Transcript QCD – from the vacuum to high temperature

QCD – from the
vacuum to high
temperature
an analytical approach
Analytical description of
phase transition
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Needs model that can account simultaneously
for the correct degrees of freedom below and
above the transition temperature.
Partial aspects can be described by more limited
models, e.g. chiral properties at small momenta.
Higgs picture of QCD
“spontaneous breaking of color “
in the QCD – vacuum
octet condensate
for Nf = 3 ( u,d,s )
C.Wetterich, Phys.Rev.D64,036003(2001),hep-ph/0008150
Many pictures …
… of the QCD vacuum have been proposed
monopoles, instantons, vortices, spaghetti vacuum …
in principle, no contradiction – there may be more than
one valid picture
most proposals say essentially nothing about the low mass
excitations in real QCD, i.e mesons and baryons
different for Higgs picture !
Electroweak phase diagram
Masses of excitations (d=3)
small MH
O.Philipsen,M.Teper,H.Wittig ‘97
large MH
Continuity
Higgs phase and confinement
can be equivalent –
then simply two different descriptions (pictures)
of the same physical situation
Is this realized for QCD ?
Necessary condition : spectrum of excitations with
the same quantum numbers in both pictures
- known for QCD : mesons + baryons -
Spontaneous breaking of color
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Condensate of colored scalar field
Equivalence of Higgs and confinement
description in real (Nf=3) QCD vacuum
Gauge symmetries not spontaneously broken in
formal sense ( only for fixed gauge )
Similar situation as in electroweak theory
No “fundamental” scalars
Symmetry breaking by quark-antiquarkcondensate
Analogy between weak and strong
interactions
Quark –antiquark condensate
Octet condensate
< octet > ≠ 0 :
 “Spontaneous breaking of color”
 Higgs mechanism
 Massive Gluons – all masses equal
 Eight octets have vev
 Infrared regulator for QCD
Electric charge
< octet > ≠ 0 :
 Spontaneous breaking of electromagnetic
U(1) symmetry
(some components of octet carry electric charge
– similar to Higgs mechanism for hypercharge
in electroweak theory)
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Combined U(1) symmetry survives
(cf. Q=I3 + ½ Y in e.w. standard model)
Electric charge of “quarks”
Flavor symmetry
for equal quark masses :
octet preserves global SU(3)-symmetry
“diagonal in color and flavor”
“color-flavor-locking”
(cf. Alford,Rajagopal,Wilczek ; Schaefer,Wilczek)
All particles fall into representations of
the “eightfold way”
quarks : 8 + 1 , gluons : 8
Related earlier ideas:
K.Bardakci,M.Halpern; I.Bars ’72
R.Mohapatra,J.Pati,A.Salam ’76
A.De Rujula,R.Giles,R.Jaffe ‘78
T.Banks,E.Rabinovici ’79
E.Fradkin,S.Shenker ’79
G. t’Hooft ’80
S.Dimopoulos,S.Raby,L.Susskind ’80
T.Matsumoto ’80
B.Iijima,R.Jaffe ’81
M.Yasue ’90
M.Alford,K.Rajagopal,F.Wilczek ’99
T.Schaefer,F.Wilczek ‘99
Color-flavor-locking
Chiral symmetry breaking :
SU(3)L x SU(3)R
Color symmetry breaking :
SU(3)c x SU(3)V
Quarks :
Gluons :
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3 x 3
8 x 1
color~
flavor
SU(3)V
SU(3)diagonal
8 + 1
8
Similar to high density QCD :
Alford,Rajagopal,Wilczek ; Schaefer,Wilczek
Octet condensate
Color symmetry breaking :
SU(3)c x SU(3)V
<χ> :
8
color~
x
8
flavor
SU(3)diagonal
1+…
Quarks and gluons carry the
observed quantum numbers of
isospin and strangeness
of the baryon and
vector meson octets !
They are integer charged!
Duality
Quantum numbers match !
Of course , there are many more excitations
(resonances ).
Strong interactions
bound states
Higgs description seems possible
- is it simple ?
Effective low energy model for QCD
Composite scalars
( quark-antiquark- bound states )
 Gauge invariance
 Approximation:
renormalizable interactions
for QCD with scalars
 Comparison with observation?
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Low energy effective action
γ=φ+χ
Simplicity
This simple effective action will yield the masses
and couplings of the baryons, pseudoscalars and
vector mesons, ( including electromagnetic
couplings by covariant derivatives ) !
