scalar qcd - ectstar.eu · axel maas with tajdar mufti scalar qcd bound states, elementary...
TRANSCRIPT
Axel Maas with Tajdar Mufti
Scalar QCD
5th of September 2013QCD TNT III
TrentoItaly
Axel Maas with Tajdar Mufti
Scalar QCDBound States, Elementary Particles
& Interaction Vertices
5th of September 2013QCD TNT III
TrentoItaly
● Only confinement – no chiral symmetry breaking● Confinement independent of Lorentz
structure
Why Scalar QCD?
● Only confinement – no chiral symmetry breaking● Confinement independent of Lorentz
structure● Simple(r) tensor structures
Why Scalar QCD?
● Only confinement – no chiral symmetry breaking● Confinement independent of Lorentz
structure● Simple(r) tensor structures● Rich bound state spectrum
Why Scalar QCD?
● Only confinement – no chiral symmetry breaking● Confinement independent of Lorentz
structure● Simple(r) tensor structures● Rich bound state spectrum● Cheap lattice simulations
● Test case for functional equations
Why Scalar QCD?
● Only confinement – no chiral symmetry breaking● Confinement independent of Lorentz
structure● Simple(r) tensor structures● Rich bound state spectrum● Cheap lattice simulations
● Test case for functional equations● Limited by (possible) triviality
● But triviality cutoff can be high enough
Why Scalar QCD?
Scalar QCD
● Gauge theory
Scalar QCD
● Gauge theory
● Gluons
L=−14
Aμ νa Aa
μ ν
Aμ νa =∂μ Aν
a−∂ν Aμa
Aμa
WA
Scalar QCD
● Gauge theory
● Gluons
● Coupling g and some numbers f abc
L=−14
Aμ νa Aa
μ ν
Aμ νa =∂μ Aν
a−∂ν Aμa+gf bc
a Aμb Aν
c
Aμa
WAWA A
Scalar QCD
● Gauge theory
● Gluons● Scalar quarks● Coupling g and some numbers f abc
L=−14
Aμ νa Aa
μ ν+(Dμij h j) + Dik
μ hk
Aμ νa =∂μ Aν
a−∂ν Aμa+gf bc
a Aμb Aν
c
Dμij=δij∂μ
Aμa
hi
W
h
AWA A
Scalar QCD
● Gauge theory
● Gluons● Scalar quarks
● Coupling g and some numbers f abc and ta
ij
● Gauge group SU(2)
L=−14
Aμ νa Aa
μ ν+(Dμij h j) + Dik
μ hk
Aμ νa =∂μ Aν
a−∂ν Aμa+gf bc
a Aμb Aν
c
Dμij=δij∂μ−igAμ
a t aij
Aμa
hi
W
h
AW
W
A
h A
A
Scalar QCD
● Gauge theory
● Gluons● Scalar quarks
● Coupling g and some numbers f abc and ta
ij
● Gauge group SU(2)● No 'baryon number'
L=−14
Aμ νa Aa
μ ν+(Dμij h j) + Dik
μ hk
Aμ νa =∂μ Aν
a−∂ν Aμa+gf bc
a Aμb Aν
c
Dμij=δij∂μ−igAμ
a t aij
Aμa
hi
W
h
AW
W
A
h A
A
Scalar QCD
● Gauge theory
● Gluons● Scalar quarks
● Couplings g, v, λ and some numbers f abc and ta
ij
● Gauge group SU(2)● No 'baryon number'
L=−14
Aμ νa Aa
μ ν+(Dμij h j) + Dik
μ hk+λ(ha ha+ −v2)2
Aμ νa =∂μ Aν
a−∂ν Aμa+gf bc
a Aμb Aν
c
Dμij=δij∂μ−igAμ
a taij
Aμa
hi
W
h
AW
W
A
h
h h
A
A
Scalar QCD
● Gauge theory
● Gluons● Scalar quarks
● Couplings g, v=0, λ=0 and some numbers f abc and ta
ij
● Scalar self-interaction set to zero● Gauge group SU(2)● No 'baryon number'
L=−14
Aμ νa Aa
