Medium Modifications of Hadrons and Electromagnetic Probe
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1 Medium Modifications of Hadrons and Texas A&M University March 17, 26
2 Outline QCD and Chiral Symmetry
3 QCD and ( accidental ) Symmetries Theory for strong interactions: QCD L QCD = 1 4 F a µν Fµν a + ψ(i /D ˆM)ψ Particle content: ψ: Quarks, including flavor- and color degrees of freedom, ˆM = diag(m u, m d, m s,...) = current quark masses A a µ: gluons, gauge bosons of SU(3) color
4 QCD and ( accidental ) Symmetries Theory for strong interactions: QCD L QCD = 1 4 F a µν Fµν a + ψ(i /D ˆM)ψ Particle content: ψ: Quarks, including flavor- and color degrees of freedom, ˆM = diag(m u, m d, m s,...) = current quark masses A a µ: gluons, gauge bosons of SU(3) color Symmetries fundamental building block: local SU(3) color symmetry in light-quark sector: approximate chiral symmetry chiral symmetry most important connection between QCD and effective hadronic models
5 Phenomenology from Chiral Symmetry In vacuum: Spontaneous breaking of chiral symmetry mass splitting of chiral partners qq-excitations of the QCD vacuum Energy (MeV) f1 (142) a1(126) f1(1285) φ(12) f(4-12) ρ (77) ω (782) P-S, V-A splitting in the physical vacuum π (14) Im Π V,A /(πs) [dim. less] V [τ > 2nπ ν τ ] A [τ > (2n+1)π ν τ ] ρ(77) + cont. a 1 (126) + cont s [GeV 2 ]
6 Phenomenology from Chiral Symmetry In vacuum: Spontaneous breaking of chiral symmetry mass splitting of chiral partners qq-excitations of the QCD vacuum Energy (MeV) f1 (142) a1(126) f1(1285) φ(12) f(4-12) ρ (77) ω (782) P-S, V-A splitting in the physical vacuum π (14) Im Π V,A /(πs) [dim. less] V [τ > 2nπ ν τ ] A [τ > (2n+1)π ν τ ] ρ(77) + cont. a 1 (126) + cont s [GeV 2 ] at high temperature/density: restoration of chiral symmetry Lattice QCD: Tc χ Tc deconf
7 Finite Temperature/Density: Idealized Theory Picture partition sum: Z(V, T, µ q, Φ) = Tr{exp[ (H[Φ] µ q N)/T ]}
8 Finite Temperature/Density: Idealized Theory Picture partition sum: Z(V, T, µ q, Φ) = Tr{exp[ (H[Φ] µ q N)/T ]} Real Time Z[V, T,µ,Φ] Imag. Time Dynamical quantities Thermodyn. potentials bulk properties T,µ analytic continuation vacuum
9 Why? γ, l ± : no strong interactions reflect whole history of collision chance to see chiral symm. rest. directly? π,... ρ/ω γ e e + a 1
10 Why? γ, l ± : no strong interactions reflect whole history of collision π, η Dalitz decays ρ/ω Φ chance to see chiral symm. rest. directly? dn/(dy dm) DD J/ Ψ π,... ρ/ω γ e ψ Drell Yan e + Low Intermediate High Mass Region > 1 fm > 1 fm <.1 fm a M [GeV/c] by A. Drees Fig
11 Vector Mesons and electromagnetic Probes photon and dilepton thermal emission rates given by same electromagnetic-current-correlation function (J µ = f Q f ψ f γ µ ψ f )
12 Vector Mesons and electromagnetic Probes q photon and dilepton thermal emission rates given by same electromagnetic-current-correlation function (J µ = f Q f ψ f γ µ ψ f ) Π < µν(q) = d 4 x exp(iq x) J µ ()J ν (x) T = 2f B (q ) Im Π (ret) µν (q) dn γ d 4 xd 3 q = α em 2π 2 gµν Im Π µν (ret) (q) f B(q ) q = q dn e + e d 4 xd 4 k = α 2 gµν 3q 2 Im Π(ret) π3 µν (q) f B (q ) q 2 =M 2 e + e to lowest order in α: e 2 Π µν Σ (γ) µν derivable from partition sum Z(V, T, µ, Φ)!
