Folie 1

Transcription

Folie 1

Lorenz von Smekal
Aktuelle Entwicklungen in der Theorie I:
Hans-Werner Hammer
Norbert Kaiser
Horst Lenske
Gabriel Martinez Pinedo
Ulf Meißner
Robert Roth
Achim Schwenk
Kerne und Sterne
– Die Entstehung der Elemente
Jens Braun
Michael Buballa
Christian Fischer
Michael Müller-Preussker
Jan Pawlowski
Owe Philipsen
Jürgen Schaffner-Bielich
Andreas Schäfer
Bernd-Jochen Schaefer
Christian Schmidt
Kernmaterie unter extremen Bedingungen
– Von der „Ursuppe“ zum Neutronenstern
Bad Honnef, Dez. 2013
Spektroskopie exotischer Kerne und Neue Anregungsmoden
• Selbst-‐konsistente HFB-‐QRPA und Mul7-‐Phonon Anregungen
H. Lenske
• Konfigura7onen mit bis zu sechs Quasiteilchen
• Neue Anregungsformen: E1/M1 Dipol-‐ und E2 Quadrupolschwingungen der Neutronenhaut • Astrophysikalische Bedeutung: Erhöhung der Zustandsdichte
Neue M1-‐Komponente in 90Zr: Kumula7ve Magne7sche Dipolstärke
Neue E1, E2 und M1 Moden vorhergesagt und experimentell bestä7gt
s-‐Prozess Nukleosynthese in AGB Sternen:
Erhöhung der Zustandsdichte durch Mul7-‐Phonon Effekte [Raut, et al. (Tsoneva), Phys. Rev. Lett. 111 (2013) 112501]
[Rusev, Tsoneva, et al. (Lenske), Phys. Rev. Lett. 110 (2013) 022503]
4 Sept. 2013 | Lorenz von Smekal | p. 2
Neutron-rich matter based on chiral EFT interactions
first complete N3LO calculation including NN, 3N, 4N interactions
A. Schwenk
applications to neutron stars and equation of state
first Quantum Monte Carlo calculations with local chiral EFT potentials
Hebeler et al. ApJ (2013)
20
this work
RG evolved
2.5
AFDMC LO
AFDMC NLO
AFDMC N2LO
ty
i
sal
15
cau
E/N [MeV]
2
R0=0.8 fm
3
Mass [M . ]
°
Gezerlis et al. PRL (2013)
1.5
R0=1.2 fm
Tews et al. PRL (2013)
10
1
5
0.5
0
8
10
12
14
16
Radius [km]
Chiral EFT and dark matter response of nuclei
spin-dependent elastic and inelastic WIMP scattering
focus on Xe isotopes, used by XENON100
[Menendez et al. PRD (2012), Klos et al. PRD (2013), Baudis et al. PRD in press]
0
0
0.05
0.1
-3
n [fm ]
0.15
the peak is not reported here, owing to ambiguity caused by detector
thresholds, the peak appears in the spectrum at an energy corresponding to the energy difference between the 1,656- and 1,184-keV transitions, which is 472(31) keV. Thus, it is probable that the 1,184- and
,472-keV transitions form a cascade that starts from the 3,699-keV
level and runs in parallel to the 1,656-keV c-ray, although the ordering
of the 1,184- and ,472-keV transitions in the decay sequence cannot
be specified here.
z
The excitation energies of 2z
1 states, E(21 ), are presented in Fig. 2b
Nature 498 (2013) 346
z
for Ca isotopes. Typically, peaks in E(21 ) systematics along isotopic
chains indicate the presence of large nuclear shell gaps, although the
correlation energy can also influence E(2z
1 ) in some instances. Indeed,
)
value
reflects the strength of the
in the case of 48Ca, the large E(2z
1
standard magic numbers Z 5 20 (proton number 20) and N 5 28 in
stable nuclei. For 52Ca, the onset of the N 5 32 subshell closure6,7,12 is
highlighted by the large increase in E(2z
1 ) relative to its even–even
(even-N and even-Z) neighbour 50Ca. The result of the present work
54
52
indicates that E(2z
1 ) for Ca is comparable to that for Ca, thus providing direct experimental evidence for the doubly magic nature of 54Ca.