μ ν+(Dμij h j) + Dik
μ hk+λ(ha ha+ −v2)2
Aμ νa =∂μ Aν
a−∂ν Aμa+gf bc
a Aμb Aν
c
Dμij=δij∂μ−igAμ
a taij
Aμa
hi
W
h
AW
W
A
h
h h
A
A
Symmetries
L=−14
Aμ νa Aa
μ ν+(Dμij h j) + Dik
μ hk+λ(ha ha+ −v2)2
Aμ νa =∂μ Aν
a−∂ν Aμa+gf bc
a Aμb Aν
c
Dμij=δij∂μ−igAμ
a taij
● Local SU(2) gauge symmetry● Invariant under arbitrary gauge transformations
Aμa→Aμ
a+(δb
a∂μ−g f bc
a Aμc)ϕ
b
ϕa(x)
hi→hi+g t aijϕ
a h j
Symmetries
L=−14
Aμ νa Aa
μ ν+(Dμij h j) + Dik
μ hk+λ(ha ha+ −v2)2
Aμ νa =∂μ Aν
a−∂ν Aμa+gf bc
a Aμb Aν
c
Dμij=δij∂μ−igAμ
a taij
● Local SU(2) gauge symmetry● Invariant under arbitrary gauge transformations
● Global SU(2) quark flavor symmetry● Acts as right-transformation on the quark field only
Aμa→Aμ
a+(δb
a∂μ−g f bc
a Aμc)ϕ
b
ϕa(x)
hi→hi+g t aijϕ
a h j
Aμa→Aμ
a hi→hi+aij h j+bij h j∗
Symmetries
L=−14
Aμ νa Aa
μ ν+(Dμij h j) + Dik
μ hk+λ(ha ha+ −v2)2
Aμ νa =∂μ Aν
a−∂ν Aμa+gf bc
a Aμb Aν
c
Dμij=δij∂μ−igAμ
a taij
QCD-like vs. Higgs-like [Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07]
g(Classical gauge coupling)f(
Cla
ssic
al H
igg
s m
ass
)
QCD-like vs. Higgs-like [Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07]
g(Classical gauge coupling)f(
Cla
ssic
al H
igg
s m
ass
)
Confinement “phase”
QCD-like vs. Higgs-like [Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07]
g(Classical gauge coupling)f(
Cla
ssic
al H
igg
s m
ass
)
Higgs “phase”
Confinement “phase”
QCD-like vs. Higgs-like
● (Lattice-regularized) phase diagram continuous
[Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07]
g(Classical gauge coupling)f(
Cla
ssic
al H
igg
s m
ass
)
Higgs “phase”
Confinement “phase”
1st order
Crossover
QCD-like vs. Higgs-like
● (Lattice-regularized) phase diagram continuous● Separation only in
fixed gauges
[Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07]
g(Classical gauge coupling)f(
Cla
ssic
al H
igg
s m
ass
)
Higgs “phase”
Confinement “phase”
1st order
Crossover
Landau gauge
QCD-like vs. Higgs-like
● (Lattice-regularized) phase diagram continuous● Separation only in
fixed gauges
[Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07]
g(Classical gauge coupling)f(
Cla
ssic
al H
igg
s m
ass
)
Higgs “phase”
Confinement “phase”
1st order
Crossover
Landau gauge
Coulomb gauge
QCD-like vs. Higgs-like
● (Lattice-regularized) phase diagram continuous● Separation only in
fixed gauges● Same physical state
space in confinement and Higgs pseudo-phases, irrespective of couplings
[Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07]
g(Classical gauge coupling)f(
Cla
ssic
al H
igg
s m
ass
)
Higgs “phase”
Confinement “phase”
1st order
Crossover
QCD-like vs. Higgs-like
● (Lattice-regularized) phase diagram continuous● Separation only in
fixed gauges● Same physical state
