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Does QCD predict light hybrid mesons?
Jozef DudekOld Dominion University & Jefferson Lab
JLab Users’ Group Workshop
Robert Edwards (JLab)Balint Joo (JLab)David Richards (JLab)Christopher Thomas (JLab)Mike Peardon (Trinity Coll., Dublin)
for the Hadron Spectrum Collaboration
2
constituent quark model
π(1300
)π(
1800
)
ρ
π
ρ(14
50)
ρ(1700
)
ρ3
π 2(1670)π 2
(188
0)
b1
a0(980)
a 0(145
0)
a 1(126
0) a2
a 4(204
0)
(historical) empirical motivation
“1S”
2
constituent quark model
π(1300
)π(
1800
)
ρ
π
ρ(14
50)
ρ(1700
)
ρ3
π 2(1670)π 2
(188
0)
b1
a0(980)
a 0(145
0)
a 1(126
0) a2
a 4(204
0)
(historical) empirical motivation
1P?
“1S”
2
constituent quark model
π(1300
)π(
1800
)
ρ
π
ρ(14
50)
ρ(1700
)
ρ3
π 2(1670)π 2
(188
0)
b1
a0(980)
a 0(145
0)
a 1(126
0) a2
a 4(204
0)
(historical) empirical motivation
1P?
2S
“1S”
2
constituent quark model
π(1300
)π(
1800
)
ρ
π
ρ(14
50)
ρ(1700
)
ρ3
π 2(1670)π 2
(188
0)
b1
a0(980)
a 0(145
0)
a 1(126
0) a2
a 4(204
0)
(historical) empirical motivation
1P?
1D
2S
“1S”
2
constituent quark model
π(1300
)π(
1800
)
ρ
π
ρ(14
50)
ρ(1700
)
ρ3
π 2(1670)π 2
(188
0)
b1
a0(980)
a 0(145
0)
a 1(126
0) a2
a 4(204
0)
(historical) empirical motivation
1P?
1F
1D
2S
“1S”
2
constituent quark model
π(1300
)π(
1800
)
ρ
π
ρ(14
50)
ρ(1700
)
ρ3
π 2(1670)π 2
(188
0)
b1
a0(980)
a 0(145
0)
a 1(126
0) a2
a 4(204
0)
(historical) empirical motivation
hybrid mesons -‐ beyond the quark model
observed meson state flavor & JPC systematics suggest “constituent quarks”
hybrid mesons -‐ beyond the quark model
observed meson state flavor & JPC systematics suggest “constituent quarks”
exotic quantum numbers
hybrid mesons -‐ beyond the quark model
observed meson state flavor & JPC systematics suggest “constituent quarks”
exotic quantum numbers
but what if excited gluonic fields play a rôle -‐ a hybrid meson, ?
possibly exotic JPC & extra ‘non-‐exotic’ states
must be ‘heavier’ or ‘harder to produce’ ?
hybrid mesons -‐ models tubes, bags & heavy glue
hybrid mesons -‐ models tubes, bags & heavy glue
flux-‐tube model0-‐+, 1-‐+, 2-‐+, 1-‐-‐
0+-‐, 1+-‐, 2+-‐, 1++roughly degenerate
hybrid mesons -‐ models tubes, bags & heavy glue
flux-‐tube model0-‐+, 1-‐+, 2-‐+, 1-‐-‐
0+-‐, 1+-‐, 2+-‐, 1++roughly degenerate
bag model 0-‐+, 1-‐+, 2-‐+, 1-‐-‐& others heavier
hybrid mesons -‐ models tubes, bags & heavy glue
flux-‐tube model0-‐+, 1-‐+, 2-‐+, 1-‐-‐
0+-‐, 1+-‐, 2+-‐, 1++roughly degenerate
bag model 0-‐+, 1-‐+, 2-‐+, 1-‐-‐& others heavier
massive quasi-‐gluons Coulomb gauge transverse (no 3-‐body) 0++, 1++, 2++, 1+-‐
0-‐-‐, 1-‐+, ...1-‐-‐ “S-‐wave”
hybrid mesons -‐ models tubes, bags & heavy glue
flux-‐tube model0-‐+, 1-‐+, 2-‐+, 1-‐-‐
0+-‐, 1+-‐, 2+-‐, 1++roughly degenerate
bag model 0-‐+, 1-‐+, 2-‐+, 1-‐-‐& others heavier
massive quasi-‐gluons Coulomb gauge transverse (no 3-‐body) 0++, 1++, 2++, 1+-‐
0-‐-‐, 1-‐+, ...1-‐-‐ “S-‐wave”
Coulomb gauge transverse (incl. 3-‐body)
0+-‐, (2+-‐)2, ...
