The Vector Probe in HeavyIon Reactions Ralf Rapp
The Vector Probe in Heavy-Ion Reactions Ralf Rapp Cyclotron Inst. + Physics Dept. Texas A&M University College Station, Texas Hot Quarks Workshop Taos Valley, 21. 07. 04
Introduction I: E. M. Probes in Strong Interactions • g-ray spectroscopy of atomic nuclei: collective phenomena • DIS off the nucleon: - parton model, PDF’s (high Q 2) - nonpert. structure of nucleon [JLAB] • thermal emission: - compact stars (? !) - heavy-ion collisions What is the electromagnetic spectrum of QCD matter? c. PT many-body (2 ↔ 2) consistent 0 0. 05 120 ½r 0 degrees of freedom? QGP (3 -body, . . . ) extrapolate 0. 3 150 -160 2 r 0 0. 75 175 5 r 0 (resonances? ) p. QCD e[Ge. Vfm-3] T [Me. V] rhadron
Outline 1. Introduction 2. Four Pillars of Electromagnetic Radiation 3. Dileptons 3. 1 Low Mass: - Axial-/Vector Correlator and Chiral Symmetry - Medium Effects and Excitation Function - Lattice QCD 3. 2 Intermediate Mass: QGP Radiation? 3. 3 RHIC 4. Photons 4. 1 QGP and Hadron Gas Emission 4. 2 SPS and RHIC Phenomenology 5. Conclusions
Introduction II: Electromagnetic Emission Rates E. M. Correlation Function: e+ e- Im Πem(M, q) = O(1) γ Im Πem(q 0=q) = O(αs ) also: e. m susceptibility (charge fluct): χ = Πem(q 0=0, q→ 0) In URHICs: • source strength: dependence on T, m. B, mp ; medium effects, … • system evolution: V(t), T(t), m. B(t) ; transverse expansion, … • nonthermal sources: e+e-: Drell-Yan, open-charm(!); g: initial/ • consistency! pre-equil.
2. ) Four Pillars of Thermal E. M. Radiation low-mass ee in-med r, w, f →ee Chiral Symmetry restoration? low-energy g hadron decays/scatt. a 1→pg , pr→pg Medium effects? Thermal rate: qq int-mass ee continuum emission p a 1→ ee , qq→ee QGP radiation? high-energy g continuum emission HG vs. QGP , O(as) QGP radiation? q 0≈0. 5 Ge. V Tmax≈0. 17 Ge. V , q 0≈1. 5 Ge. V Tmax=0. 5 Ge. V
3. ) Low-Mass Dileptons + Chiral Symmetry Im Πem(M) ~ Im Dvec(M) vector-meson spectral functions dominated by r-meson → chiral partner: a 1(1260) Vacuum At Tc: Chiral Restoration p. QCD cont. Chiral breaking: Q 2 < 3 Ge. V 2
3. 1. 1 Vector Mesons in Medium: Many-Body Theory Sp Sp + > N, p, K… (i) SPS Conditions • r-meson “melts” in hot and dense matter • baryon density r. B more important than temperature > r B*, a 1, K 1. . . Constraints: - branching ratios B, M→r. N, rp - g. N, g. A absorpt. , p. N→r. N - QCD sum rules, lattice r. B/r 0 0 0. 1 0. 7 2. 6
(ii) Vector Mesons at RHIC Dilepton Emission Rates [qq→ee] [qq+O(a s)] baryon effectsin-med important at r. B, tot =0! : HG even ≈ in-med QGP sensitive to r. Btot. Quark-Hadron =r. B+r. B- , f more robust Duality ? ! ↔ OZI
3. 1. 2 Low-Mass Dileptons in URHICs Top SPS Energy BEVALAC/SIS Lower SPS Energy DLS • baryon effects important! • precision test by NA 60!? • • enhancement still: enhancementincreases! DLS puzzle → HADES!?
3. 1. 3 Current Status of a 1(1260) Sr + Sp > + N(1520)… Exp: - HADES (p. A): a 1→(p+p-)p - URHICs (A-A) : a 1→ pg > > Sp > a 1 D, N(1900)… . . .