Moreover, in Fig. 2c, E(2z
53,54
1 ) systematics for the N 5 30, 32 and 34
isotonic chains are presented for even–even nuclei from Ar (Z 5 18) to
Ge (Z 5 32). A comparison of the energies for Ca and Ni along each
isotonic chain is emphasized, because these two species are host to
magic proton cores with Z 5 20 and 28, respectively. For the N 5 30
58
isotones, we note that E(2z
Ni lies 0.4 MeV above its Ca
1 ) for
counterpart. In the case of 60Ni and 52Ca, however, which fall on the
5 32 line
in Fig. 2c, E(2z
1 ) becomes strongly enhanced for Ca
[Steppenbeck et al., Nature 502N(2013)
207]
present work. Discussions of the systematics of E(3{
1 ) along the Ca
isotopic chain and specific details of the nature of those excitations,
which are understood as nucleon cross-shell excitations, are provided
in refs 7, 26. Because the data point for 54Ca continues the general trend
of the experimental systematics well, a spin–parity assignment of 32
seems plausible for the 3,699-keV state. It is stressed, however, that these
spin–parity quantum numbers could not be confirmed from the experimental data and are therefore suggested only as tentative assignments.
Shell-model predictions of excited states for 54Ca are presented in
Schwenk
Fig. 2b. Here we report calculations performed in A.
the sd–fp–sdg
model
space (specifically, the 1d5/2, 1d3/2, 2s1/2, 1f7/2, 1f5/2, 2p3/2, 2p1/2, 1g9/2,
1g7/2, 2d5/2, 2d3/2 and 3s1/2 SPOs) using a modified GXPF1B shellmodel Hamiltonian14 with an adjustment to the strength (–0.15 MeV)
of the np3/2–nf5/2 monopole interaction between neutrons. Details on
other components of the effective interaction are provided in ref. 26.
The calculations indicate that the 2z
1 state is primarily a consequence
of a neutron particle–hole excitation across the N 5 34 subshell gap
52
and, despite E(2z
1 ) being lower than in Ca as a result of the correlation energy, the strength of the N 5 34 subshell gap (the np1/2–
nf5/2 SPO energy gap for 54Ca) is in fact similar to the one at N 5 32
(the np3/2–np1/2 SPO energy gap for 52Ca). More specifically, our
52
calculations suggest that although E(2z
Ca is very similar
1 ) for
to the np3/2–np1/2 SPO energy gap at N 5 32, the effect of the correlation energy reduces E(2z
1 ) by ,0.5 MeV relative to the np1/2–nf5/2
SPO energy gap for 54Ca. The difference is mainly attributed to
the larger ground-state correlation energy of 52Ca, which is understood from the relative strengths of the Æp3/2p3/2jVjp1/2p1/2æJ50 and
Frontier in Ca isotopes
Ca masses measured at ISOLTRAP
establish prominent N=32 shell closure
excellent agreement with NN+3N predictions
Energy (MeV)
a
b
4
c
5
4
2
1
32
E(2+1)
1
1
34
22
26
N
30
34
18
N
Figure 2 | Systematics of excited-state energies in even–even Ca isotopes
and neighbouring nuclei. a, Theoretical predictions of the energy of the first
21 state for 52Ca (N 5 32) and 54Ca (N 5 34) (refs 14–16, 19–24). The solid blue
line represents the experimental result for 52Ca (refs 6, 7). b, Energies of the first
21 (filled symbols) and 32 (open symbols) levels for even–even 42–54Ca
2+ energy from RIBF suggests
new magic number N=34
54Ca
2
3
Theory
Experiment
N = 30
N = 32
N = 34
52Ca
3
2
3
E(3–1)
22
26
30
34
Z
isotopes. The results of the present study are indicated by diamonds at N 5 34.
The solid and dashed lines are shell-model predictions of the first 21 and 32
energies, respectively (see text for details). c, E(2z
1 ) along the N 5 30, 32 and 34
[Holt,
Menendez,
J.Phys.
(2013)
isotonic
chains.
The solid andSchwenk,
dashed lines are
intended G40
to guide
the eye.075105]
Vertical dotted lines represent the standard magic numbers.
2 0 8 | N AT U R E | VO L 5 0 2 | 1 0 O C T O B E R 2 0 1 3
©2013 Macmillan Publishers Limited. All rights reserved
Ab Initio Nuclear Structure from QCD
-40
experiment
-60
E [MeV]
-80
-100
!