space in confinement and Higgs pseudo-phases, irrespective of couplings● Asymptotic states depend on whether
ground states for given JPC
F are stable
[Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07]
g(Classical gauge coupling)f(
Cla
ssic
al H
igg
s m
ass
)
Higgs “phase”
Confinement “phase”
1st order
Crossover
Non-aligned gauges
● Explicit charge direction inconvenient beyond perturbation theory
[Maas, MPLA'12]
Non-aligned gauges
● Explicit charge direction inconvenient beyond perturbation theory
● Define a gauge without preferred direction
[Maas, MPLA'12]
Non-aligned gauges
● Explicit charge direction inconvenient beyond perturbation theory
● Define a gauge without preferred direction● Local part fixed to Landau gauge by
● Gribov-Singer ambiguity fixed by minimal prescription
● Introduces usual Faddeev-Popov ghosts
∂μ Aμa=0
[Maas, MPLA'12]
Non-aligned gauges
● Explicit charge direction inconvenient beyond perturbation theory
● Define a gauge without preferred direction● Local part fixed to Landau gauge by
● Gribov-Singer ambiguity fixed by minimal prescription
● Introduces usual Faddeev-Popov ghosts● Global part fixed by
● Aligned Landau gauges also possible
∂μ Aμa=0
[Maas, MPLA'12]
⟨h⟩=0
Differentiating phases [Maas, MPLA'12, Caudy & Greensite'07]
Differentiating phases
● How to distinguish phases?
[Maas, MPLA'12, Caudy & Greensite'07]
Differentiating phases
● How to distinguish phases?● Relative orientation
● is the magnetization
⟨∫hdx∫hdy ⟩
∫hdx
[Maas, MPLA'12, Caudy & Greensite'07]
Differentiating phases
● How to distinguish phases?● Relative orientation
● is the magnetization● But not so important anyway...
⟨∫hdx∫hdy ⟩
∫hdx
[Maas, MPLA'12, Caudy & Greensite'07]
Typical spectra
“Higgs”
[Maas, Mufti PoS'12, unpublished]
Typical spectra
“Higgs”
[Maas, Mufti PoS'12, unpublished, Maas MPLA'13]
Higgs
W
Typical spectra
“Higgs” “QCD”
[Maas, Mufti PoS'12, unpublished]
Typical spectra
● Rather different low-lying spectra● 0++ lighter in (Landau gauge) QCD-like region● 1-- lighter in (Landau gauge) Higgs-like region
“Higgs” “QCD”
[Maas, Mufti PoS'12, unpublished]
Typical spectra
● Rather different low-lying spectra● 0++ lighter in (Landau gauge) QCD-like region● 1-- lighter in (Landau gauge) Higgs-like region
● Use as operational definition of phase
“Higgs” “QCD”
[Maas, Mufti PoS'12, unpublished]
Phase diagram [Maas, Mufti, unpublished]
Phase diagram
“Higgs”
“QCD”
● Complicated real phase diagram
[Maas, Mufti, unpublished]
Phase diagram
“Higgs”
“QCD”
● Complicated real phase diagram● QCD-like behavior even for negative bare mass
[Maas, Mufti, unpublished]
Phase diagram
“Higgs”
“QCD”
● Complicated real phase diagram● QCD-like behavior even for negative bare mass● Similar bare couplings for both physic types