3. 1. 4 Comparison of Hadronic Models to LGT calculate integrate More direct! Proof of principle, not yet meaningful (need unquenched)
3. 2 Intermediate-Mass Dileptons: NA 50 (SPS) e. m. corr. continuum-like: Im Πem ~ M 2 (1+as/p+…) QGP+ HG! Thermal Fireball (chem-off-eq) Ti≈210 Me. V , HG-dominated [RR+Shuryak ’ 99] Hydrodynamics (chem-eq) Ti≈300 Me. V, QGP-dominated [Kvasnikowa, Gale+Srivastava ’ 02]
3. 3 Dilepton Spectrum at RHIC MB Au-Au (200 Ge. V) [R. Averbeck, PHENIX] [RR ’ 01] • low mass: thermal dominant • int. mass: cc e+X , rescatt. ? e -X run-4 eagerly awaited …
4. ) Thermal Photons Hot and Dense Hadron Gas Emission Rates q + q (g) → g (q) + γ Low energy: vector dominance Quark-Gluon Plasma “Naïve” LO: q q Im Πem(q 0=q) ~ Im Dvec(q 0=q) g But: other contributions in O(αs) collinear enhanced Dg=(t-m. D 2)-1~1/αs r Sp High energy: meson exchange p Bremsstrahlung Pair-ann. +scatt. HG ≈(LPM) in-med QGP ! + ladder. Total resummation [Aurenche etal ’ 00, Arnold, Moore+Yaffe ’ 01] Sp γ p, a 1, w r p to be understood… [Kapusta, Lichard+Seibert ’ 91, … , Turbide, RR+Gale’ 04]
4. 2 Comparison to Data I: WA 98 at SPS Hydrodynamics: QGP + HG [Huovinen, Ruuskanen+Räsänen ’ 02] • T 0≈260 Me. V, QGP-dominated • still true if pp→g. X included Expanding Fireball + p. QCD [Turbide, RR+Gale’ 04] • p. QCD+Cronin at qt >1. 5 Ge. V T 0=205 Me. V suff. , HG dom.
4. 2 Comp. to Data II: WA 98 “Low-qt Anomaly” Expanding Fireball Model [Turbide, RR+Gale’ 04] • current HG rate much below • 30% longer t. FB 30% increase Include pp→ppg S-wave • slight improvement • in-medium “s” or D ? !
4. 2 Perspectives on Data III: RHIC Predictions for Central Au-Au • large “pre-equilibrium” yield from parton cascade (no LPM) • thermal yields ~ consistent • QGP undersat. small effect PHENIX Data • consistent with p. QCD only • disfavors parton cascade • not sensitive to thermal yet
5. ) Conclusions • Thermal E. M. Radiation from QCD matter - hard: high-E photons, intermediate-M dileptons: p. QCD QGP radiation? ! - soft: low-E g , low-M l+l- : Pem(M, q) chiral restoration? ! • extrapolations into phase transition region in-med HG and QGP shine equally bright lattice calculations? deeper reason? • phenomenology for URHIC’s promising; precision data+theory needed for definite conclusions • much excitement ahead: PHENIX, NA 60, HADES, ALICE, … and theory!
Additional Slides
2. Thermal Photon Radiation 2. 1 Generalities Emission Rate per 4 -volume and 3 -momentum T Im Πem(q 0=q) many-body language: p γ r transverse photon selfenergy cut kinetic theory: p γ r p in-medium effects, resummations, … 2 |M|2
2. 3. 1 Hot Hadronic Matter: p-r-a 1 Gas Chiral Lagrangian + Axial/Vector-mesons, e. g. HLS or MYM: • (g 0, m 0, s, x) fit to mr, a 1 , Gr, a 1 D/S and G(a 1→pγ) not optimal [Song ’ 93, Halasz etal ’ 98, …] HLS MYM Kap. ’ 91 (no a 1) • Photon-producing reactions: p γ p p r r γ p, a 1 p mostly at dominant (q 0>0. 5 Ge. V) q 0<0. 5 Ge. V a 1 -strength problematic p, a 1 gauge invariance!
