Propagation of Spectral Functions and Dilepton Production
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Transcript of Propagation of Spectral Functions and Dilepton Production
B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 1
B. Kampfer I Institute of Radiation Physics I www.hzdr.de
Propagation of Spectral Functions and Dilepton Production (Imprints of Chiral Restoration on Dielectron Spectra)
B. Kämpfer
Helmholtz-Zentrum Dresden-Rossendorf Technische Universität Dresden
Changes of hadron properties in mediumcarry signals of the way in whichthe vacuum changes in a nuclear environment W. Weise, NPA 574 (1994) 347c
- the hydro picture: local equilibrium- kinetic approach: BRoBUU- rho meson: VOC- AdS/QCD: emissivities and spectral fncts- theory: making particles, e.g. e+ e-
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The Hydro Picture
- ignore pre-equilibrium- sum contributions over space + time till f.o.*)- add free decays after f.o. (hadronic cocktail)
*) only local equilibrium emissivities are needed
Wightman fnct
ret. Green fnct
schematic hydro: T(t), n(t)
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Old DreamGMOR ora la BR or Joffe
fireball evolutionfor SIS18
Eur.Phys.J. A17 (2003) 83-87 caveat:riding on a steep bckgdisappearence of the signal
f.o.
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Kinetic Approaches: Transport Models
- evolve distribution functions in space + time- species are coupled via coll. terms + decays (problems: detailed balance, cross sections)- mean field(s) included - propagate spectral functions
many realizations are at our disposal (Frankfurt, Giessen, Tubingen, ...)
here: BRoBUU = derivate of Giessen evolved by Barz, Wolf, Zetenyi, Schade „much room for improvements“
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BUU Transport Codepropagation of broad resonances
Kadanoff-Baym Cassing-Juchem, Leupold (2000)test particles
ansatz
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The Open Nuclear & Particle Physics Journal 3 (2010) 1,arXiv 0910.1541, nucl-th/0605036, Barz et al.
Spectral Functions: extreme mass shifts
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Mass Evolution toward Freeze Out red: time instant of disappearence
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tiny in-medium effects (even with extreme paramerters)
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Prediction: Au + Au
postdictions: C+C (1.04 AGeV - DLS, 1 AGeV – HADES)
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QCD Sum Rules: Predictions of Medium Modifications?
(i) as solution of integral eq. (Fredholm 1): too scarce information on OBE side
(ii) MEM:
(iii) moments: mean (= center of gravity) – OK variance (= width) skewness (= deformation) kurtosis (= up/down shot)
too large gapin powers of M
(iv) insert hadronic model
(v) pole + continuum ansatz
truncate: i < 6 (8, 12)
Titov, BK, PRC (2007)
Kwon, Weise, PRC (2010):another hierarchy+chiral gap
Gubler, Morita, Oka, PRL (2011)
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QCD sum rules: hadron spectral moments QCD condensates (n,T), Landau
Kwon, Procura, Weise PRC (2008):
num. irrelevant
Hatsuda, Lee PRC (1992):
center of gravity
maximum flatness in Borel window
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chiraltransformations
VOC: keep even conds., but set odd conds. to zero
Bordes, Dominguez, Pennarrocha, Schilcher JHEP (2006):
reconstruct from QCD sum rule
Hilger, Thomas, BK, Leupold PLB (2012)
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rho Meson and a Schematic VOC Scenario(vanishing of chirally odd condenstates: VOCOC = V(OC) VOC)
chiral restoration: <q q> 0 (large density/temperature)
vac
VOC
2
spec
tral
mom
ent
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vacuum: parameterize the spectral function
consistent QCD sum rule result
data: ALEPH (2005),
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VOC
vackeep width
keeppeak
improvement of Leupold, Peters, Mosel NPA (1998)
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VOC: minimum scenario of chiral restoration broadening as signal of chiral restoration
disclaimer: at chiral restoration more can happen
VOC
much less influence of VOC
NA60
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Chiral Partners
chiraltransf.
with open charm
Hilger, BK, Leupold PRC (2011)chiral QCD sum rules
splitting of spectral densities between chiral partnersmust be driven by order parameters of spontaneouschiral symmetry breaking only
Wigner‘s nondegeneracy
Hohler, Rapp, Nucl.Phys. A892 (2012) 58
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the case of V-A
in contrast to Weinberg‘s sum rules: no Goldstone propertieson r.h.s. (qQ currents are not conserved)
heavy quark symmetry: degeneracy of V – P, A - S
vacuum: Hayashigaki, Terasaki 0411285Reinders, Rubinstein, Yazaki PR (1985)
r.h.s.: „order parameters“ of chiral symm. breaking
Hilger, Buchheim, BK, Leupold PPNP(2012):
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AdS/QCD
5D Riemann: x,z 4D Minkowski: x
semi-class. gravity strongly coupled gauge theo.