[Maas, Mufti, unpublished]
Phase diagram
“Higgs”
“QCD”
● Complicated real phase diagram● QCD-like behavior even for negative bare mass● Similar bare couplings for both physic types
[Maas, Mufti, unpublished]
Propagators
● 3 propagators
Propagators
● 3 propagators● Gluon D
ab x− y= A
a x A
b y
Propagators
● 3 propagators● Gluon
● 1 scalar dressing function
D
ab x− y= A
a x A
b y
Dμ ν( p)=(δμν−pμ pν
p2)D ( p)
Propagators
● 3 propagators● Gluon
● 1 scalar dressing function● Ghost
D
ab x− y= A
a x A
b y
DGab x− y = c
ax cb
y
Dμ ν( p)=(δμν−pμ pν
p2)D ( p)
Propagators
● 3 propagators● Gluon
● 1 scalar dressing function● Ghost
● Negative semi-definite
D
ab x− y= A
a x A
b y
DGab x− y = c
ax cb
y
Dμ ν( p)=(δμν−pμ pν
p2)D ( p)
−DG( p)
Propagators
● 3 propagators● Gluon
● 1 scalar dressing function● Ghost
● Negative semi-definite● Both renormalize multiplicatively
D
ab x− y= A
a x A
b y
DGab x− y = c
ax cb
y
Dμ ν( p)=(δμν−pμ pν
p2)D ( p)
−DG( p)
Propagators
● 3 propagators● Gluon
● 1 scalar dressing function● Ghost
● Negative semi-definite● Both renormalize multiplicatively● Scalar
D
ab x− y= A
a x A
b y
DGab x− y = c
ax cb
y
Dμ ν( p)=(δμν−pμ pν
p2)D ( p)
−DG( p)
DHij(x− y )= <hi
(x)h j+( y)>
Propagators
● 3 propagators● Gluon
● 1 scalar dressing function● Ghost
● Negative semi-definite● Both renormalize multiplicatively● Scalar
● Requires more complicated renormalization
D
ab x− y= A
a x A
b y
DGab x− y = c
ax cb
y
Dμ ν( p)=(δμν−pμ pν
p2)D ( p)
−DG( p)
DH (μ)=DHtl (μ)
DH (μ) '=DHtl (μ) '
DHtl(p)=1 /(p2+mr
2)
μ=mr
DHij(x− y )= <hi
(x)h j+( y)>
Gluon propagator [Maas, EPJC'11 Maas, Mufti PoS'12, unpublished]
Gluon propagator
● Significantly volume-dependent● Decoupling-type
[Maas, EPJC'11 Maas, Mufti PoS'12, unpublished]
Gluon propagator
● Significantly volume-dependent● Decoupling-type● Positivity violating
[Maas, EPJC'11 Maas, Mufti PoS'12, unpublished]
Gluon propagator
● Significantly volume-dependent● Decoupling-type● Positivity violating● Little impact when changing scalar sector
[Maas, EPJC'11 Maas, Mufti PoS'12, unpublished]
Ghost propagator [Maas, EPJC'11 Maas, Mufti PoS'12, unpublished]
Ghost propagator
● Infrared enhanced● But likely not divergent
[Maas, EPJC'11 Maas, Mufti PoS'12, unpublished]
Ghost propagator
● Infrared enhanced● But likely not divergent
● Derive a running coupling from p6DG
2D
[Maas, EPJC'11 Maas, Mufti PoS'12, unpublished]
Ghost propagator
● Infrared enhanced● But likely not divergent
● Derive a running coupling from p6DG
2D
[Maas, EPJC'11 Maas, Mufti PoS'12, unpublished]
Ghost propagator
● Infrared enhanced● But likely not divergent
● Derive a running coupling from p6DG
2D
● Not strongest at lowest bound state masses
