Transcript Folie 1

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 medium
carry signals of the way in which
the 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+ epage 1
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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)
Wightman fnct
ret. Green fnct
*) only local equilibrium emissivities are needed
schematic hydro: T(t), n(t)
page 2
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Old Dream
fireball
evolution
for SIS18
page 3
GMOR or
a la BR or Joffe
Eur.Phys.J. A17 (2003) 83-87
f.o.
caveat:
riding on a
steep bckg
disappearence
of the signal
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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“
page 4
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BUU Transport Code
propagation of broad resonances
test particles
Kadanoff-Baym  Cassing-Juchem, Leupold (2000)
ansatz
page 5
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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
page 6
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Mass Evolution toward Freeze Out
red: time instant of disappearence
page 7
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page 8
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tiny in-medium effects (even with extreme paramerters)
page 9
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page 10
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Prediction: Au + Au
postdictions: C+C (1.04 AGeV - DLS, 1 AGeV – HADES)
page 11
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QCD Sum Rules: Predictions of Medium Modifications?
truncate: i < 6 (8, 12)
(i)
as solution of integral eq. (Fredholm 1):
too scarce information on OBE side
(ii) MEM: Gubler, Morita, Oka, PRL (2011)
Titov, BK, PRC (2007)
(iii) moments: mean (= center of gravity) – OK
variance (= width)
too large gap
skewness (= deformation)
in powers of M
kurtosis (= up/down shot)
(iv) insert hadronic model
Kwon, Weise, PRC (2010):
another hierarchy+chiral gap
(v) pole + continuum ansatz
page 12
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QCD sum rules:
hadron spectral moments  QCD condensates (n,T), Landau
center of gravity
maximum flatness in Borel window
Kwon, Procura, Weise PRC (2008):
num. irrelevant
Hatsuda, Lee PRC (1992):
page 13
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chiral
transformations
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)
page 14
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rho Meson and a Schematic VOC Scenario
(vanishing of chirally odd condenstates: VOCOC = V(OC)  VOC)
2
chiral restoration: <q q>  0 (large density/temperature)
spectral moment
vac
page 15
VOC
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vacuum: parameterize the spectral function
data: ALEPH (2005),
 consistent QCD sum rule result
page 16
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VOC
vac
keep
width
keep
peak
improvement of Leupold, Peters, Mosel NPA (1998)
page 17
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NA60
VOC
VOC: minimum scenario of chiral restoration
 broadening as signal of chiral restoration
disclaimer: at chiral restoration more can happen
much less influence of VOC
page 18
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Chiral Partners
Hohler, Rapp, Nucl.Phys. A892 (2012) 58
chiral
transf.
with open charm
chiral QCD sum rules
Hilger, BK, Leupold PRC (2011)
Wigner‘s nondegeneracy
splitting of spectral densities between chiral partners
must be driven by order parameters of spontaneous
chiral symmetry breaking only
page 19
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the case of V-A
r.h.s.: „order parameters“ of chiral symm. breaking
vacuum:
Hayashigaki, Terasaki 0411285
Reinders, Rubinstein, Yazaki PR (1985)
in contrast to Weinberg‘s sum rules: no Goldstone properties
on r.h.s. (qQ currents are not conserved)
heavy quark symmetry: degeneracy of V – P, A - S
Hilger, Buchheim, BK, Leupold PPNP(2012):
page 20
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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
page 21
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Example 1: only dilaton  medium
bottom-up approach: EoS (lattice QCD)  dilaton potential
ansatz: Gubser type pot.
+ polynom. distortions
page 22
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lattice QCD, SU(3) gauge theory, Borsanyi et al., 1204.6184
page 23
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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
page 24
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Example 2: meson in vector channel
Abelian field strength of V
soft-wall model:
AdS/QCD, soft-wall model,
Cui. Takeuchi, Wu, 1112.5923
(T in GeV)
mass shift
JHEP 1204 (2012) 144
page 25
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Schwarzschild BH  Reissner-Nordstrom BH: chem. pot.
AdS/QCD, soft-wall model, Colangelo, Giannuzzi, Nicotri, 1201.1564, JHEP 1205 (2012) 076
mass shift + broadening
vision: beyond soft-wall ansatz  dilaton consistent with EoS
problem: missing unique QCD results with quarks
page 26
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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?
page 27
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q qbar production by chiral mass shift m(t)
Michler et al., arXiv:1208.6565
page 28
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Dynamical Schwinger Effect
tG = 10
Blaschke, BK, Schmidt, Panferov, Prozorkevich,
E(t) = E0 sin (νt) exp (−t^2/tG^2 )
page 29
.
Smolyansky
arXiv:1301.1640
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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
page 30
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Width of Strangeonium
p
proposed by Hernandez, Oset, ZPA (1992)
BUU
PLB (2011)
page 31
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in Valencia – Paryev models:
Oset, Cabrera,...
prediction of broadening:
Klingl, Wass, Weise, PLB (1998)
analog in omega and phi photo-production
e+
e-
CLAS, PRL (2011)
CBELSA-TAPS
PRL (2008)
CLAS PRL (2010)
page 32
Spring-8: Ishikawa et al., PLB (2005)
V
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ANKE data:
Phys.Rev. C85 (2012) 035206
BRoBUU: H. Schade
page 33
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ANKE PRC (2012)
BUU: H. Schade
mystery: phi phase space
p
cms(pN)
A
y
stopping power of nuclear matter
page 34
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Hot/Dense Medium in AdS/CFT
1998:
Maldacena,
Gubser, Klebanov, Polyakov
Witten
class. gravity in 5D
decoupled in strong-coupling limit
asymptotically AdS + black brane  thermo field theory:
hQCD
5D gravity setting: Riemann-Hilbert + scalar field
graviton
page 35
dilaton
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condensate = vacuum + density dep. part
GOR
lattice
scalar
>
Narison
fac. hyp.
charmonium
sigma term
QCD trace
anomaly
fac. hyp.
q density
twist-2
DIS pdf
DIS pdf
twist-3 pdf
DIS pdf
GLS SR
if real condensate:
couples to gravity
page 36
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OBE sides: medium effects
vac
med.
 significant medium effects
vac
elaboration of hadronic sides
for light-light mesons
med.
Kapusta, Shuryak PRD (1994)
Hohler, Rapp, Nucl.Phys. A892 (2012) 58
page 37
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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
page 38
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