Photon emission within a quark meson model F . Wunderlich and B. Kämpfer FAIRNESS 2014 Seite 1 Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Introduction QCD = theory of strong interactions [textbook of Y NDURAIN ] (success of quark model, cross sections, [D URR et al. Science 322 (2008)] hadron masses from lattice,...) Open questions: [CBM Physics book] nature and properties of sQGP, mass generation, chiral + deconfjnement phase transition, ... supercrit. 2 phases CP large scale experiments running or under construction (RHIC, LHC, FAIR, NICA,...) one particular question: existence, position and properties of a CP fjgure from: [Wikipedia.org] Page 2 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Introduction Screenshots from: [http://www.msm.cam.ac.uk/doitpoms/tlplib/solid-solutions/videos/laser1.mov] Page 3 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Introduction Screenshots from: [http://www.msm.cam.ac.uk/doitpoms/tlplib/solid-solutions/videos/laser1.mov] Page 4 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Introduction Screenshots from: [http://www.msm.cam.ac.uk/doitpoms/tlplib/solid-solutions/videos/laser1.mov] Page 5 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Introduction Screenshots from: [http://www.msm.cam.ac.uk/doitpoms/tlplib/solid-solutions/videos/laser1.mov] Page 6 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Introduction HIC create region of hot and dense QCD matter → explosion → detection most particles: pions created at the edge of the fjreball want: information from the hot interior one way: electromagnetic probes Page 7 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Remark on photons from HIC [R APP ,W AMBACH Adv.Nucl.Phys. 25 (2000)] many sources of photons: ● hard photons from parton collisions ● thermal photons from the hydro stage ● decay of hadrons this work: focus on medium (equilibrium) properties, i.e. emissivity Page 8 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
The qm-model Our question: “Are there em signatures charakteristic for a CP?” Due to universality: replace in a 1st step QCD by efgective model with appropriate symmetries: qm-model [S CHAEFER , W AMBACH Nucl.Phys. A757 (2005)] [S CAVENIUS et al. Phys.Rev. C64 (2001)] L qm γ = L qm + L em + L γ μ ∂ μ − g (σ+ i γ 5 ⃗ L qm =ψ( i γ τ⃗ π))ψ + 1 2 + 1 2 +λ 2 + ⃗ 2 (∂ ρ ⃗ ν ) ρ ) 2 − v 2 ) 2 − H σ 2 (∂ ν σ π 4 (σ π μ A μ ψ+ 1 ν + 1 ν ) − A ν A + π + π − ( p + ν − p − L em =− eq f ψ γ 2 e π 2 e π A ν π L γ = 1 ρκ F ρ κ 4 F Page 9 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Photon emission - general remarks photon rate essentially given by the imaginary part of the retarded photon self energy [T extbook of K APUSTA and G ALE ] 3 R ω d ν ( k ν ;T , μ) n B ( p ν u ν ;T , μ) 3 ∼ Im Π R ν dk two important restrictions: γ strong λ m.f.p. ≫ r fireball ≫λ m.f.p - size: - (local) thermal equilibrium HIC: OK (success of hydro) Page 10 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Separation of scales strong interaction: much shorter timescale, much higher energy scale (compared to em) → separation of scales → em interaction “sees“ only particles dressed by strong interaction em interaction is small correction to thermodynamic properties → for thermodynamic properties: ignore em contribution → for photon emission: insert quasiparticle properties (e.g. masses) into formulas Page 11 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Mean field analysis [S CAVENIUS et al. Phys.Rev. C64 (2001)] qualitative correct results with simple approx In this context: - setting meson fjelds to their expectation values. Expectation value minimizes free energy Ω( T , μ)≡ ̃ Ω(〈σ〉 , 〈π〉 ,T , μ) Curvatures of free energy at minimum → masses 2 ~ m ϕ =∂ Ω(ϕ ,T , μ) ∣ ϕ=⟨ϕ⟩ 2 ∂ϕ - exactly solving the remaining fermionic path integral - including photons: like QED Page 12 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Mean field analysis - drawbacks no dynamic mesons → missing contribution to pressure → only photon-quasiquark-coupling, no pion-photon-vertex missing pressure in MFA µ =0 MeV Page 13 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Linearized fluctuations Self consistent method to introduce (small) fmuctuations detailed description: [B OWMAN ,K APUSTA : Phys.Rev. C79 (2009)],[B OWMAN , diss.] [M OCSY et al. Phys.Rev. C70 (2004)] - integrate out quarks - quadratic approximation for the remaining efgective mesonic potential - solve self consistency relations for meson masses Page 14 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
vac = 700 MeV model parameters fjxing: m σ vac = 135 MeV m π Thermodynamics - MFA vac = 312 MeV m q f π = 93 MeV exploratory study: as simple as possible → MFA m q / MeV m σ / MeV m π / MeV Page 15 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Thermodynamics - MFA exploratory study: as simple as possible → MFA m q / MeV m σ / MeV m π / MeV Page 16 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Thermodynamics – linearized fluctuations m q / MeV m σ / MeV m π / MeV Page 17 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Character of the PT MFA lin. fmuc. Page 18 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Influence of meson fluctuations MFA lin. fmuc. ( 2 ) /χ 0 ( 2 ) ( 2 ) /χ 0 ( 2 ) χ χ Page 19 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
The retarded photon self energy leading order + + … + + Π ∼ After Matsubara summation: 2 3 p + … ~ 1 3 ∫ d n F ( E p ) n F (ω− E p )× + … Im 2 E p ( 2 π) This looks exactly like kinetic theory! So: forget photon propagator! Just specify all photon producing processes and calculate momentum integrals. Page 20 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Interpretation annihilation: Compton scattering: application of optical theorem Im Π= C × ∑ | M ( i → f +γ)| 2 Page 21 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Photon emission MFA: only quarks emitt photons ω = 50 MeV QED-like rates leading order: ω = 1250 MeV no Compton-contrib. (photons are not in equilib.) Page 22 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Photon emission, lin. fluct: Quarks and pions emit photons Compton processes possible LO with π : Page 23 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Photon emission lin. fluct: q +¯ q →γ+π q +π→ γ+ q ω = 10 MeV ω = 50 MeV ω = 1250 MeV ω = 1250 MeV Page 24 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Photon emission, lin. fluct: LO with σ : Page 25 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Photon emission lin. fluct: q +̄ q →γ+σ q +σ→ γ+ q ω = 10 MeV ω = 50 MeV ω = 1250 MeV ω = 1250 MeV Page 26 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Photon rates µ =270MeV µ =0MeV µ =360MeV Page 27 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
Photon rates µ=27 0 MeV µ= 0 MeV µ=36 0 MeV Page 28 Member of the Helmholtz Association Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de
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