Light Vector Mesons in Medium From Constraints to

Light Vector Mesons in Medium: From Constraints to Predictions Ralf Rapp Cyclotron Institute + Dept. of Physics & Astronomy Texas A&M University College Station, Texas USA EMMI RRTF Symposium “Emissivity of Matter under Extreme Conditions: l+l- + c. S” GSI (Darmstadt, Germany), 09. 10. 13

1. ) EM Spectral Function + QCD Phase Structure • Electromagn. spectral function - √s ≤ 1 Ge. V : non-perturbative - √s > 1. 5 Ge. V : pertubative (“dual”) e+e- → hadrons ~ Im Pem / M 2 • Modifications of resonances ↔ phase structure: hadronic matter → Quark-Gluon Plasma? • Thermal e+e- emission rate from hot/dense matter (lem >> Rnucleus ) Im Πem(M, q; m. B, T) • Temperature? Degrees of freedom? • Deconfinement? Chiral Restoration? √s = M

Outline 2. ) Axial-/Vector Mesons in Vacuum - Massive Yang-Mills - Observables + Sum Rules 3. ) Vector Mesons in Medium + Constraints - Hadronic Many-Body Theory - p. N→r. N, g. N/A Absorption 4. ) Predictions I: Cold Matter - g. N/A → e+e-N/A - w Spectral Function 5. ) Theoretical Tests in Medium - Sum Rules - Lattice-QCD 6. ) Predictions II: Hot Matter 7. ) Conclusions

2. ) Axial/Vector Mesons in Vacuum Introduce r, a 1 as gauge bosons into free p +r +a 1 Lagrangian p r propagator: • 3 parameters: mr(0), g, Lr |Fp|2 dpp

2. 2 Massive Yang-Mills Revisited • Problems in phenomenology of AV spectral function: too little strength, zero in a 1 width • (very) recent advance: [Hohler+RR ‘ 13] - full r propagator in a 1 selfenergy - vertex corrections preserving PCAC • recovers quantitative fit to t-decays • “saves” local-gauge approach • enables to more rigorously address chiral restoration in medium

2. 3 Weinberg Sum Rules • Quantify chiral symmetry breaking via observable spectral functions • Vector (r) - Axialvector (a 1) spectral splitting [Weinberg ’ 67, Das et al ’ 67] t→(2 n)p [ALEPH ‘ 98, OPAL ‘ 99] t→(2 n+1)p p. QCD • Key features of “fit”: [Hohler+RR ‘ 12] ground (r, a 1) + excited states (r’, a 1’), universal continuum (p. QCD!)

3. ) Vector Mesons in Medium + Constraints ● Hadronic Many-Body Theory ● p. N→r. N, g. N + g. A Absorption

3. 1 r-Meson in Matter: Many-Body Theory interactions with hadrons from heat bath In-Medium r-Propagator r Dr(M, q; m. B, T) = [M 2 – (mr(0))2 - rpp - r. B - r. M ]-1 rpp = p r p [Chanfray et al, Herrmann et al, Urban et al, Weise et al, Koch et al, …] • Direct r-Hadron Scattering [Haglin, Friman et al, RR et al, Post et al, …] r. B, M = r p + > R=D, N(1520), a 1, K 1. . . > • In-Medium Pion Cloud h=N, p, K … • estimate couplings from R→ r + h • quantitatively: comprehensive constraints

3. 2 Production Processes from r Spectral Function ↔ Cuts (imag. parts) of Selfenergy Diagrams: p N-1 D r p p r > r B N N-1 p resonance Dalitz decays p N → D → g. N p r → a 1 → g p meson-exchange scattering p N → g. N , g. D Bremsstrahlung NN → g NN, g ND, g DD

3. 2. 2 Constraints I: p. N→ r. N Scattering background (Lp. NN=400 Me. V) [Urban, Buballa, RR+Wambach ’ 98] • strong constraint on pion cloud coupling to nucleons • similarly small cutoff in p. N → D → p. N scattering!

3. 2. 3 Constraints II: Nuclear Photo-Absorption total nuclear g -absorption cross section > N-1 r > r in-medium r -spectral function at photon point D, N*, D* g N → B* direct resonance p p g N → p N, D meson exchange

3. 2. 4 r Spectral Function in Nucl. Photo-Absorption On the Nucleon On Nuclei g. N g. A p-ex • sensitive to r. NB couplings • non-resonant pion background consistent with small Lp. NN • 2. +3. resonances melt (selfconsistent N(1520)→Nr) [Urban, Buballa, RR+Wambach ’ 98]

4. ) Predictions I: Cold Matter ● g. N→r. N, g. N, A →e+e-N, A ● w in Medium

4. 1 Predictions I: Nuclear r + e+e- Photoproduction (a) Production Amplitude: t-channel [Oh+Lee ‘ 04] + resonances (r spectr. fct. !) g d → e +e - X r g + N g N→ r. N (b) Medium Effects: • r propagator in cold nuclear matter Im Dr [1/Me. V 2] [Riek et al ’ 08, ‘ 10] M [Ge. V] CLAS

4. 1. 2 Comparison to CLAS Data • average qr ~ 2 Ge. V average r. N(Fe) ~ 0. 4 r 0 • free norm: c 2 =1. 08 (in-med. r) vs. 1. 55 (vac. r) • need low momentum cut + absolute cross section!

