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