IT-NCSM
"
MR-IM-SRG
▼
▲
CCSD
Λ-CCSD(T)
-120
-140
-160
. -180
chiral NN+3N
14
16
•  ground8breaking(advances(in(ab(ini5o(
theory(from(light(to(heavy(nuclei(with(
chiral(NN+3N(interac5ons([PRC(88,(054319((2013);((
PRC(87,(021303(R)((2013);(PRC(87,(034307((2013);(PRL(109,052501((2012)]
(
•  example:(ab(ini5o(calcula5on(of(oxygen(
ground(states(highlights(predic5ve(power(
of(chiral(Hamiltonians(and(consistency(of(
many8body(approaches([PRL(110,(242501((2013)](
AO
12
R. Roth
•  nuclear(structure(theory(rooted(in(QCD(
via(chiral(effec5ve(field(theory(
18
20
22
24
26
A
•  low$energy*nuclear*reac.ons*for*
nuclear*astrophysics*at*the*same*level*
[PRC*88,*054622*(2013)]**
•  transfer*complete*ab*ini.o*toolbox*to*
hypernuclear*structure**
•  example:*first*ab*ini.o*calcula.ons*of*
1
p$shell*hypernuclei*[in*prep.]**
[NLO chiral YN: Haidenbauer, Petschauer, Kaiser, Meißner, Weise, Nucl. Phys. A915 (2013) 24]
Halo Physics in Ca Isotope Chain
Halo
HaloPhysics
PhysicsininCa
CaIsotope
IsotopeChain
ChainH.-W. Hammer
●
●
●
●
Emergence of effective halo
Emergence of effective halo
degrees of freedom in Ca
degrees of freedom in Ca
Ab
initio coupled cluster
●
Ab initio coupled cluster
calculations with chiral forces for
calculations
60Ca
61Ca with chiral forces for
and
60Ca and 61Ca
62Ca predicted to be 2-neutron
62Ca predicted to be 2-neutron
●
halo using halo EFT
halo using halo EFT
Matter
radius of order tens of fm
●
Matter radius of order tens of fm
possible → heaviest halo to date
possible → heaviest halo to date
Possibility
of excited Efimov
●
Matter
radii vs. S2n
●
Possibility
of excited Efimov
●
Matter radii vs.
S2n
62
state in Ca
if
S
>230
keV
2n
62
state in Ca if S2n>230 keV
Hagen,
Hagen,
Hammer,Hammer,
Platter, Phys.Platter,
Rev. Lett.Phys.
111 (2013)
132501
[Hagen,
Hagen,
Rev.
Lett. 111 (2013) 132501]
Hagen, Hagen, Hammer, Platter, Phys. Rev. Lett. 111 (2013) 132501
Nuclear Lattice Effective Field Theory
U. Meißner
NLEFT for medium-mass nuclei
• Kerne bis 28Si zu NNLO
• zu wenig Repulsion zwischen Alpha Clustern
Experiment
NNLO
NNLO + 4Neff
→ Überbindung, korrigiert durch effektive 4N
[Lähde, Epelbaum, Krebs, Meißner & Rupak, arXiv:1311.0477]
4
He
8
Be
12
C
16
O
20
Ne
24
Viability of carbon-based life
Mg
28
Si
-400
-350 -300
-250 -200 -150 -100
E (MeV)
-50
0
• End-of-the-world-plot: Variationen von
2-3% Quarkmassen, 2.5% Feinstrukturkonstante
→ hinreichende Synthese von 12C und 16O
[Epelbaum, Krebs, Lähde, Lee, Meißner, PRL 110 (2013) 112502; EPJA 49 (2013) 82]
Heavy Element Nucleosynthesis in Supernovae
G. Martinez-Pinedo
11.2 M⨀ Fe-core supernova
8.8 M⨀ electron-capture supernova
(Observational data normalized to calculated abundance at Z=40)
Nucleosynthesis outcome is sensitive to the neutron richness of the ejecta (Ye):
•  Related to nuclear symmetry energy [Martínez-Pinedo, Fischer, and Huther, Lohs, PRL 109, 251104 (2012)]
•  Influenced by Neutrino oscillations [Wu, Fischer, Huther, Martinez-Pinedo, and Qian, arXiv:1305.2382]
µ [MeV]
:
udy
Development of an RG approach
applications
for aRecent
study of the energy
density functional
ation]
of energy density functional methods
[S. Kemler, J. Braun, J. Phys. G (2013) within CRC 634]
@
[U , n] =
U ·n+
"
✓
1
1
n · V 2b · n + Tr V 2b ·
2
2
2
[U , n]
n n
◆
1
G. Martinez-Pinedo
#
Nucleus,
here: onlytwo-body (2b)
interaction
background
potential U
Nuclear matrix elements
of 0νββ decay
EDF allows the calculation of the masses
along the whole nuclear chart"
Ca
•  EDF benchmarked against new
data for calcium isotopes. "
•  EDF as an alternative/complement to
large scale shell model calculations for
neutron rich nuclei."