0-‐+, 1-‐+, 2-‐+, 1-‐-‐
1+-‐ “P-‐wave”
hybrid mesons -‐ models tubes, bags & heavy glue
flux-‐tube model0-‐+, 1-‐+, 2-‐+, 1-‐-‐
0+-‐, 1+-‐, 2+-‐, 1++roughly degenerate
without much data -‐ nothing much to constrain them ...
bag model 0-‐+, 1-‐+, 2-‐+, 1-‐-‐& others heavier
massive quasi-‐gluons Coulomb gauge transverse (no 3-‐body) 0++, 1++, 2++, 1+-‐
0-‐-‐, 1-‐+, ...1-‐-‐ “S-‐wave”
Coulomb gauge transverse (incl. 3-‐body)
0+-‐, (2+-‐)2, ...
0-‐+, 1-‐+, 2-‐+, 1-‐-‐
1+-‐ “P-‐wave”
spectrum from lattice QCD
two-‐point correlator e.g.
spectrum from lattice QCD
two-‐point correlator e.g.
as a sum of QCD eigenstates
spectrum from lattice QCD
two-‐point correlator e.g.
as a sum of QCD eigenstates
e.g. 1-‐-‐two-‐point correlator matrix
spectrum from lattice QCD
two-‐point correlator e.g.
as a sum of QCD eigenstates
e.g. 1-‐-‐two-‐point correlator matrix
each state comes from an orthogonal combination of
solve by using a ‘Rayleigh-‐Ritz’-‐style variational approach -‐ “diagonalize the matrix”
optimal operator :
mesonic operator basis
fermion bilinears with up to three covariant derivatives -‐ project into good JPC
actually also have to project into irreducible representations of the cubic symmetry group
# of operators
~J=0
~J=1
~J=2
~J=2
~J=3
this is by far the largest operator set ever used in a calculation like this
isovector spectrum
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
mπ ~ 700 MeV
isovector spectrum
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
mπ ~ 700 MeV
isovector spectrum
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
mπ ~ 700 MeV
0.1 0.2 0.3 0.4500
1000
1500
2000
2500
3000
exotic JPC -‐ before
lattice QCD exotic meson spectrum circa 2006
0.1 0.2 0.3 0.4 0.5 0.61.0
1.5
2.0
2.5
quenched
dynamical
mπ ~ 7
00 MeV
mπ ~ 5
00 MeV
mπ ~ 3
00 MeV
exotic JPC -‐ before
lattice QCD exotic meson spectrum circa 2006
0.1 0.2 0.3 0.4 0.5 0.61.0
1.5
2.0
2.5
quenched
dynamical
mπ ~ 7
00 MeV
mπ ~ 5
00 MeV
mπ ~ 3
00 MeV
others?
0.1 0.2 0.3 0.4 0.5 0.61.0
1.5
2.0
2.5
quenched
dynamical
dynamical
exotic JPC -‐ after
2+-‐, 1-‐+, 0-‐-‐
exotic JPC -‐ after
2+-‐, 1-‐+, 0-‐-‐
0.1 0.2 0.3 0.4 0.5 0.61.0
1.5
2.0
2.5
dynamical
understanding & interpreting ?
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
systematics of a pair
mπ ~ 700 MeV
1S
2S
3S?
1D
2D?1G?
1P
2P
1F
understanding & interpreting ?
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
systematics of a pair
mπ ~ 700 MeV
1S
2S
3S?
1D
2D?1G?
1P
2P
1F?
understanding & interpreting ? try (model-‐dependent) analysis of matrix elements
1-‐-‐
understanding & interpreting ? try (model-‐dependent) analysis of matrix elements
1-‐-‐
hybrid?
