1. Dielectron Spectral Functions and Chiral Symmetry
(where masses are coming from?)
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

2. LHC at CERN: searching Higgs, SUSY, the unknown, QGP
P. Higgs 1964

3. SM Higgs: Mass Matters (Die Masse macht‘s)
M [GeV]
vacuum parameters:
the new ether?

4. QCD  Dyson Schwinger eqs.  quark propagator
B. Muller
Mass [MeV]
constituent quark mass [GeV]
strong
interaction s
SSB à la Higgs
chiral
limit
u, d
M. Viebach
nuclei = protons + neutrons = u‘s + d‘s
electrons (from Higgs): 0.025% of atomic mass

5. QCD ground state (vacuum)
Hadrons = Excitations of QCD Ground State
QCD ground state (vacuum)
n,T

6. QCD Vacuum < 6%: Colangelo et al. PRL 2001 SSB of chiral symmetry
QCD trace anomaly:
breaking of dilatation symmetry
Brodsky, Shrock, PRC (2010): condensates are included in hadron masses
Condensates are not condensates being constant in space and time

7. Dilute Gas Approx.

8. condensate = vacuum + density dep. part
GOR
lattice
sigma term
>
QCD trace
anomaly
scalar
charmonium
Narison
fac. hyp.
fac. hyp.
q density
twist-2
DIS pdf
DIS pdf
twist-3 pdf
DIS pdf
GLS SR

9. 4-q cond. = order parameter of chiral symmetry?
list of 4-q conds.: Thomas, Hilger, BK, NPA 795 (2007) 19

11. shifts & splittings of atomic spectral lines
Zeeman & Stark Effects
Vacuum
Mag. Field
shifts & splittings of atomic spectral lines
Hadrons in Nuclear Matter:
shifts of hadron energies („mass shifts“)?
new structures (ph exct) in spectral fncts?
courtesy PANDA
pA:
Scheinast et al.
(KaoS), PRL 2006
pA: CBM
p_bar A: PANDA
understanding
hadronic part
of QCD

12. Dropping Masses? Volkov 1935 Phys. Lett. 19 (1966) 702 not yet found
not found

13. from Durham data base

14. Nucleus as QCD Laboratory
Bonn
Mainz
Jülich
Darmst.
Hadrons as Excitations of/above Vacuum
 Probes of Changed QCD Vacuum?

15. 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)
skewness (= deformation)
kurtosis (= up/down shot)
too large gap
in powers of M
(iv) insert hadronic model
Kwon, Weise, PRC (2010):
another hierarchy+chiral gap
(v) pole + continuum ansatz

16. hadron spectral moments  QCD condensates (n,T), Landau
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):

17. VOC: keep even conds., but set odd conds. to zero
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)

18. rho Meson and a schematic VOC scenario2
(vanishing of chirally odd condenstates: VOCOC = V(OC)  VOC)
chiral restoration: <q q>  0 (large density/temperature)
vac
spectral moment
VOC

19. vacuum: parameterize the spectral function
data: ALEPH (2005),
 consistent QCD sum rule result

20. VOC vac keep width keep peak
improvement of Leupold, Peters, Mosel NPA (1998)

21. 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

22. Chiral Partners with open charm chiral transf. 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

23. r.h.s.: „order parameters“ of chiral symm. breaking
the case of V-A
FAIR
r.h.s.: „order parameters“ of chiral symm. breaking
Hayashigaki, Terasaki
Reinders, Rubinstein, Yazaki PR (1985)
vacuum:
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):

24. Weinberg Sum Rules ALEPH data
vacuum: Hohler, Rapp, Nucl.Phys. A892 (2012) 58
ALEPH data

25. Chiral Mixing at Low Temperatures
Dey, Eletsky, Ioffe, PLB 252 (1990) 620
toward chiral restoration
Holt, Hohler, Rapp, PRD 87 (2013)
Holt, Hohler, Rapp, PRD 87 (2013)

26. Holography: mesons in vector channel
Abelian field strength of V
soft-wall model:
mass shift
AdS/QCD, soft-wall model,
Cui. Takeuchi, Wu,
(T in GeV)
JHEP 1204 (2012) 144

27. prediction from 2009: Au + Au
The Open Nuclear & Particle Physics Journal 3 (2010) 1,
arXiv , nucl-th/ , Barz et al.

