Introduction
Chiral properties
Spectral properties
Summary
Traces of a fixed point
unravelling the phase diagram at large Nf
A. Deuzeman
Centre for Theoretical Physics
University of Groningen, The Netherlands
Universe in a Box, August 26th, 2009
A. Deuzeman
Traces of a fixed point
Introduction
Chiral properties
Spectral properties
Summary
Outline
1
Introduction
Framework
Context
2
Chiral properties
3
Spectral properties
Where to look?
The beta function
A. Deuzeman
Traces of a fixed point
Introduction
Chiral properties
Spectral properties
Summary
Framework
Context
Extending QCD
Our focus is extended QCD.
SU(3) gauge interaction
fundamental fermions
Thermodynamical observations as probes.
A. Deuzeman
Traces of a fixed point
Introduction
Chiral properties
Spectral properties
Summary
Framework
Context
A rich landscape of transitions
Quark gluon plasma
Hadronic phase
Conformal window
Hadronic phase
Coulomb phase
Strongly coupled phase
A. Deuzeman
Traces of a fixed point
Introduction
Chiral properties
Spectral properties
Summary
Framework
Context
Results at Nf = 8
Transition at NT = 6
A. Deuzeman
Traces of a fixed point
Introduction
Chiral properties
Spectral properties
Summary
Framework
Context
Results at Nf = 8
Transition at NT = 12
A. Deuzeman
Traces of a fixed point
Introduction
Chiral properties
Spectral properties
Summary
Framework
Context
Results at Nf = 8
Perturbative scaling
A. Deuzeman
Traces of a fixed point
Introduction
Chiral properties
Spectral properties
Summary
Framework
Context
Technical details
Current study:
Staggered flavours, using RHMC
O(a) improved action
No tadpole improvement
Range of fermion masses
A. Deuzeman
Traces of a fixed point
Introduction
Chiral properties
Spectral properties
Summary
No thermal scaling at Ns =16 . . .
A. Deuzeman
Traces of a fixed point
Introduction
Chiral properties
Spectral properties
Summary
. . . or elsewhere
●
●
0.8
●
●
●
0.7
●
factor(T)
●
●
●
0.6
●
pbp
0.5
6
●
8
●
16
●
24
●
32
●
48
●
●
●
0.4
●
factor(L)
●
0.3
●
32
● ●
● ●
● ●
● ●
● ● ●
●
● ●
● ●
● ●
● ●
● ●
● ●
● ●
●●●
● ●
● ●
● ●
● ●●●
● ●
● ● ●
● ●
●
0.2
0.1
2.5
3.0
16
24
●
●
3.5
4.0
●
●
●
● ●
4.5
beta
A. Deuzeman
Traces of a fixed point
●
5.0
Introduction
Chiral properties
Spectral properties
Summary
Cross over shows up in plaquette
0.7
●
●
●
●
●
●
●
●
●
●
●
0.6
●
0.5
TrU 3
●
●
●●
●●
●●
●●
●●
●●
●
●●
●
●
●
●
●●
●●
●●
●●
●●
●
●
●
●
0.4
0.3
●
0.2
0.1
0.0
0.0
0.1
0.2
0.3
β−1
A. Deuzeman
Traces of a fixed point
0.4
Introduction
Chiral properties
Spectral properties
Summary
Chiral symmetry restoration?
A. Deuzeman
Traces of a fixed point
Introduction
Chiral properties
Spectral properties
Summary
What does this show?
Consistent with a non-thermal transition between a chirally
symmetric and broken phase.
Compatible with Nf = 12 being in the conformal window.
Hard to show true chiral symmetry restoration!
Maybe we’re just close to the conformal window?
A. Deuzeman
Traces of a fixed point
Introduction
Chiral properties
Spectral properties
Summary
Where to look?
The beta function
Phases from bare coupling
c
Nf
Nf*
-
+
S
A
g*
S
gc
A
A. Deuzeman
Traces of a fixed point
Introduction
Chiral properties
Spectral properties
Summary
Where to look?
The beta function
Clean correlators at β=3.6
A. Deuzeman
Traces of a fixed point
Introduction
Chiral properties
Spectral properties
Summary
Where to look?
The beta function
Noisy correlators at β=5.0
A. Deuzeman
Traces of a fixed point
Introduction
Chiral properties
Spectral properties
Summary
Where to look?
The beta function
Sticking to the strong side
Good looking effective mass just after transtition
Strong increase of FV effects in region after β = 4.0.
Not unexpected inside the conformal window
Focus on what should be the Coulomb region
A. Deuzeman
Traces of a fixed point
Introduction
Chiral properties
Spectral properties
Summary
Where to look?
The beta function
Pion mass interpolation
A. Deuzeman
Traces of a fixed point
Introduction
Chiral properties
Spectral properties
Summary
Where to look?
The beta function
Rho mass interpolation
A. Deuzeman
Traces of a fixed point
Introduction
Chiral properties
Spectral properties
Summary
Where to look?
The beta function
Pseudoscalar over vector mass
●
●
●
●
●
0.85
●
●
●
●
●
●
●
0.80
●
factor(mass)
R
●
●
0.75
●
0.70
●
3.5
3.6
β
A. Deuzeman
3.7
3.8
Traces of a fixed point
3.9
●
0.04
●
0.05
●
0.06
●
0.07
Introduction
Chiral properties
Spectral properties
Summary
Where to look?
The beta function
Lines of constant physics
0.866(12)
0.856(10)
0.822(09)
0.872(15)
0.858(12)
0.838(10)
0.792(07)
0.861(21)
0.859(16)
0.842(13)
0.820(11)
0.861(27)
0.845(21)
0.826(14)
A. Deuzeman
Traces of a fixed point
Introduction
Chiral properties
Spectral properties
Summary
Where to look?
The beta function
Lattice spacing with coupling
A. Deuzeman
Traces of a fixed point
Introduction
Chiral properties
Spectral properties
Summary
Measurements
Thermal transition appears absent in SU(3) with twelve
staggered flavours of fundamental fermions.
The sign of the non-perturbative lattice beta function
implies a Coulomb phase just before chiral symmetry is
lost.
Consistent with the Miransky-Yamawaki scenario.
A. Deuzeman
Traces of a fixed point
Introduction
Chiral properties
Spectral properties
Summary
Implications
Weakening interaction means we will reach the
perturbative regime, with an opposite sign for the beta
function
Assuming analyticity of the beta function and small cut-off
effects, the presence of a Coulomb phase implies the
presence of a fixed point.
A. Deuzeman
Traces of a fixed point