(spin-singlet)
understanding & interpreting ? try (model-‐dependent) analysis of matrix elements
hybrid?
ground state is dominantly
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.0 0.1 0.2 0.3 0.4
500
1000
1500
2000
2500
3000
1-‐-‐
understanding & interpreting ? try (model-‐dependent) analysis of matrix elements
hybrid?
ground state is dominantly
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.0 0.1 0.2 0.3 0.4
500
1000
1500
2000
2500
3000
1st excited state is dominantly
0.0 0.1 0.2 0.3 0.4
500
1000
1500
2000
2500
3000
1-‐-‐
understanding & interpreting ? try (model-‐dependent) analysis of matrix elements
hybrid?
ground state is dominantly
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.0 0.1 0.2 0.3 0.4
500
1000
1500
2000
2500
3000
1st excited state is dominantly
0.0 0.1 0.2 0.3 0.4
500
1000
1500
2000
2500
3000
2nd excited state is dominantly
with some
0.0 0.1 0.2 0.3 0.4
500
1000
1500
2000
2500
3000
1-‐-‐
understanding & interpreting ? try (model-‐dependent) analysis of matrix elements
hybrid?
ground state is dominantly
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.0 0.1 0.2 0.3 0.4
500
1000
1500
2000
2500
3000
1st excited state is dominantly
0.0 0.1 0.2 0.3 0.4
500
1000
1500
2000
2500
3000
2nd excited state is dominantly
with some
0.0 0.1 0.2 0.3 0.4
500
1000
1500
2000
2500
3000
3rd excited state is dominantly
hybrid?
with some
0.0 0.1 0.2 0.3 0.4
500
1000
1500
2000
2500
3000
1-‐-‐
the lightest hybrid supermultiplet ?
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
mπ ~ 700 MeV
1S
2S
3S?
1D
2D?1G?
1P
2P
1F
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0-‐+
1-‐-‐2-‐+ 1-‐+
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Does QCD predict light hybrid mesons?
YES
Does QCD predict light hybrid mesons?
YES
* Light hybrid mesons may be observed only for heavy quark masses, risk of large hadronic widths has not been determined. The Hadron Spectrum Collaboration offers no guarantee that they can be produced in photoproduction.
*
models in light of what we’ve seen
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
flux-‐tube
1-‐+ 0+-‐ 2+-‐
bag
1-‐+ 0+-‐ 2+-‐
quasi-‐gluon1-‐-‐ “S-‐wave”
1-‐+ 0+-‐ 2+-‐ 0-‐-‐
quasi-‐gluon1+-‐ “P-‐wave”
1-‐+ 0+-‐ 2+-‐
exotic state degeneracy pattern
✘? ✔?✔? ✘✘
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0-‐+
1-‐-‐2-‐+ 1-‐+
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
have the ‘right’ complete lightest hybrid supermultiplet
* Light hybrid mesons may be observed only for heavy quark masses, risk of large hadronic widths has not been determined. The Hadron Spectrum Collaboration offers no guarantee that they can be produced in photoproduction.
addressing the small print
calculate at lighter quark masses increased computational cost
just a matter of time ...
* Light hybrid mesons may be observed only for heavy quark masses, risk of large hadronic widths has not been determined. The Hadron Spectrum Collaboration offers no guarantee that they can be produced in photoproduction.
addressing the small print
observing states as decaying resonances
scattering of composite objects in non-‐perturbative field theory !
* Light hybrid mesons may be observed only for heavy quark masses, risk of large hadronic widths has not been determined. The Hadron Spectrum Collaboration offers no guarantee that they can be produced in photoproduction.
addressing the small print
observing states as decaying resonances
scattering of composite objects in non-‐perturbative field theory !
-70
-60
-50
-40
-30
-20
-10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
HooglandLosty
CohenDurusoyex
pt.
-15
-10
-5
0
5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
HooglandLosty
CohenDurusoyex
pt.
Isospin=2 ππ scattering
* Light hybrid mesons may be observed only for heavy quark masses, risk of large hadronic widths has not been determined. The Hadron Spectrum Collaboration offers no guarantee that they can be produced in photoproduction.
addressing the small print
observing states as decaying resonances
scattering of composite objects in non-‐perturbative field theory !