•  EDF is able to compute all possible
0vββ candidates including deformation
and pairing fluctuations.#
T. R. Rodríguez and G. Martínez Pinedo, PRL 105, 252503 (2010)
A. Arzhanov, T. R. Rodríguez, G. Martínez-Pinedo, in preparation.
K. Sieja, T. R. Rodríguez, K. Kolos, and D. Verney,
Phys. Rev. C 88, 034327 (2013)
T. R. Rodríguez and G. Martínez Pinedo, PLB 719, 174 (2013)
N. López-Vaquero et al., PRL 111, 142501 (2013)
J. Beller, et al., PRL. 111, 172501 (2013)
Strangeness fluctuations & quark number susceptibilities
C. Schmidt
2nd order quark number
susceptibility
strangeness fluctuations &
baryon-strangeness correlations
0.30
0.98
non-int. quarks
q SB
2/ 2
0.97
0.25
NLA
0.96
0.20
0.95
B
χB
2 -χ4
0.15
0.94
v1
0.10
3d pert.
0.93
v2
0.92
0.05
uncorr.
hadrons
0.00
140
180
220
0.91
T [MeV]
260
300
340
[Bazavov et al. (BNL-Bielefeld), PRL 111 (2013) 082301]
0.9
T [MeV]
300
400
500
600
700
800
900
1000
[Bazavov et al. (BNL-Bielefeld), arXiv:1309.2317]
QCD in a magnetic field
Lattice QCD: QCD in a magnetic field
A. Schäfer
1311.2559: QCD is paramagnetic. The inhomogeneous magnetic field in heavy ion collisions generates pressure gradients of comparable size as geometric ones at LHC energies.
The renormalized magnetization of the QCD vacuum for different
temperatures. Orange line: Prediction of the Hadron Resonance Gas model.
[Bali, Bruckmann, Endrödi, Schäfer, arXiv:1311.2559]
EoS with twisted-mass Wilson fermions
T >0
M. MüllerPreussker
Nf = 2 + 1 + 1
Nf = 2
O(a)
mπ ! 400
µ
∆l,s =
"Re(L)#R = "Re(L)# exp (V (r0 )/2T )
2.5
1
Nf = 2+1+1, a ∼ 0.086
Nf = 2+1+1, a ∼ 0.078
Nf = 2+1+1, a ∼ 0.061
Nf = 2, Nτ = 12
200
300
400
T [MeV]
500
600
5
0.6
0.4
0
0.2
-5
0
-10
-0.2
gauge part
10
#−3p
T4
∆l,s
"Re(L)#R
Nf = 2+1+1, a ∼ 0.086
Nf = 2+1+1, a ∼ 0.078
Nf = 2+1+1, a ∼ 0.061
0.8
1.5
= a dβ
da "Sg #sub
15
1
2
0
"−3p
T4
µ
"ψψ#Tl =0 − µsl "ψψ#Ts =0
1.2
mπ ∼ 400 MeV
0.5
"ψψ#l − µsl "ψψ#s
Nf = 2+1+1, a ∼ 0.086
Nf = 2+1+1, a ∼ 0.078
Nf = 2+1+1, a ∼ 0.061
Nf = 2, Nτ = 12
mπ ∼ 400 MeV
150
200
250
300 350
T [MeV]
400
450
200
300
400
T [MeV]
500
600
QCD Greens Functions
gluon propagator
On two-ab-initio
and three-point
functions
of Landau gauge Yang-Mills theory
DSE result
(quenched)
includes vertex DSEs
ZHp2 L
GHp2 L
4
T = 187 MeV Quenched
T = 187 MeV Lattice
T = 215 MeV Lattice
T = 235 MeV Lattice
T = 187 MeV DSE
T = 215 MeV DSE
T = 235 MeV DSE
6
‡
Ê
‡
2
3
5
‡Ê
‡Ê
4
‡‡
Ê‡
‡ ‡Ê
Ê
‡‡
Ê‡Ê‡
Ê
‡ ‡Ê‡‡‡
Ê Ê‡‡
Ê ‡‡
Ê ‡‡‡
3
ÊÊÊ
‡‡Ê‡‡
Ê‡‡‡
Ê Ê‡Ê‡Ê
‡‡Ê‡
‡
0Ê
‡
0
L
Ê‡ ‡Ê
‡
‡
Ê