[Maas, EPJC'11 Maas, Mufti PoS'12, unpublished]
Scalar quark propagatorm
r=1 GeV
[Maas, EPJC'11 Maas, Mufti PoS'12, unpublished]
Scalar quark propagator
● Requires mass renormalization● Tree-level mass zero: “Mass generation”
mr=1 GeV
[Maas, EPJC'11 Maas, Mufti PoS'12, unpublished]
Scalar quark propagator
● Requires mass renormalization● Tree-level mass zero: “Mass generation”
● No sign (yet) of positivity violation
mr=1 GeV
[Maas, EPJC'11 Maas, Mufti PoS'12, unpublished]
Scalar quark propagator
● Requires mass renormalization● Tree-level mass zero: “Mass generation”
● No sign (yet) of positivity violation
mr=0.25 GeV
[Maas, EPJC'11 Maas, Mufti PoS'12, unpublished]
Vertices
Vertices● Three 3-point vertices
● 4-point vertices too expensive
Vertices● Three 3-point vertices
● 4-point vertices too expensive● Ghost-gluon vertex <Aμ
a cb c̄c> =Dμ νad DG
beDGcfΓνd e f
[Cucchieri, Maas, Mendes, PRD'06,'08 Maas, Mufti PoS'12, unpublished]
Vertices● Three 3-point vertices
● 4-point vertices too expensive● Ghost-gluon vertex <Aμ
a cb c̄c> =Dμ νad DG
beDGcfΓνd e f
GA c c̄=Γ
tl<A c c̄> /(Γ
tlDDGDGΓtl)
[Cucchieri, Maas, Mendes, PRD'06,'08 Maas, Mufti PoS'12, unpublished]
Vertices● Three 3-point vertices
● 4-point vertices too expensive● Ghost-gluon vertex
● 3-gluon vertex
<Aμa cb c̄c> =Dμ ν
ad DGbeDG
cfΓνd e f
GA c c̄=Γ
tl<A c c̄> /(Γ
tlDDGDGΓtl)
<Aμa Aν
b Aρc> = Dμα
ad Dνβbe Dρ γ
cfΓαβγd e f
GA3=Γ
tl<AAA> /(Γ
tlDDDΓtl)
[Cucchieri, Maas, Mendes, PRD'06,'08 Maas, Mufti PoS'12, unpublished]
Vertices● Three 3-point vertices
● 4-point vertices too expensive● Ghost-gluon vertex
● 3-gluon vertex
● Scalar-gluon vertex
<Aμa cb c̄c> =Dμ ν
ad DGbeDG
cfΓνd e f
GA c c̄=Γ
tl<A c c̄> /(Γ
tlDDGDGΓtl)
<Aμa Aν
b Aρc> = Dμα
ad Dνβbe Dρ γ
cfΓαβγd e f
GA3=Γ
tl<AAA> /(Γ
tlDDDΓtl)
<Aμa hi h j + > =Dμν
ad DHik DG
jmΓνdkm
GA hh +
=Γtl<A hh +
> /(ΓtlDDHDHΓ
tl)
[Cucchieri, Maas, Mendes, PRD'06,'08 Maas, Mufti PoS'12, unpublished]
Vertices● Three 3-point vertices
● 4-point vertices too expensive● Ghost-gluon vertex
● 3-gluon vertex
● Scalar-gluon vertex
● tF makes vertex flavor-conserving
● Flavor-violating vertex vanishes● Flavor conserved
<Aμa cb c̄c> =Dμ ν
ad DGbeDG
cfΓνd e f
GA c c̄=Γ
tl<A c c̄> /(Γ
tlDDGDGΓtl)
<Aμa Aν
b Aρc> = Dμα
ad Dνβbe Dρ γ
cfΓαβγd e f
GA3=Γ
tl<AAA> /(Γ
tlDDDΓtl)
<Aμa hi t Fh
j +> =Dμ ν
ad DHik DG
jmΓνdkm
GAhh +
=Γtl<A htF h
+> /(Γ
tlDDHDH Γtl)
[Cucchieri, Maas, Mendes, PRD'06,'08 Maas, Mufti PoS'12, unpublished]
Vertices● Three 3-point vertices
● 4-point vertices too expensive● Ghost-gluon vertex
● 3-gluon vertex
● Scalar-gluon vertex
● Two momentum configurations
<Aμa cb c̄c> =Dμ ν
ad DGbeDG
cfΓνd e f
GA c c̄=Γ
tl<A c c̄> /(Γ
tlDDGDGΓtl)
<Aμa Aν
b Aρc> = Dμα
ad Dνβbe Dρ γ