-70
-60
-50
-40
-30
-20
-10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
HooglandLosty
CohenDurusoyex
pt.
-15
-10
-5
0
5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
HooglandLosty
CohenDurusoyex
pt.
Isospin=2 ππ scattering
0
0.2
0.4
0.6
0.8
1
400 600 800 1000 1200 1400
0
0.2
0.4
0.6
0.8
1
400 600 800 1000 1200 1400
0
0.2
0.4
0.6
0.8
1
400 600 800 1000 1200 1400
0
0.2
0.4
0.6
0.8
1
400 600 800 1000 1200 1400
mπ=481MeV
mπ=421MeV
mπ=330MeV
mπ=290MeV
Isospin=1 ππ scattering
Feng, Jansen, Renner
* Light hybrid mesons may be observed only for heavy quark masses, risk of large hadronic widths has not been determined. The Hadron Spectrum Collaboration offers no guarantee that they can be produced in photoproduction.
addressing the small print
determining coupling to photons is relatively straighforward
t-‐channel meson exchange
p N
γM’
M
production modeling
* Light hybrid mesons may be observed only for heavy quark masses, risk of large hadronic widths has not been determined. The Hadron Spectrum Collaboration offers no guarantee that they can be produced in photoproduction.
addressing the small print
determining coupling to photons is relatively straighforward
t-‐channel meson exchange
p N
γM’
M
production modelingγ
M’
M
photocoupling / transition form-‐factor
lattice calculation of this
* Light hybrid mesons may be observed only for heavy quark masses, risk of large hadronic widths has not been determined. The Hadron Spectrum Collaboration offers no guarantee that they can be produced in photoproduction.
addressing the small print
determining coupling to photons is relatively straighforward
t-‐channel meson exchange
p N
γM’
M
production modelingγ
M’
M
photocoupling / transition form-‐factor
lattice calculation of this0 1 2 3 4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Q2 / GeV
V(Q
2 )
CLEO ‘08
p = 000
p = 100
e.g. in charmonium
0 1 2 3 4-0.1
0.1
0.2
0.3
0.4
0.5
0.6
0
CLEO ‘08PDG ‘08
p = 000
p = 100
Q2 / GeV
V(Q
2 )
“Isoscalar meson spectroscopy from lattice QCD” -‐ arXiv:1102.4299 [hep-‐lat] (2011) (PRD in press)“The phase-‐shift of isospin-‐2 ππ scattering from lattice QCD” -‐ PRD.83.071504 (2011)“Toward the excited meson spectrum of dynamical QCD” -‐ PRD.82.034508 (2010)“Highly excited and exotic meson spectrum from dynamical lattice QCD” -‐ PRL.103.262001 (2009)“A novel quark-‐field creation operator construction for hadronic physics in lattice QCD” -‐ PRD.80.054506 (2009)
Robert Edwards (JLab)Balint Joo (JLab)David Richards (JLab)Christopher Thomas (JLab)Mike Peardon (Trinity Coll., Dublin)
for the Hadron Spectrum Collaboration
Does QCD predict light hybrid mesons?