4. 2 Predictions II: w-Meson in Nuclear Matter w p p r r Dw(M, q; m. B, T) = [M 2 - mw 2 - wrp ]-1 • In-Medium pr Cloud from existing p + r propagators [Cabrera+RR’ 13] • large effect from spacelike r-sobars (t-channel); Gwrp(r 0) ≈ 150 Me. V • soft formfactor similar to p cloud in r-meson; !

5. ) Theoretical Tests in Medium ● QCD + Weinberg Sum Rules ● Lattice-QCD Correlators

5. 1 Test I: QCD + Weinberg Sum Rules (T>0) [Hatsuda+Lee’ 91, Asakawa+Ko ’ 93, Klingl et al ’ 97, Leupold et al ’ 98, Kämpfer et al ‘ 03, Ruppert et al ’ 05] [Weinberg ’ 67, Das et al ’ 67; Kapusta+Shuryak ‘ 94] T [Ge. V] r. V, A/s Vacuum s [Ge. V 2] T=140 Me. V T=170 Me. V [Hohler et al ‘ 12] • melting scenario compatible with chiral restoration • microscopic calculation of in-medium axialvector to be done

5. 2 Test II: Thermal Lattice QCD • Euclidean Correlation fct. Lattice (quenched) [Ding et al‘ 10] Hadronic Many-Body • “Parton-Hadron Duality” of lattice and in-medium hadronic!? [RR ‘ 02]

6. ) NA 60 Multi-Meter: Accept. -Corrected Spectra Spectrometer Emp. scatt. ampl. + T-r approximation Hadronic many-body Chiral virial expansion Chronometer Thermometer [CERN Courier 11/’ 09] • Low-mass: sensitive to r-meson spectral shape close to Tpc

7. ) Conclusions • Quantitatively constrained in-medium r SF (p. N → r. N, nucl. g abs. ) • Compatible with g. N → r. N, medium effects in g. A → e+e-A • Large w width from pr cloud • Tests of chiral restoration: - QCD + Weinberg sum rules (T=0 ~ Tpc) - enhancement in lattice QCD correlators • In progress: - Massive Yang-Mills in medium - exclusive channels in spectral functions • Dilepton Phenomenology for URHICs: versatile + precise tool (spectro-, chrono-, thermo- + bar(y)o-meter)

-Im Pem /(C T q 0) 5. 2. 2 Back to Spectral Function • suggestive for approach to chiral restoration and deconfinement

4. 1 Nuclear Photoproduction: r Meson in Cold Matter g+A→ e +e - X e+ g r Eg ≈ 1. 5 -3 Ge. V [CLAS+Gi. BUU ‘ 08] • extracted “in-medium” r-width Gr ≈ 220 Me. V - small? ! e-

qq - / qq -0 4. 10 Chiral Condensate + r-Meson Broadening effective hadronic theory • h = mq h|qq|h > 0 contains quark core + pion cloud + h cloud ~ + > > = h core + p p • matches spectral medium effects: resonances + pion cloud • resonances + chiral mixing drive r-SF toward chiral restoration r

4. 5 r-Meson Spectral Functions “at SPS” Hot + Dense Matter Hot Meson Gas r. B/r 0 0 0. 1 0. 7 2. 6 m. B =330 Me. V [RR+Wambach ’ 99] [RR+Gale ’ 99] • r-meson “melts” in hot/dense matter • baryon density r. B more important than temperature

4. 7 Intermediate Mass: “Chiral Mixing” [Dey, Eletsky +Ioffe ’ 90] • low-energy pion interactions fixed by chiral symmetry = 0 0 • mixing parameter • degeneracy with perturbative spectral fct. down to M~1 Ge. V • physical processes at M ≥ 1 Ge. V: pa 1 → e+e- etc. (“ 4 p annihilation”)

2. 5 QCD Sum Rules: r and a 1 in Vacuum • dispersion relation: • lhs: hadronic spectral fct. [Shifman, Vainshtein+Zakharov ’ 79] • rhs: operator product expansion • 4 -quark + gluon condensate dominant

4. 6 Light Vector Mesons “at RHIC + LHC” • baryon effects remain important at r. B, net = 0: sensitive to r. B, tot= r. B + r. B (r-N = r-N, CP-invariant) • w also melts, f more robust ↔ OZI [RR ’ 01]

5. 3 Summary of Dilepton Rates: HM, QGP, Lattice d. Ree /d. M 2 ~ ∫d 3 q f B(q 0; T) Im Pem • Lattice-QCD rate somwhat below Hard-Thermal Loop • hadronic → QGP toward Tpc: resonance melting + chiral mixing • Quark-Hadron Duality at all Mee? ! (QGP rates chirally restored!)