28. BUU Transport Code propagation of broad resonances test particles
(Kadanoff-Baym  Cassing-Juchem, Leupold)
ansatz

29. The Open Nuclear & Particle Physics Journal 3 (2010) 1,
arXiv , nucl-th/ , Barz et al.
Spectral Functions: extreme mass shifts

30. Mass Evolution toward Freeze Out
red: time instant of disappearence A

31. Old Dream fireball evolution for SIS18 caveat: riding on a steep bckg
GMOR
a la BR or Joffe
Old Dream
fireball
evolution
for SIS18
Eur.Phys.J. A17 (2003) 83-87
caveat:
riding on a
steep bckg
disappearence
of the signal
f.o.

32. 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
Weinberg type sum rules: chiral restoration means degeneracy of
vector and axialvector spectral functions

33. HADES data: Agakishev et al. PRL `07 BUU: Barz et al. `06/optim. NA50
C(2AGeV) + C
T = 108 MeV
NA50
Gallmeister
et al. `01
T =
170 MeV

34. Width of Strangeonium p BUU PLB (2011)
proposed by Hernandez, Oset, ZPA (1992)
BUU
PLB (2011)

35. in Valencia – Paryev models:
Oset, Cabrera,...
prediction of broadening:
Klingl, Wass, Weise, PLB (1998) V e+ e-
analog in omega and phi photo-production
CLAS, PRL (2011)
CBELSA-TAPS
PRL (2008)
Spring-8: Ishikawa et al., PLB (2005)
CLAS PRL (2010)

36. ANKE data:
Phys.Rev. C85 (2012)
BRoBUU: H. Schade

37. 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?

38. q qbar production by chiral mass shift m(t)
Michler et al., arXiv:

39. Dynamical Schwinger Effect
tG = 10
Blaschke, BK, Schmidt, Panferov, Prozorkevich,
Smolyansky. arXiv:
E(t) = E0 sin (νt) exp (−t^2/tG^2 )

40.  problem of particle production in dynamical systems
AdS/CFT Emissivities
Baier,Stricker, Taanila, Vuorinen, Phys.Rev. D86 (2012) , 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

41. mystery: phi phase space
ANKE PRC (2012)
BUU: H. Schade
mystery: phi phase space p
cms(pN) A y
stopping power of nuclear matter

42. QCD Condensates and the Vacuum
presence of hadrons changes (expells a part of) the vacuum
QDC Sum Rules
hadron spectral function

43. aside: rho-omega interference
QCD sum rule

44. Hadrons = Quarks + Gluons
gauge invariance
from Higgs (electroweak)
explicit chiral symmetry breaking
Goldstone hadrons:
Gell-Mann
Oakes
Renner
(1968)
spontaneous breaking of approx. chiral symmetry
Colangelo
Gasser
Leutwyler
(2001)
real hadrons:

45. 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

46. Example 1: only dilaton  medium
bottom-up approach: EoS (lattice QCD)  dilaton potential
ansatz: Gubser type pot.
+ polynom. distortions

47. lattice QCD, SU(3) gauge theory, Borsanyi et al., 1204.6184

48. benefit: w/o further input  spectral functions
 transport coefficients
not universal
(as, e.g. sheary viscosity/entropy)
but sensitive dependence
on pot. parameters

49. OBE sides: medium effects
vac
med.
 significant medium effects
vac
elaboration of hadronic sides
for light-light mesons
med.
Kapusta, Shuryak PRD (1994)

50. Schwarzschild BH  Reissner-Nordstrom BH: chem. pot.
AdS/QCD, soft-wall model, Colangelo, Giannuzzi, Nicotri, , JHEP 1205 (2012) 076
mass shift + broadening
vision: beyond soft-wall ansatz  dilaton consistent with EoS
problem: missing unique QCD results with quarks