13 Vector Mesons and chiral symmetry vector and axial-vector mesons correlators of the respective currents Π µν V /A (p) := d 4 x exp(ipx) JV ν /A ()J µv /A (x) ret
14 Vector Mesons and chiral symmetry vector and axial-vector mesons correlators of the respective currents Π µν V /A (p) := d 4 x exp(ipx) JV ν /A ()J µv /A (x) ret Ward-Takahashi Identities from chiral symmetry Weinberg-sum rules f 2 π = π 2 α s O χsb = dp 2 πp 2 [Im Π V (p, ) Im Π A (p, )] dp 2 π [Im Π V (p, ) Im Π A (p, )] spectral functions of vector (e.g. ρ) and axial vector (e.g. a 1 ) directly related to order parameters of chiral symmetry!
15 Vector Mesons and chiral symmetry Im Π V,A /(πs) [dim. less] V [τ > 2nπ ν τ ] A [τ > (2n+1)π ν τ ] ρ(77) + cont. a 1 (126) + cont s [GeV 2 ]
16 Vector Mesons and chiral symmetry Im Π V,A /(πs) [dim. less] V [τ > 2nπ ν τ ] A [τ > (2n+1)π ν τ ] ρ(77) + cont. a 1 (126) + cont s [GeV 2 ] Spectral Function Spectral Function "ρ" Dropping Masses? "a 1 " pert. QCD Mass Melting Resonances? "ρ" pert. QCD "a 1 " Mass
17 Models different models with chiral symmetry: equivalent only on shell ( low-energy theorems )
18 Models different models with chiral symmetry: equivalent only on shell ( low-energy theorems ) model-independent conclusions only in low-temperature/density limit (chiral perturbation theory) or from lattice-qcd calculations
19 Models different models with chiral symmetry: equivalent only on shell ( low-energy theorems ) model-independent conclusions only in low-temperature/density limit (chiral perturbation theory) or from lattice-qcd calculations use phenomenological hadronic many-body theory (HMBT) to assess medium modifications of vector mesons
20 Models Phenomenological HMBT [Chanfray et al, Herrmann et al, Rapp et al,...] for vector mesons ππ interactions and baryonic excitations ρ π B *, a 1, K 1,... ρ ρ ρ π N, K, π,...
21 Models Phenomenological HMBT [Chanfray et al, Herrmann et al, Rapp et al,...] for vector mesons ππ interactions and baryonic excitations ρ π B *, a 1, K 1,... ρ ρ ρ π N, K, π,... Baryon (resonances) important, even at RHIC with low net baryon density n B n B reason: n B +n B relevant (CP inv. of strong interactions)
22 The meson sector (vacuum) most important for ρ-meson: pions ρ π ρ F π (q 2 ) q 2 [GeV 2 ] δ 1 1 [deg.] M ππ [GeV]
23 The meson sector (matter) Pions dressed with N-hole-, -hole bubbles Ward-Takahashi vertex corrections mandatory!
24 The meson sector (contributions from higher resonances) 7 Im Σ ρ /m ρ [MeV] T=15MeV q=.3gev ω sum a 1 1 K 1 h 1 π f 1 3 sum Re Σ ρ /m ρ [MeV] ω K 1 a M [GeV]
25 The baryon sector (vacuum) ρ B *, a 1, K 1,... ρ N, K, π,... P = 1-baryons: p-wave coupling to ρ: N(939), (1232), N(172), (195) P = 1-baryons: s-wave coupling to ρ: N(152), (162), (17)
26 Photoabsorption on nucleons and nuclei 6 4 N ( b) σ µ q (MeV)
27 Photoabsorption on nucleons and nuclei 6 6 full bkgd 1/3 bkgd N ( b) σ µ 4 2 σ γa /A (µb) q (MeV) q (MeV)
28 Dilepton rates: Hadron gas QGP dr ee /dm 2 [fm 4 GeV 2 ] free HG in med HG free QGP in med QGP T=15MeV T=18MeV in-medium hadron gas matches with QGP similar results also for γ rates quark-hadron duality? does it work with chiral model? hidden local symm.+baryons? [Harada, Yamawaki et al.] M ee [GeV]
29 Dilepton rates at SpS (d 2 N ee /dηdm) / (dn ch /dη) [1MeV] % Central Pb(158AGeV)+Au <N ch >=25 p t >.2GeV 2.1<η<2.65 Θ ee >35mrad Cocktail QGP CERES free ππ in-med. ππ + QGP drop ρ-mass + QGP M ee [GeV] Spectral Function Spectral Function "ρ" Dropping Masses? "a 1 " pert. QCD Mass Melting Resonances? "ρ" pert. QCD "a 1 " Mass