4. 1. 2 Comparison to CLAS Data Eg ≈1. 5 -3 Ge. V, uniform production points, decay distribution with in-med Gr Density at r Decay Point • average qr ~ 2 Ge. V average r. N(Fe) ~ 0. 4 r 0 • free norm: c 2 =1. 08 vs. 1. 55 in-med vs. vac r spectral function • need low momentum cut + absolute cross section!

4. 4 r-Meson Spectral Function in Nuclear Matter In-med. p-cloud + r+N→B* resonances [Urban et al ’ 98] r+N→B* resonances (low-density approx. ) In-med. p-cloud + r+N → N(1520) [Post et al ’ 02] r. N=r 0 Constraints: g N , g A p N →r N PWA • Consensus: strong broadening + slight upward mass-shift • Constraints from (vacuum) data important quantitatively [Cabrera et al ’ 02] r. N=0. 5 r 0 r. N=r 0

6. 1 Space-Time Evolution + Equation of State • Evolve rates over fireball expansion: • 1. order → lattice Eo. S: - enhances temperature above Tc - increases “QGP” emission - decreases “hadronic” emission Au-Au (200 Ge. V) • initial conditions affect lifetime • simplified: parameterize space-time evolution by expanding fireball • benchmark bulk-hadron observables [He et al ’ 12]

6. 1. 2 Bulk Hadron Observables: Fireball Model [van Hees et al ’ 11] • Mulit-strange hadrons freeze-put at Tpc • Bulk-v 2 saturates at ~Tpc

6. 2 Di-Electron Spectra from SPS to RHIC Pb-Au(8. 8 Ge. V) Au-Au (20 -200 Ge. V) QM 12 Pb-Au(17. 3 Ge. V) • consistent excess emission source • suggests “universal” medium effect around Tpc • FAIR, LHC? [cf. also Bratkovskaya et al, Alam et al, Bleicher et al, Wang et al …]

6. 3. 3 Spectrometer m+m- Excess Spectra In-In(17. 3 AGe. V) [NA 60 ‘ 09] Mmm [Ge. V] [van Hees+RR ’ 08] • in-med r + 4 p + QGP • invariant-mass spectrum directly reflects thermal emission rate! Thermal m+m- Emission Rate

6. 4 Conclusions from Dilepton “Excess” Spectra • thermal source (T~120 -230 Me. V) • in-medium r meson spectral function - avg. Gr (T~150 Me. V) ~ 350 -400 Me. V Gr (T~Tpc) ≈ 600 Me. V → mr - “divergent” width ↔ Deconfinement? ! • M > 1. 5 Ge. V: QGP radiation • fireball lifetime “measurement”: t. FB ~ (6. 5± 1) fm/c (In-In) [van Hees+RR ‘ 06, Dusling et al ’ 06, Ruppert et al ’ 07, Bratkovskaya et al ’ 08, Santini et al ‘ 10] Mmm [Ge. V]

6. 6. 2 Thermal Photon Radiation thermal + prim. g [van Hees, Gale+RR ’ 11] • flow blue-shift: Teff ~ T √(1+b)/(1 -b) , b~0. 3: T ~ 220/1. 35 ~ 160 Me. V • “small” slope + large v 2 suggest main emission around Tpc • other explanations…? [Skokov et al ‘ 12; Mc. Lerran et al ‘ 12]

6. 7 Direct Photons at LHC Spectra Elliptic Flow ● ALICE [van Hees et al in prep] • similar to RHIC (not quite enough v 2) • non-perturbative photon emission rates around Tpc?

6. 3. 4 Sensitivity of Dimuons to Equation of State • partition QGP/HG changes, low-mass spectral shape robust [cf. also Ruppert et al, Dusling et al…]

6. 3. 5 NA 60 Dimuons with Lattice Eo. S + Rate First-Order Eo. S + HTL Rate Lattice Eo. S + Lat-QGP Rate In-In (17. 3 Ge. V) Tin =190 Me. V Tc =Tch =175 Me. V [van Hees+RR ’ 08] Tin =230 Me. V Tpc =Tch =175 Me. V Mmm [Ge. V] • partition QGP/HG changes, low-mass spectral shape robust [cf. also Ruppert et al, Dusling et al…]

6. 3. 6 Chronometer In-In Nch>30 • direct measurement of fireball lifetime: t. FB ≈ (6. 5± 1) fm/c • non-monotonous around critical point?