( five parameters , to be later determined by QCD )
New scalar interactions
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Gauge covariant kinetic term
Effective potential
Yukawa coupling to quarks
Calculability
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Remember : no fundamental scalars
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Effective couplings should be calculable
from QCD – i.e. gauge coupling or
confinement scale
Effective octet potential
simple instanton computation
χ0 = 150 MeV
U
χ
Mρ = 850 MeV
Chiral anomaly !
Masses of physical particles
determine three phenomenological parameters
Phenomenological parameters
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5 undetermined
parameters
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predictions
Chiral perturbation theory
+ all predictions of chiral perturbation theory
+ determination of parameters
First conclusions
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Spontaneous color symmetry breaking plausible
in QCD
QCD - computation of effective vector mass
needed
Simple effective action can account for mass
spectrum of light baryons and mesons as well as
their couplings
Gluon - Meson duality
Quark - Baryon duality
Nonlinear formulation
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Use of nonlinear fields makes physical content
of the effective action more transparent.
Similar to nonlinear fields for pions
Selection of nonlinear fields follows symmetry
content of the theory
Gauge invariance
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Higgs picture is a guide for ideas and a way to compute
gauge invariant quantities at the end
Intuition can be misleading for certain questions
Effective action, U( φ,χ ) : gauge invariant
Nonlinear fields : gauge singlets
Only assumptions :
A) minimum of U preserves global SU(3)
B) minimum not for χ=0
( for appropriate gauge and normalization of χ )
Nonlinear fields : π,K,η, η’
Nonlinear fields : diquark cloud
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The product W•v
transforms as an
antidiquark
B=-2/3
v : color triplet
How quarks get dressed as baryons
Gauge bosons/vector mesons
All fields except v are gauge singlets
Effective action in terms of physical fields
Effective action in terms of physical fields
linear fields
nonlinear fields
Insert expressions
for ψ,A,χ,φ
Nonlinear local symmetry
Has been investigated since long ago in the
context of chiral theories, describes ρ - bosons
Here :
 Not postulated
 Consequence of local color symmetry +
“SSB”
 Gauge bosons = gluons = ρ - bosons
Predictions correct !
Reparameterization symmetry
Decomposition into nonlinear
fields is not unique. E.g.
N can be multiplied by unitary
transformation from left, and
W from right.
local U(3)
reparameterization symmetry
infinitesimal transformation
Baryons
Pion nucleon coupling
Two more
successful
predictions
F,D are
not fixed
by chiral
symmetry !
Pseudoscalar mesons
Kinetic term for
pseudoscalar mesons as
in chiral perturbation
theory
meson decay constant
Vector mesons
Electromagnetic interactions
include by
covariant
derivative
ρ - couplings
ρ - couplings
experiment :
prediction :
Vector dominance is realized by Higgs picture of QCD
Connection to gauge invariant
formulation for linear fields
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Vector channel : use singlet fields
(in addition to A,φ,χ ; fermions omitted here )
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Solve field equations for colored bosons
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Γ[φ,ρ] contains directly the information for gauge
invariant correlation functions
A - ρ mixing
Insert solution A[ρ]
Mixing produces
mass shift
Conclusion (2)
Phenomenology
works well for
simple effective action
Chiral phase transition
at high temperature
High temperature phase transition in QCD :
Melting of octet condensate
Lattice simulations :
Deconfinement temperature = critical temperature
for restoration of chiral symmetry
Why ?
Simple explanation :
Temperature dependent effective potential
Temperature corrections to effective
octet potential
Vacuum effective potential ( T=0 )
Interesting relation between Tc
and η’ properties
A simple mean field calculation
Conclusions ( 3 )
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Coherent picture for phase diagram of QCD
is emerging
Gluon meson duality allows for analytical
calculations
Quark-baryon duality :
Direct contact to quantities of nuclear physics
Questions ?
Lattice tests
a) Continuity
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Add “fundamental” scalar octets and start in
perturbative Higgs phase
( large negative mass term ).
Remove scalars continuously by increasing the
mass term to large positive values
Phase transition or analytical crossover ?
Challenges
Instanton computation of U(φ,χ)
(improve by nonperturbative flow equation )
 Check continuity between Higgs and
confinement description by lattice simulation
 Explicit construction of a local diquark operator
with transformation Wv
(nonvanishing expectation value )
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