2. 3. 1. b Hadronic Formfactors • quantitative analysis: account for finite hadron size • improves a 1 phenomenology • t-channel exchange: gauge invariance nontrivial [Kapusta etal ’ 91] simplified approach: [Turbide, Gale+RR ’ 04] with Factor 3 -4 suppression At intermediate and High photon energies
2. 3. 2 Further Meson Gas Sources (i) Strangeness Contributions: SU(3)F MYM p γ K K* ~25% of pp→ργ (ii) w t-Channel [Turbide, Gale +RR ’ 04] p K* p w r γ p p γ K ~40% of pr→pγ ! Gwrp large! potentially important … (iii) Higher Resonances Ax-Vec: a 1, h 1→pg, Vec: f 1→rg , K 1→Kg w, w’’→pg other: p(1300)→pg K*→Kg a 2(1320)→pg
2. 3. 3 Baryonic Contributions • use in-medium r –spectral funct: • constrained by nucl. g-absorption: r Sp Sp B*, a 1, K 1. . . > N, p, K… g N → p N, D g N → B* > [Urban, Buballa, RR+Wambach ’ 98] g. N g. A p-ex
2. 3. 3(b) Photon Rates from r Spectral Function: Baryons + Meson-Resonances • baryonic contributions dominant for q 0<1 Ge. V (CERES enhancement!) • also true at RHIC+LHC: m. B=220 Me. V at T=180 Me. V, m. B=0
2. 3. 4 HG Emission Rates: Summary • w t-channel (very) important at high energy • formfactor suppression (2 -4) • strangeness significant m. B=220 Me. V [Turbide, RR+Gale ’ 04] • baryons at low energy
2. 3. 5 In-Medium Effects • many-body approach: encoded in vector-spectral function, relevant below M , q 0 ~ 1 -1. 5 Ge. V • “dropping masses”: large enhancement due to increased phase space [Song+Fai ’ 98, Alam etal ’ 03] unless: vector coupling decreases towards Tc (HLS, a→ 1) [Harada+Yamawaki ’ 01, Halasz etal ’ 98]
2. 3. 6 Hadron Gas vs. QGP Rate • complete in-med QGP rate factor ~2 larger than naïve LO QGP • total HG rate (bottom-up) very similar to in-med QGP (top-down) “quark-hadron duality” ? • also found for dileptons, no explanation yet …
3. 2 Thermal Evolution: QGP→ Mix→ HG HG: chemistry and trans. chemistry [LHC]flow T [Ge. V] QGP: initial conditions [SPS] • t 0=1 fm/c → t 0=0. 5 fm/c: ~2 -3 • s=Cd. QGT 3; d. QG=40 → 32: ~2 • pre-equilibrium? ! • R~exp(3 mp) for pg , … • conserved BB pr use→entropy • yield up at of lowmqpt>0 , down above • build-up (Np=const) • large blue shiftcooling from coll. flow • accelerated
4. 2 Non-Thermal Photon Sources Initial hard production: pp → γX Nuclear Effects: p. A → g. X scaling with x. T=2 p. T /√s , + power-law fit [Srivastava ’ 01] • “Cronin”: gaussian kt-smear. • cf. p. A → πX • AA: <Dkt 2>AA≈ 2<Dkt 2>p. A
Photon Properties in Colorsuperconductors
2. 2. 4 In-Medium Baryons: D(1232) long history in nuclear physics ! ( p. A , g. A ) e. g. nuclear photoabsorption: MD, GD up by 20 Me. V little attention at finite temperature D-Propagator at finite r. B and T in-medium p-cloud, (1+ f p - f N) > > + > DN-1 > D Sp NN-1 [van Hees + RR ’ 04] > vertex corrections incl. g’ (“induced interaction”) + + . . . > p. D→N(1440), N(1520), D(1600) thermal p-gas
(ii) D(1232) in URHICs broadening: Bose factor, p. D→B repulsion: p. DN-1, p. NN-1 not yet included: (p. N→D)
3. 1 Continuity? ! E. M. Emission Rates Light Hadron “Masses” [Shuryak, Zahed, Brown ’ 04] However: peak in susceptibilities at Tc ↔ ms → 0 Observables ? e+e-+pg, fluct, pp, J/y, . . .
2. 2. 6 Observables in URHICs (i) Lepton Pairs e+ e. Im Πem(M, q) γ (ii) Photons Im Πem(q 0=q) [Turbide, Gale+RR ’ 03] baryon density effects! • consistent with dileptons • pp Brems with soft s at low q?
3. 3 Dilepton Spectrum at RHIC
4. 3 Perspectives on Data III: RHIC Predictions for Central Au-Au • large “pre-equilibrium” yield from parton cascade (no LPM) • thermal yields ~ consistent • QGP undersat. small effect PHENIX Data • consistent with initial only • disfavors parton cascade • not sensitive to thermal yet
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