‡Ê
‡
Ê‡
Ê
Ê
‡
‡
3
1
unquenched, Markus
finite TQ. Huber
4
Z
•
2
‡
‡
‡
1
‡
Ê
2
1
2
3
4
5
p@GeVD
1
0.0
0
0.5 0
‡
1.0
Ê
‡
1.5
1
‡
2.0
Ê
2.5
‡
2
Ê
‡
3.0
p@GeVD
p [GeV]
Figure[Huber,
1: TheLvS,
gluon
and ghost dressing functions Z(p2 ) and G(p2 )[Luecker,
in comparison
with lattice data [7].
JHEP 1304 (2013) 149;
Fischer, PLB 718 (2013) 1036;
The red/continuous
lines
vertexetand
arXiv:1311.0702
] represent the results with a dynamic ghost-gluon
Aouane
al., the
PRDoptimized
87 (2013)effective
114502]
three-gluon vertex, the green/dashed lines a reference calculation with a bare ghost-gluon vertex and the
three-gluon vertex of ref. [40].
AH0;p2 ,p2 L
1.4
AHp ;p
,pSmekal
L
4 Sept. 2013 | Lorenz
von
| p. 13
2
1.4
2
2
3
QCD thermodynamics
•
J. Pawlowski
unquenched glue dynamics for models
[Haas, Stiele, Braun, Pawlowski, Schaffner-Bielich, PRD 87 (2013) 076004;
Fister, Pawlowski, PRD 88 (2013) 045010]
2+1 flavor PQM-model
3
P/T
4
2.5
8
Wuppertal-Budapest, 2010
PQM FRG
PQM eMF
PQM MF
Wuppertal-Budapest, 2010
HotQCD Nt=8, 2012
HotQCD Nt=12, 2012
PQM FRG
PQM eMF
PQM MF
7
6
( - 3P)/T4
3.5
2
1.5
1
5
4
3
2
0.5
Pressure
0
-0.6 -0.4 -0.2
0
0.2
0.4
0.6
Interaction
measure
1
0
-0.6
-0.4
-0.2
0
0.2
0.4
t restoration and deconfinement in QC2 D with two flavors of tstaggered quarks
Chiral
0.6
David Scheffler
[Herbst, Mitter, Pawlowski, Schaefer, Stiele, arXiv:1308.3621]






Polyakov-loop potentials from lattice simulations
[Langfeld, Pawlowski, PRD 88 (2013) 071502]
[Smith, Dumitru, Pisarski, LvS, PRD 88 (2013) 054020;
Scheffler, Schmidt, Smith, LvS, arXiv:1311.4324]



•














of the SU(2) Polyakov loop at b = 2.577856 (left) and b = 2.635365 (right)
4 Sept. Figure
20131:|Distribution
Lorenz von
Smekal | p. 14

2+1 flavor QCD phase diagram from DSEs
C. Fischer
zero chemical potential
1
• µ=0: Quark-Condensate reproduced
• Polyakov-loop potential at finite µ
• 2+1 flavor phase diagram
Lattice QCD
Quark Condensate
dressed Polyakov Loop
[Luecker, Fischer, Fister, Pawlowski, arXiv:1308.4509;
Fischer, Fister, Luecker, Pawlowski, arXiv:1306.022]
Δl,s(T)/Δl,s(0)
0.8
0.6
0.4
0.2
200
0
100
C.S. Fischer, J. Luecker / Physics Letters B 718 (2013) 1036–1043
150
T [MeV]
200
250
1041
T [MeV]
150
100
Chiral crossover
Chiral first order
From Polyakov-loop potential
From dressed Polyakov loop
Critical end-point
50
0
0
50
100
µ [MeV]
150
200
Fig. 8. The light (lower surface) and strange (upper surface) quark condensate as a
function of temperature and chemical potential.