6. 4 Summary of EM Probes at SPS In(158 AGe. V)+In Mmm [Ge. V] • calculated with same EM spectral function!

6. 1 Fireball Evolution in Heavy-Ion Collisions Thermal Dilepton Spectrum: Isentropic Trajectories in the Phase Diagram m. N [Ge. V] t [fm/c] • “chemical” freezeout Tchem~ Tc ~170 Me. V, “thermal” freezeout Tfo ~ 120 Me. V • conserve entropy + baryon no. : Ti → Tchem → Tfo • time scale: hydrodynamics, fireball VFB(t ) = (z 0+vz t ) p (r 0 + 0. 5 a┴ t 2)2

6. 3. 2 NA 60 Data Before Acceptance Correction emp. ampl. + fireball hadr. many-body + fireball chiral virial + hydro schem. broad. /drop. + HSD transport • Discrimination power of model calculations improved, but … • can compensate spectral “deficit” by larger flow: lift pairs into acceptance

6. 3. 7 Dimuon pt-Spectra + Slopes: Barometer Effective Slopes Teff • slopes originally too soft • increase fireball acceleration, e. g. a┴ = 0. 085/fm → 0. 1/fm • insensitive to Tc = 160 -190 Me. V

2. 4. 4 Weinberg (Chiral) Sum Rules + Order Parameters • Moments Vector-Axialvector [Weinberg ’ 67, Das et al ’ 67] • In Medium: energy sum rules at fixed q [Kapusta+Shuryak ‘ 93] • correlators (rhs): effective models (+data) promising synergy! • order parameters (lhs): lattice QCD

D. 1 r -Hadron Interactions in Hot Meson Gas Effective Lagrangian (h = p, K, r) e. g. , A=a 1, h 1 fix G via G(a 1→rp) ~ G 2 v 2 PS ≈ 0. 4 Ge. V, … Generic features: • cancellations in real parts • imaginary parts strictly add up r > R > resonance-dominated: r + h → R, selfenergy: h

D. 2 w EM Formfactor “bare” VDM formfactor Include hadronic formfactor

2. 5 Dimuon pt-Spectra and Slopes: Barometer pions: Tch=175 Me. V a┴ =0. 085/fm • vary fireball evolution: e. g. a┴ = 0. 085/fm → 0. 1/fm • both large and small Tc compatible with excess dilepton slopes pions: Tch=160 Me. V a┴ =0. 1/fm

4. 3. 3 Acceptance-Corrected NA 60 Spectra [van Hees + RR ‘ 08] • rather involved at p. T>1. 5 Ge. V: Drell-Yan, primordial/freezeout r , …

4. 5 EM Probes in Central Pb-Au/Pb at SPS Di-Electrons [CERES/NA 45] Photons [WA 98] • consistent description with updated fireball (a. T=0. 045→ 0. 085/fm) [van Hees+RR ‘ 07] • very low-mass di-electrons ↔ (low-energy) photons [Liu+RR ‘ 06, Alam et al ‘ 01]

Model Comparison of r-SF in Hot/Dense Matter • Im V ~ Im. TVN r. N + Im. TVp rp ~ s. VN, Vp + dispersion relation for Re. TV [Eletsky, Belkacem, Ellis, Kapusta ’ 01] [RR+Wambach ’ 99] [Eletsky etal ’ 01] • first sight: reasonable agreement • second sight: differences! r. B vs. r. N • Implications for NA 60 interpretation? !

3. 3 The Role of Light Vector Mesons in HICs Contribution to invariant mass-spectrum: thermal emission t. FB ~ 10 fm/c after freezeout t. V ~ 1/GVtot Gee [ke. V] Gtot [Me. V] (Nee )thermal (Nee )cocktail ratio r (770) w(782) f(1020) 6. 7 150 (1. 3 fm/c) 1 0. 13 7. 7 0. 6 8. 6 (23 fm/c) 0. 09 0. 21 0. 43 1. 3 4. 4 (44 fm/c) 0. 07 0. 31 0. 23 In-medium radiation dominated by r -meson! Connection to chiral symmetry restoration? !

2. 4. 2 Evaluation of Chiral Sum Rules in Vacuum • pion decay constants • chiral quark condensates • vector-axialvector splitting (one of the) cleanest observable of spontaneous chiral symmetry breaking • promising (best? ) starting point to search for chiral restoration