Jozef DudekOld Dominion University & Jefferson Lab
isoscalar mesons
isovector correlator :
isoscalar mesons
isovector correlator :
isoscalar (with just light quarks) correlator :
-‐2
isoscalar mesons
isovector correlator :
isoscalar (with just light quarks) correlator :
-‐2 noisy
need inversion from all t
GPUs ideal for the ‘grunt’ work
isoscalar mesons
isoscalar (with light & strange) :
-‐2
-‐
⎧｜
⎩
⎫｜
⎭｜｜
｜｜
diagonalising gives the mixing
-‐√2
-‐√2
isoscalar spectrum
ETMC (2009) [2-‐flavour, extrap. to phys. quark mass]ρ/ω splitting of 27(10) MeV
very few results due to the difficulty of calculation
C. Michael et al (UKQCD, 2001) [heavy quarks, 2-‐flavour theory]found f1/a1 , b1/h1 , ρ/ω splittings consistent with zero
isoscalar spectrum
0.5
1.0
1.5
2.0
2.5
exotics
isoscalar
isovector
YM glueball
negative parity positive parity
M / GeV
η
η’
mπ ~ 420 MeV
RBC/UKQCD (2010)
ETMC (2009) [2-‐flavour, extrap. to phys. quark mass]ρ/ω splitting of 27(10) MeV
very few results due to the difficulty of calculation
C. Michael et al (UKQCD, 2001) [heavy quarks, 2-‐flavour theory]found f1/a1 , b1/h1 , ρ/ω splittings consistent with zero
isoscalar spectrum
0.5
1.0
1.5
2.0
2.5
exotics
isoscalar
isovector
YM glueball
negative parity positive parity
isoscalar spectrum
0.5
1.0
1.5
2.0
2.5
exotics
isoscalar
isovector
YM glueball
negative parity positive parity
isoscalar spectrum
0.5
1.0
1.5
2.0
2.5
exotics
isoscalar
isovector
YM glueball
negative parity positive parity
0.0 0.1 0.2 0.3 0.4
500
1000
1500
2000
2500
3000
0.0 0.1 0.2 0.3 0.4
500
1000
1500
2000
2500
3000
0.0 0.1 0.2 0.3 0.4
500
1000
1500
2000
2500
3000
1D
1F1-‐+
M / GeV
level ordering ?
mπ ~ 4
00 MeV
mπ ~ 7
00 MeV
real* resonances
but we can’t be satisfied with this ...
APS April meeting 2011
*complex
real* resonances
but we can’t be satisfied with this ...
APS April meeting 2011
*complex
the spectrum should not be this simple
enhancements in the meson-‐meson scattering continuum
excited states should be resonances
real* resonances
but we can’t be satisfied with this ...
in finite volume only discrete meson-‐meson states
but we aren’t seeing them !
APS April meeting 2011
*complex
the spectrum should not be this simple
enhancements in the meson-‐meson scattering continuum
excited states should be resonances
real* resonances
but we can’t be satisfied with this ...
in finite volume only discrete meson-‐meson states
but we aren’t seeing them !
APS April meeting 2011
*complex
the spectrum should not be this simple
enhancements in the meson-‐meson scattering continuum
excited states should be resonances
0.4
0.6
0.8
1.0
1.2
1.4
1.6
increasingvolume
AB
real* resonances
but we can’t be satisfied with this ...
in finite volume only discrete meson-‐meson states
but we aren’t seeing them !
APS April meeting 2011
*complex
the spectrum should not be this simple
enhancements in the meson-‐meson scattering continuum
excited states should be resonances
0.4
0.6
0.8
1.0
1.2
1.4
1.6
increasingvolume
AB
our operators closely resemble single hadrons ...
and not meson-‐meson pairs ~
28
parity doubling & chiral symmetry restoration ?
0.0 0.1 0.2 0.3 0.4
500
1000
1500
2000
2500
3000
0.0 0.1 0.2 0.3 0.4
500
1000
1500
2000
2500
3000
0.0 0.1 0.2 0.3 0.4
500
1000
1500
2000
2500
3000
1-‐-‐
0-‐+
2-‐+
overlaps with decreasing quark mass
cubic complications ...
integer spin not a good quantum number
restricted rotational symmetry of a cube
APS April meeting 2011
cubic complications ...
integer spin not a good quantum number
restricted rotational symmetry of a cube
APS April meeting 2011
E
cubic complications ...
integer spin not a good quantum number
restricted rotational symmetry of a cube
APS April meeting 2011
⎭⎬⎫E
cubic complications ...
integer spin not a good quantum number
restricted rotational symmetry of a cube
APS April meeting 2011
⎭⎬⎫ ⎫ ⎬ ｜ ⎭｜
E
cubic complications ...
‘solved’ by careful operator construction
APS April meeting 2011
construct operators of definite J in the continuum
“subduce” into the cubic group irreps
if the rotational symmetry is “restored”and then
operators respect cubic symmetry, but are ‘preconditioned’ to be J-‐diagonal
... but does it work in practice ?
cubic complications ...
APS April meeting 2011
0.6
0.8
1.0
1.2
1.4
1.6
(26)
clear dominance of a single spin for each state
J=1
J=3
J=4
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