Table 1
flavors as|well
as the
Location of CEP and the curvature for N f = 2 and4N Sept.
f = 2 + 12013
Lorenz
N f = 2 flavor result in the HTL approximation of Ref. [23].
Nf
CEP
T c (µ = 0)
κ
[Luecker, Fischer, PLB 718 (2013) 1036]
Fig. 9. The phase diagram for two plus one flavors. The light colors (top lines) show
the N f = 2 results as a comparison.
2 +Smekal
1 case as |compared
von
p. 15 to N f = 2. This effect may be explained by
the different strength of the back-reaction of the quarks onto the
gluon sector. For N f = 2 + 1 the back-reaction is stronger, result-
Solid-state phases of QCD from DSEs
M. Buballa
color superconductivity
•
120
T [MeV]
80
CP
40
20
Chiral density wave
hom. spinodals
hom. 1st order
hom. 2nd order
150
100
60
chiral density waves
200
140
T [MeV]
•
100
50
1st order
region
2SC
CFL
0
0 100 200 300 400 500 600 700 800 900
0
0
100
200
300
400
500
µ [MeV]
µ [MeV]
[Müller, Buballa, Wambach, EPJA 48 (2013) 96]
[Müller, Buballa, Wambach, PLB 727 (2013) 240]
Group “Strongly
Interacting
Fermions”
FRG: Quark-Meson-Model
(Jens Braun, TU Darmstadt)
mics of 2+1 flavor QCD: quark-meson model
RG-improved
Polyakov-loop
• with axial
anomaly potential
R. Stiele, J. Braun, J. M. Pawlowski, J. Schaffner-Bielich, Phys. Rev. D (2013),
(2+1 flavor) collaboration]
Darmstadt-Frankfurt-Heidelberg
7
tYM ( tglue )
6
UPloop = UYM
4
3
HotQCD
HISQ Nτ = 12 & 8
Bazavov et al.,
arXiv:1210.6312
[R. A. Tripolt, J. Braun, B. Klein, B.-J. Schaefer, arXiv:1308.0164,
Darmstadt-Munich-Giessen collaboration]
T [MeV]
5
B.-J. Schaefer
Shift of the CEP in a finite volume:
RG
study
of thevolume
quark-meson-model
• CEP
in finite
Wuppertal-Budapest
Borsanyi et al.,
JHEP 11, 2010
2
1
0
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
reduced temperature t
µ [MeV]
- and spin-imbalanced
1d Fermi gases:
[Mitter, Schaefer, arXiv:1308.3176;
Mitter, Schaefer,phase
Strodthoff,
LvS, instudy
prep.]
l finite-temperature
diagram
Development
an Schaefer,
RG approach
[Tripolt, Braun,of
Klein,
arXiv:1308.0164]
for a study of the energy density functional
Braun, J. Drut, arXiv:1311.0179, Darmstadt-North Carolina collaboration]
[S. Kemler, J. Braun, J. Phys. G (2013) within CRC 634]
@
FFLO
(inhomogeneous/
BCS
(homogeneous)
[U , n] =
"
✓
1
1
U · n + n · V 2b · n + Tr V 2b ·
2
2
2
[U , n]
n n
◆
1
#
Finite isospin chemical potential
J. Schaffner-Bielich
•
PQM without pion condensation
•
ase Transition at Nonzero µiso
QM with pion condensation
and fluctuations
1
➔
Tc / Tc0
PQM
Nf = 2+1
mπ = 138 MeV
0.9
PQM, Nf = 2
mπ = 400 MeV
Lattice, Nf = 2
mπ = 400 MeV
0.8
χPT + Fuzzy Bag
Nf = 2, mπ = 115 MeV
χPT + Fuzzy Bag
Nf = 2, mπ = 544 MeV
0.7
0
0.5
1
1.5
2
µI / mπ
e data[for
Nf Fraga,
= 2 atSchaffner-Bielich,
mπ ≈ 400 MeVarXiv:1307.2851;
Stiele,
Cea,D’Elia,
Cosmai Papa,
et al., PRD
85 (2012)2012)
094512]
, Cosmai,
Sanfilippo
[Kamikado, Strodthoff, LvS, PLB 718 (2013) 1044;
Detmold, Orginos, Shi, PRD 86 (2012) 054507]
of PQM model at nonzero isospin chemical potential: shows
trend, but phase transition line drops too strongly!
