Photon emission within a quark meson model F . Wunderlich and B. - - PowerPoint PPT Presentation

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Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de

Photon emission within a quark meson model

F . Wunderlich and B. Kämpfer

FAIRNESS 2014

Member of the Helmholtz Association Page 2 Falk Wunderlich | institute for radiation physics | division for hadron physics | www.hzdr.de

Introduction

QCD = theory of strong interactions (success of quark model, cross sections, hadron masses from lattice,...) Open questions: nature and properties of sQGP, mass generation, chiral + deconfjnement phase transition, ... large scale experiments running

• r under construction

(RHIC, LHC, FAIR, NICA,...)

• ne particular question:

existence, position and properties of a CP

[CBM Physics book] [textbook of YNDURAIN] [DURR et al. Science 322 (2008)] 2 phases CP supercrit. fjgure from: [Wikipedia.org]

Member of the Helmholtz Association Page 3 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]

Member of the Helmholtz Association Page 4 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]

Member of the Helmholtz Association Page 5 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]

Member of the Helmholtz Association Page 6 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]

Member of the Helmholtz Association Page 7 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

• ne way: electromagnetic probes

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Remark on photons from HIC

[RAPP,WAMBACH 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

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The qm-model

Lqm γ=Lqm+Lem+Lγ Lqm=ψ(i γ

μ∂μ−g(σ+i γ 5⃗

τ⃗ π))ψ +1 2 (∂ν σ

ν) 2+1

2 (∂ρ ⃗ π

ρ) 2+λ

4 (σ

2+ ⃗

π

2−v 2) 2−H σ

Lem=−eqf ψ γ

μ Aμ ψ+1

2 eπ

+π − Aν A ν+1

2 e π Aν π

+π −( p+ ν−p− ν )

Lγ=1 4 F

ρκ Fρ κ

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

[SCHAEFER, WAMBACH Nucl.Phys. A757 (2005)] [SCAVENIUS et al. Phys.Rev. C64 (2001)]

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Photon emission - general remarks

photon rate essentially given by the imaginary part of the retarded photon self energy

ω d

3R

dk

3 ∼Im ΠR ν ν (k ν;T ,μ)nB( p νuν;T ,μ)

[T extbook of KAPUSTA and GALE]

two important restrictions:

• size:
• (local) thermal equilibrium

HIC: OK (success of hydro)

λm.f.p.

γ

≫rfireball≫λm.f.p

strong

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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

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Mean field analysis

qualitative correct results with simple approx In this context:

• setting meson fjelds to their expectation values.

Expectation value minimizes free energy Curvatures of free energy at minimum → masses

• exactly solving the remaining fermionic path integral
• including photons: like QED

[SCAVENIUS et al. Phys.Rev. C64 (2001)]

Ω(T ,μ)≡̃ Ω(〈σ〉,〈π〉,T ,μ) mϕ=∂

2~

Ω(ϕ,T ,μ) ∂ϕ

2

∣ϕ=⟨ϕ⟩

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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

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Linearized fluctuations

Self consistent method to introduce (small) fmuctuations detailed description:

• integrate out quarks
• quadratic approximation for the remaining

efgective mesonic potential

• solve self consistency relations for meson masses

[BOWMAN,KAPUSTA: Phys.Rev. C79 (2009)],[BOWMAN, diss.] [MOCSY et al. Phys.Rev. C70 (2004)]

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Thermodynamics - MFA

exploratory study: as simple as possible → MFA

mσ/MeV mπ/MeV mq/ MeV

model parameters fjxing: mσ

vac=700 MeV

mπ

vac=135 MeV

mq

vac=312 MeV

f π= 93 MeV

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Thermodynamics - MFA

exploratory study: as simple as possible → MFA

mσ/MeV mπ/MeV mq/ MeV

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Thermodynamics – linearized fluctuations

mσ/MeV mπ/MeV mq/ MeV

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Character of the PT

• lin. fmuc.

MFA

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Influence of meson fluctuations

• lin. fmuc.

MFA

χ

(2)/χ0 (2)

χ

(2)/χ0 (2)

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The retarded photon self energy

leading order After Matsubara summation: This looks exactly like kinetic theory! So: forget photon propagator! Just specify all photon producing processes and calculate momentum integrals.

+ … + +

Π ∼

+

Im

+ … ~ 1 (2π)

3∫ d 3 p

2E p nF(E p)nF(ω−Ep)× + …

2

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Interpretation

Im Π=C×∑|M (i→f +γ)|

2

annihilation: Compton scattering: application of optical theorem

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Photon emission MFA:

ω = 50 MeV ω = 1250 MeV

• nly quarks emitt photons

QED-like rates leading order: no Compton-contrib. (photons are not in equilib.)

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Quarks and pions emit photons Compton processes possible LO with π:

Photon emission, lin. fluct:

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Photon emission lin. fluct:

q+¯ q→γ+π q+π→ γ+q

ω = 1250 MeV ω = 50 MeV ω = 10 MeV ω = 1250 MeV

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Photon emission, lin. fluct:

LO with σ:

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Photon emission lin. fluct:

ω = 10 MeV ω = 1250 MeV

q+̄ q→γ+σ q+σ→ γ+q

ω = 1250 MeV ω = 50 MeV

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Photon rates

µ=270MeV µ=360MeV µ=0MeV

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Photon rates

µ=0 MeV µ=270 MeV µ=360 MeV

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Summary and outlook

calculated thermodynamics and photon emissivity to 1st

• rder within the QMM (linear sigma model with quarks)

MFA + beyond MFA more fmuctuations / FRG folding with hydro evolution

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Thank you for your attention!

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Fluctuation measures