>

>

>

>qLqR

qL-qR

--

Consequences:• effective quark mass: ↔ mass generation!?

• near-massless Goldstone bosons 0,±

• “chiral partners” split: M ≈ 0.5GeV

00 |qq|m*q

JP=0± 1± 1/2±

2

41

aq Gq)m̂Agi(q QCDL

• 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: |q2| ≤ 2 GeV2

Constituent Quark Mass

)(2AVs

dsf

V

,A /

s

2.3 Chiral Symmetry and Dileptons

[Fodor et al ’10]

0qq/)T(qq

T [MeV]

Chiral Condensate

Vacuum

qqm

ds

q

AV

)(

V

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 a1 as gauge bosons into chiral Lagrangian

2

21 g)(gintL

1202 )]M()m(M[)M(D )(

|F|2

propagator:

• 3 parameters: m

(0), g,

• EM formfactor

• phase shift

24)0(2 |)(|)(|)(| MDmMF

)(Re

)(Imtan)( 1

MD

MDM

3.2 Meson in Hot + Dense Matter

D(M,q;B,T) = [M2- m2- - 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), a1, K1,...

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/0

0 0.1 0.7 2.6

Hot + Dense Matter

[RR+Gale ’99]

Hot Meson Matter

[RR+Wambach ’99]

B =330MeV

3.3 QCD + Weinberg Sum Rules

√s [GeV]

2)(1 f

sds AV

[Weinberg ’67, Das et al ’67]

qqmds qAV )( 2)()( qqcsds sAV

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 + a1 into chiral pion lagrangian:

• problems with vacuum phenomenology

→ global gauge?

• Improvement - full propagator in a1 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 GasTemperature 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 MN*(T) → MN (T) ≈ MNvac

)()(

)()(~)(

GG

GGdTR

“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]-

)T,q(fq

qdMd Mxd

d N Be e0

0

3

23

2e m

24 2

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:qd

d Rq

qd)(Vd

d M

d N th erml l

F B

th erml l

f o

40

3

2 20

[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 ~ Tpc ~ 150MeV - spectrometer

• Intermediate mass: T ~ 200 MeV - thermometer

• Total yield: fireball lifetime FB =7 ± 1fm/c - chronometer

Invariant-Mass Excess Spectrum

<Nch>=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

<Nch>=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-v2

JP=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 00002

31

210

21

222

|q)q(|αcI|qq|mI

fIFrfI

sq

πA

M[GeV]

4.1.2 Sensitivity to Spectral Function

• avg. (T~150MeV) ~ 370 MeV (T~Tc) ≈ 600 MeV → m

• driven by (anti-) baryons

In-Medium -Meson Width

• compatible with predictions from melting meson• “universal” source around Tpc

[P. Huck et al. (STAR), QM14]

3.3 Low-Mass e+e Excitation Function: 20-200 GeV

3.2.2 Dimuon pt-Spectra + Slopes: Barometer

• slopes originally too soft • need stronger fireball acceleration, e.g. a┴ = 0.085/fm → 0.1/fm

• insensitive to Tc = 160-190 MeV

Effective Slopes Teff

3.3.1 Photon Puzzle!?

• Teffexcess = (220±25) 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]

Spectra Elliptic Flow

4.2 Low-Mass Dileptons: Chronometer

• first “explicit” measurement of interacting-fireball lifetime: FB ≈ (7±1) fm/c

In-In Nch>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 mT

RHIC

[Deng,Wang, Xu+Zhuang ‘11]

QGPHG

2.2 Chiral Condensate + -Meson Broadening

qq

/ q

q0

-

-

effective hadronic theory

• h = mq h|qq|h > 0 contains quark core + pion cloud

= hcore + 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

]T/q[)]T/(q[

)T;q,q(d q

)T;q,( i ii i 2s inh21c o s h

2 0

00

e m

0

0e m

• Analyticity:

)T,(G

)T,(G

V

V

fre e

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

pT -Sliced Mass Spectra

mT -Slopes

x 100

• spectral shape as function of pair-pT

• entangled with transverse flow (barometer)

• Thermal rates folded over coarse-grained UrQMD medium evolution• good description in (M,qt) • 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 ≤ Tc (constrained by• closely confirmed by hydro hadron data)• exotic mechanisms: glasma BE? Magnetic fields+ UA(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 Tpc?

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=125-180MeV)• enrich with (low-) pt 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]

qd

d Rq

qdM)(Vd

d Md N th erm

F B

th erm f o

40

3

0

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 “Tc”

• v2bulk 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

• 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 calculationfix density 0.40

• -broadening reduced at high 3-momentum; need low momentum cut!