ng terms? missing physics? related to problem of magnetic
ysis? (Stiele, Fraga, Schaffner-Bielich, arXiv:1307.2851)
scaled trace anomaly
Finite isospin density
• QM model
Wuppertal-Budapest
Borsanyi et al.,
JHEP 11, 2010
3
polarised fermi gases
universal mean field PD
250
Bazavov et al.,
arXiv:1210.6312
4
2
1
0
-0.4
Sarma crossover
2nd order
1st order
-0.3
-0.2
-0.1
0
0.1
0.2
J.0.3Braun
0.4
reduced temperature t
200
T [MeV]
Sa
µI = m⇡
200
150
100
normal
a
superfluid
Mass-• and spin-imbalanced 1d Fermi gases:
1d Fermi gases
First full finite-temperature phase diagram study
Mass- and spin-imbalanced
[D. Roscher, J. Braun, J. Drut, arXiv:1311.0179, Darmstadt-North Carolina collaboration]
50
Sarma crossover
1st order
0
0
502nd order
100
180
150
µq [MeV]
160
140
250
300
normal
µq =
120
200
FFLO
(inhomogeneous/
“crystalline”)
100
rm
80
mass
imbalance
a
pion condensation
60
40
20
0
BCS
(homogeneous)
Sa
T [MeV]
rm
spin imbalance
CEP
0
50
100
150
200
250
µq [MeV]
300
350
400
[Roscher, Braun, Drut, arXiv:1311.0179]
[Kamikado, Strodthoff, LvS, PLB 718 (2013) 1044]
nB
∆( 32 + )
d(1+ )
0.08
d(0− )
0.06
m effective lattice QCD
Finite baryon density
0.04
d(0+ )
N ( 21 − )
0.02
Philipsen etlattice
al., PRL theory
110 (2013)
cally 3D effective
•
0.00
lattice simulations of G2-QCD
•
for heavy quarks (QCD)
0.00
Onset to nuclear matter, pion mass ~ 20 GeV
14
12
0.003
Towards nuclear
matter from effective lattice QCD
T = 20 MeV
nq
0.70
0.80
no fermion-sign problem
1
G2 baryon spectroscopy
Σ
0.5
2
0.003
Sign problem mild, handled algorithmically
0.0025
0.001
0.0005
Extension to lighter quarks: higher orders
0.996
0.998
µB / mB
Light quarks (eff. action not yet convergent):
0.0
0.2
0.4
0.6
0.8
1.0
1.2
aµ
0.10
1.4
1.6
1.8
2.0
0
∆( 32 − )
∆( 32 + )
0.0015
0.08
d(1− )
0.001
nB
0.0005
1
0
1.002
0.994
0.996
0.998
µB / mB
d1stpoint
st order
order 1
nuclear
liquid
gas transition
with
endtransition
point
nuclear
liquid
gas
with end point
crossover, high T
0.12
0
0.002
nB / mB3
Allows study of heavy cold and dense matter
T = 20 MeV
T = 10 MeV
T = 5 MeV
T = 2.5 MeV
1
1.002
n q a3
nB / mB3
0.60
!P "
8
4
0.0015
first order, very low T
µ
0.50
1.5
FIG. 14: Quark
number density heavy ensemble
erValid for very heavy quarks
0.994
0.40
6
Philipsen et al., PRL 110 (2013)
3d effective lattice theory, calculated analytically
by strong coupling
0.002 + hopping expansions
0
0.30
quark matter
10
T = 10 MeV
T = 5 MeV
T = 2.5 MeV
0.20
2
nuclear matter onset, pion mass ~ 20 GeV
0.0025
0.10
N ( 21 + )
+
0.06
d(1 )
d(0− )
0.04
N ( 21 − )
d(0+ )
0.02
crossover, high T
N ( 12 + )
0.00
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
µ
µa
15: Quark number
light
ensemble
[Maas, LvS, FIG.
