search for chiral symmetry restoration in qcd matter ralf rapp cyclotron institute + dept of phys...
TRANSCRIPT
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
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
/ 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!