X(x, z) gauge-inv. Operators (x)
asymp. AdS black brane: T (Hawking) s (Bekenstein)
semi-class. functional correlation functions breaking conf. sym. by mass scale, e.g. dilation + potential
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Example 1: only dilaton medium
bottom-up approach: EoS (lattice QCD) dilaton potential
ansatz: Gubser type pot. + polynom. distortions
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lattice QCD, SU(3) gauge theory, Borsanyi et al., 1204.6184
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benefit: w/o further input spectral functions transport coefficients
not universal (as, e.g. sheary viscosity/entropy)but sensitive dependence on pot. parameters
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AdS/QCD, soft-wall model, Cui. Takeuchi, Wu, 1112.5923(T in GeV)
JHEP 1204 (2012) 144
Example 2: meson in vector channel
Abelian field strength of Vsoft-wall model:
mass shift
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AdS/QCD, soft-wall model, Colangelo, Giannuzzi, Nicotri, 1201.1564, JHEP 1205 (2012) 076
Schwarzschild BH Reissner-Nordstrom BH: chem. pot.
vision: beyond soft-wall ansatz dilaton consistent with EoSproblem: missing unique QCD results with quarks
mass shift + broadening
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e+ e- Production: Theory
coupling to an external field/environment particle production- gravitation: cosmic expansion (Basler, BK 1990)- homog. E(t) field: dyn. Schwinger effect- E = const field: Schwinger effect- m(t) due to chiral restoration (Greiner et al. 1995, 1996, 2012)
mimicks E(t), looks like dyn. Schwinger effect,non-Markovian process
problem: what are particles, quasi-particles, out-states?
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q qbar production by chiral mass shift m(t)
Michler et al., arXiv:1208.6565
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Blaschke, BK, Schmidt, Panferov, Prozorkevich,
Smolyansky. arXiv:1301.1640 E(t) = E0 sin (νt) exp (−t^2/tG^2 )
tG = 10
Dynamical Schwinger Effect
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Summary
Medium changes of condensates (should) drive medium modifications of hadrons
difficult to identify rho, omega mass shifts (if there are any)in AA via inv. e+e- mass spectra (BRoBUU)
QCD sum rules: no direct link to shape of hadron spect. fncts. Landau term vs. density effects in condensates omega: significant density dependence of 4q conds. needed to balance Landau damping term Thomas, Hilger, BK PRL 2005
chiral sum rules most favorable
dream:AdS/CFT correspondence AdS/QCD: EoS, transport coeff. + hadrons
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BUU
Width of Strangeoniump
proposed by Hernandez, Oset, ZPA (1992)
PLB (2011)
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in Valencia – Paryev models:
analog in omega and phi photo-production
CLAS, PRL (2011)
CLAS PRL (2010)
CBELSA-TAPSPRL (2008)
prediction of broadening:Klingl, Wass, Weise, PLB (1998)
Spr
ing-
8: Is
hika
wa
et a
l., P
LB (
2005
)
V e+e-
Oset, Cabrera,...
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ANKE data:Phys.Rev. C85 (2012) 035206
BRoBUU: H. Schade
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ANKE PRC (2012)
BUU: H. Schade
mystery: phi phase space
stopping power of nuclear matter
p Acms(pN)
y
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Hot/Dense Medium in AdS/CFT1998:Maldacena,Gubser, Klebanov, PolyakovWitten
class. gravity in 5D
asymptotically AdS + black brane thermo field theory: hQCD
5D gravity setting: Riemann-Hilbert + scalar field
graviton dilaton
decoupled in strong-coupling limit
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condensate = vacuum + density dep. part
q density
sigma term
QCD trace anomaly
GORlattice
charmoniumscalar
twist-2 DIS pdf
DIS pdf
DIS pdf
GLS SR
fac. hyp.
twist-3 pdf
fac. hyp.
>Narison
if real condensate:couples to gravity
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OBE sides: medium effects
significant medium effects
Kapusta, Shuryak PRD (1994)
elaboration of hadronic sides for light-light mesons
vac
med.
vac
med.
Hohler, Rapp, Nucl.Phys. A892 (2012) 58
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AdS/CFT Emissivities
Baier,Stricker, Taanila, Vuorinen, Phys.Rev. D86 (2012) 081901, JHEP 1207 (2012) 094
at T > 200 MeV, one obtains the thermalization time scale ~ 0.1 fm/c, which one might compare with the typical production time of dileptons with mass/energy larger than 5 GeV, tau_p < 0.04 fm/c. It appears that dilepton pairs produced early on have a reasonable chance to escape the system while it is still out of thermal equilibrium.
problem of particle production in dynamical systems