cfΓαβγd e f
GA3=Γ
tl<AAA> /(Γ
tlDDDΓtl)
<Aμa hi t Fh
j +> =Dμ ν
ad DHik DG
jmΓνdkm
GAhh +
=Γtl<A htF h
+> /(Γ
tlDDHDH Γtl)
[Cucchieri, Maas, Mendes, PRD'06,'08 Maas, Mufti PoS'12, unpublished]
Vertices● Three 3-point vertices
● 4-point vertices too expensive● Ghost-gluon vertex
● 3-gluon vertex
● Scalar-gluon vertex
● Two momentum configurations
<Aμa cb c̄c> =Dμ ν
ad DGbeDG
cfΓνd e f
GA c c̄=Γ
tl<A c c̄> /(Γ
tlDDGDGΓtl)
<Aμa Aν
b Aρc> = Dμα
ad Dνβbe Dρ γ
cfΓαβγd e f
GA3=Γ
tl<AAA> /(Γ
tlDDDΓtl)
<Aμa hi t Fh
j +> =Dμ ν
ad DHik DG
jmΓνdkm
GAhh +
=Γtl<A htF h
+> /(Γ
tlDDHDH Γtl)
[Cucchieri, Maas, Mendes, PRD'06,'08 Maas, Mufti PoS'12, unpublished]
Vertices● Three 3-point vertices
● 4-point vertices too expensive● Ghost-gluon vertex
● 3-gluon vertex
● Scalar-gluon vertex
● Two momentum configurations
<Aμa cb c̄c> =Dμ ν
ad DGbeDG
cfΓνd e f
GA c c̄=Γ
tl<A c c̄> /(Γ
tlDDGDGΓtl)
<Aμa Aν
b Aρc> = Dμα
ad Dνβbe Dρ γ
cfΓαβγd e f
GA3=Γ
tl<AAA> /(Γ
tlDDDΓtl)
<Aμa hi t Fh
j +> =Dμ ν
ad DHik DG
jmΓνdkm
GAhh +
=Γtl<A htF h
+> /(Γ
tlDDHDH Γtl)
A Ap p
[Cucchieri, Maas, Mendes, PRD'06,'08 Maas, Mufti PoS'12, unpublished]
Vertices● Three 3-point vertices
● 4-point vertices too expensive● Ghost-gluon vertex
● 3-gluon vertex
● Scalar-gluon vertex
● Two momentum configurations
<Aμa cb c̄c> =Dμ ν
ad DGbeDG
cfΓνd e f
GA c c̄=Γ
tl<A c c̄> /(Γ
tlDDGDGΓtl)
<Aμa Aν
b Aρc> = Dμα
ad Dνβbe Dρ γ
cfΓαβγd e f
GA3=Γ
tl<AAA> /(Γ
tlDDDΓtl)
<Aμa hi t Fh
j +> =Dμ ν
ad DHik DG
jmΓνdkm
GAhh +
=Γtl<A htF h
+> /(Γ
tlDDHDH Γtl)
A Ap=0 p
[Cucchieri, Maas, Mendes, PRD'06,'08 Maas, Mufti PoS'12, unpublished]
Vertices● Three 3-point vertices
● 4-point vertices too expensive● Ghost-gluon vertex
● 3-gluon vertex
● Scalar-gluon vertex
● Two momentum configurations
<Aμa cb c̄c> =Dμ ν
ad DGbeDG
cfΓνd e f
GA c c̄=Γ
tl<A c c̄> /(Γ
tlDDGDGΓtl)
<Aμa Aν
b Aρc> = Dμα
ad Dνβbe Dρ γ
cfΓαβγd e f
GA3=Γ
tl<AAA> /(Γ
tlDDDΓtl)
<Aμa hi t Fh
j +> =Dμ ν
ad DHik DG
jmΓνdkm
GAhh +
=Γtl<A htF h
+> /(Γ
tlDDHDH Γtl)
A Ap=0
q k with q=-k
p
[Cucchieri, Maas, Mendes, PRD'06,'08 Maas, Mufti PoS'12, unpublished]
Vertices● Three 3-point vertices
● 4-point vertices too expensive● Ghost-gluon vertex
● 3-gluon vertex
● Scalar-gluon vertex
● Two momentum configurations
<Aμa cb c̄c> =Dμ ν
ad DGbeDG
cfΓνd e f
GA c c̄=Γ
tl<A c c̄> /(Γ
tlDDGDGΓtl)
<Aμa Aν
b Aρc> = Dμα
ad Dνβbe Dρ γ
cfΓαβγd e f
GA3=Γ
tl<AAA> /(Γ
tlDDDΓtl)
<Aμa hi t Fh
j +> =Dμ ν
ad DHik DG
jmΓνdkm
GAhh +
=Γtl<A htF h
+> /(Γ
tlDDHDH Γtl)
A Ap=0
q k with q=-k
p
q k
p2=q2=k2
[Cucchieri, Maas, Mendes, PRD'06,'08 Maas, Mufti PoS'12, unpublished]
Ghost-gluon vertex
● Only small deviations from tree-level● Like in Yang-Mills theory● Strongest effect at bound state mass scale
[Maas, Mufti PoS'12, unpublished]