Wellegehausen
& Wipf,density
PRD 86
(2012)
111901(R);
Wellegehausen, LvS, Maas, Wipf, arXiv:1310.7745 ]
[Fromm et al. (Philipsen), PRL 110 (2013) 122001]
Spectral functions
Yang Mills theory
J. Pawlowski
FRG plus MEM
viscosity over entropy ratio
transv. gluon spectral function
1.2
MEM result
T=1.44 Tc
hês
•
1.0
MEM fit
0.8
Meyer H2007ê2009LHSU3L
Nakamura H2005LHSU2L
KSS bound
0.6
0.4
0.2
0.0
0
1
2
3
TêT_c
T=0
PRL 109, 252001 (2012)
week ending
[Haas, Fister, Pawlowski,
arXiv:1308.4960]
21 DECEMBER 2012
PHYSICAL REVIEW LETTERS
We stress again, however, that mg is not a measurable
quantity; strictly speaking, it is just the scale where positivity violations in the gluon set in.
In this Letter we presented the first nonperturbative
20
solution of the gluon and ghost propagators in the complex
momentum plane together with an extraction of their
respective spectral functions. Our results agree with expec10
tations based on the corresponding Schwinger functions
discussed in Refs. [8,9]. We presented solutions for the
decoupling case; a comprehensive comparison with scaling
0
will beStrauss,
given elsewhere.
Besides the Kellermann,
considerable theoreti-PRL
Fischer,
cal interest in these functions, they are also a necessary
input into the calculations of glueball masses within the
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
|p| [GeV]
framework of Bethe-Salpeter equations. Corresponding
results will be detailed in a subsequent work.
FIG. 5 (color online). Results for the gluon spectral function
We thank Reinhard Alkofer, Jan Pawlowski, and Lorenz
and the ghost spectral function as a function of momentum.
von Smekal for fruitful discussions. This work has been
4 Sept. 2013
| Lorenz
von Smekal
| p. 21Grant
supported
by the Helmholtz
Young Investigator
grid of momentum points which are displayed explicitly,
No. VH-NG-332 and the Helmholtz International Center
whereas the interpolation is done via Chebychev polynofor FAIR within the LOEWE program of the State of Hesse.
30
ghost: ρG
gluon: ρg
analytically continued DSEs
[
109 (2012) 252001]
4
Slide for Lorenz
•
Spectral functions
analytically continued FRG
QM model
@L-2
UVD
@L-2
UVD
T=10 MeV
@L-2
UVD
T=150 MeV
rp
rp
100
2
1
5
6
2
6
3
1
4
1
1 5
4
6
0.01
3
0.01
rs
-4
0.01
w @MeVD 10
rs
-4
100
200
300
@L-2
UVD
400
500
600
700
rp
0
100
200
@L-2
UVD
m=292 MeV
rs
300
400
500
600
700
rs
1
2
4
6
1:
100
⇤ !
200
300
, 2:
400
500
⇤ ! ⇡⇡ , 3:
600
700
⇤ ! ¯
w @MeVD 10-4
0
, 4: ⇡ ⇤ !
400
m=292.97 MeV
1
rp
100
200
300
⇡ , 5: ⇡ ⇤ ⇡ !
1
6
4
0.01
10-4
0
300
3
1
1
0.01
200
100
3
1
100
rs
100
2
w @MeVD 10-4
0
@L-2
UVD
m=292.8 MeV
rp
100
rs
100
rp
3
0
T=200 MeV
5
100
10
finite T and µ
0.01
400
500
600
700
w @MeVD 10-4
0
50
100 150 200 250
, 6: ⇡ ⇤ ! ¯
[R.-A. Tripolt, N. Strodthoff, L. von Smekal and J. Wambach, arXiv:1311.0630 [hep-ph]]
[Kamikado, Strodthoff, LvS, Wambach, arXiv:1302.6199; Tripolt, Strodthoff, LvS, Wambach, arXiv:1311.0630]
November 15th, 2013 | TU Darmstadt | Jochen Wambach | Real Time Spectral Functions from the FRG | 1

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