30 New NA6 Dimuon Data intermediate mass range: Mixing of Π V with Π A (Dey, Eletsky, Ioffe 9) Π (T ) V = (1 ɛ)π V + ɛπ A, ɛ = 1 T π (T, µ π ) 2 T π (T c, ) dn µµ /dm [a.u.] central In-In all p T with ω + φ total 4π mix RW QGP DD NA M [GeV] (hep-ph/6384) Fireball model time evolution absolute normalization! good overall agreement with data sensitive to ω and φ! ω: similar model as for ρ φ: less well known; width assumed 8 MeV
31 New NA6 Dimuon Data dn µµ /dm [a.u.] 2π contributions+ρb interactions from Rapp+Wambach 99 intermediate mass range: Mixing of Π V with Π A Π (T ) V = (1 ɛ)π V + ɛπ A, ɛ = 1 T π (T, µ π ) 2 T π (T c, ) central In-In p T <.5 GeV with ω + φ total 4π mix RW QGP DD NA M [GeV] same absolute normalization! Corona effect for high p T? dn µµ /dm [a.u.] central In-In p T >1. GeV with ω + φ total 4π mix RW QGP DD NA M [GeV]
32 New NA6 Dimuon Data Chiral reduction formalism (Steele, Yamagishi, Zahed 96) based on chiral symmetry and Veltman-Bell master equations virial expansion medium modifications from vacuum correlators (restricted to low π/b densities) Im Π V,A /(πs) [dim. less] V [τ > 2nπ ν τ ] A [τ > (2n+1)π ν τ ] ρ(77) + cont. a 1 (126) + cont s [GeV 2 ] σ [µb] Fit pn average fit includes (123), N * (152), N * (172) M [GeV]
33 New NA6 Dimuon Data dn µµ /dm [a.u.] central In-In all p T total SYZ virial QGP DD NA M [GeV] underestimates medium effects on the ρ (due to low-density approximation? No broadening!) intermediate masses: mixing less pronounced indication of chiral restoration?
34 New NA6 Dimuon Data dn µµ /dm [a.u.] central In-In p T <.5 GeV total SYZ virial QGP DD NA M [GeV] dn µµ /dm [a.u.] central In-In p T >1. GeV total SYZ virial QGP DD NA M [GeV] underestimates medium effects on the ρ (due to low-density approximation? No broadening!) intermediate masses: Less effect of mixing indication of chiral restoration?
35 New NA6 Dimuon Data (semicentral) dn µµ /dm [a.u.] semicentral In-In all p T with ω and φ total 4π mix RW QGP DD NA6 dn µµ /dm [a.u.] semicentral In-In p T <.5 GeV with ω and φ total 4π mix RW QGP DD NA M [GeV] dn µµ /dm [a.u.] semicentral In-In p T >1. GeV with ω and φ total 4π mix RW QGP DD NA M [GeV] M [GeV]
36 Challenges for Experiment Direct signature for chiral restoration: spectra for ρ and a 1 mesons degenerate π ± γ invariant mass spectrum a 1 spectral function X a 1.64 ρ.7 ω only π γ! a 2.3 π(13)??? Γ X πγ[mev]
37 Challenges for Experiment Direct signature for chiral restoration: spectra for ρ and a 1 mesons degenerate π ± γ invariant mass spectrum a 1 spectral function X a 1.64 ρ.7 ω only π γ! a 2.3 π(13)??? Γ X πγ[mev] counts / [ 12 MeV/c 2 ] 4 2 M peak = 722 MeV/c 2 Nb - LH 2 data ω-spectral function from CBELSA/TAPS M π γ [MeV/c 2 ]
38 Challenges for Experiment Photon rate q dn γ /d 3 q [GeV 2 ] Central Pb Pb s 1/2 =17.3AGeV new Hadron Gas QGP (T =25MeV) pqcd ( k t 2=.2) Sum WA98 Data 2.35<y< q t [GeV] ππ ρ ππγ not enough to explain enhancement New development (Liu/Rapp work in progress): πk K πkγ Consistency with dileptons
39 Challenges for Theory Need a fully chiral model π π S σ N 1/2 + π S N(1535) 1/2 π P ρ S ρ a 1 π S π P 3/2+ π S ρ S N(152) D(17) 3/2 3/2 How to treat (axial-) vector mesons (gauge model?) Approximation scheme for both dynamical properties (spectral functions) and thermodynamic bulk properties (phase diagram)?
40 Conclusions chiral symmetry: important feature to connect QCD hadronic effective models important property of (s)qgp: How is chiral symmetry restored? electromagnetic probes may provide most direct insight invariant-mass spectra for chiral partners: here ρ and a 1 low-energy photons dileptons (puzzle?) a lot to do also for theory consistent chiral scheme for hadrons self-consistent treatment of (axial-) vector particles equation of state including in-medium modifications vs. statistical models with free hadron properties
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