3-gluon vertex
● Infrared suppressed● Sets in at bound state mass scale● Absence of (supposed) sign change of
Yang-Mills theory at small momenta?
[Maas, Mufti PoS'12, unpublished]
Scalar-gluon vertex [Maas, Mufti PoS'12, unpublished]
● Essentially tree-level● No indications for infrared effects (yet?)
Scalar-gluon vertex [Maas, Mufti PoS'12, unpublished]
● Essentially tree-level● No indications for infrared effects (yet?)
● Different than a (pseudo-)confining 1-gluon exchange
● As in the quenched case [Maas, PoS'11, unpublished]
Scalar-gluon vertex
● Essentially tree-level● No indications for infrared effects (yet?)
● Different than a (pseudo-)confining 1-gluon exchange
● As in the quenched case [Maas, PoS'11, unpublished]
[Maas, Mufti PoS'12, unpublished]
Summary● Scalar QCD a role model for QCD
● Scalar theory simpler...
Summary● Scalar QCD a role model for QCD
● Scalar theory simpler...● ...but distinction to Higgs-like physics
complicated
Summary● Scalar QCD a role model for QCD
● Scalar theory simpler...● ...but distinction to Higgs-like physics
complicated● Test case for functional methods
Summary● Scalar QCD a role model for QCD
● Scalar theory simpler...● ...but distinction to Higgs-like physics
complicated● Test case for functional methods
● Propagators in QCD-like region similar to Yang-Mills theory
Summary● Scalar QCD a role model for QCD
● Scalar theory simpler...● ...but distinction to Higgs-like physics
complicated● Test case for functional methods
● Propagators in QCD-like region similar to Yang-Mills theory● Positivity violating gluon● Scalar quark not obviously positivity violating
Summary● Scalar QCD a role model for QCD
● Scalar theory simpler...● ...but distinction to Higgs-like physics
complicated● Test case for functional methods
● Propagators in QCD-like region similar to Yang-Mills theory● Positivity violating gluon● Scalar quark not obviously positivity violating
● Vertices Yang-Mills-like
Summary● Scalar QCD a role model for QCD
● Scalar theory simpler...● ...but distinction to Higgs-like physics
complicated● Test case for functional methods
● Propagators in QCD-like region similar to Yang-Mills theory● Positivity violating gluon● Scalar quark not obviously positivity violating
● Vertices Yang-Mills-like● No infrared effects in the scalar-gluon vertex
Summary● Scalar QCD a role model for QCD
● Scalar theory simpler...● ...but distinction to Higgs-like physics
complicated● Test case for functional methods
● Propagators in QCD-like region similar to Yang-Mills theory● Positivity violating gluon● Scalar quark not obviously positivity violating
● Vertices Yang-Mills-like● No infrared effects in the scalar-gluon vertex
● So far...no obvious confinement