0-%012)+*%3#$4$5€¦ · $f"./+&! @;& 8&7$%"2$...

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


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)


1P?

“1S”

2


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)


1P?

2S

“1S”

2


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)


1P?

1D

2S

“1S”

2


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)


1P?

1F

1D

2S

“1S”

2


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)


hybrid mesons -‐ beyond the quark model

observed meson state flavor & JPC systematics suggest “constituent quarks”



exotic quantum numbers



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


flux-‐tube model0-‐+, 1-‐+, 2-‐+, 1-‐-‐

0+-‐, 1+-‐, 2+-‐, 1++roughly degenerate


flux-‐tube model0-‐+, 1-‐+, 2-‐+, 1-‐-‐


bag model 0-‐+, 1-‐+, 2-‐+, 1-‐-‐& others heavier


flux-‐tube model0-‐+, 1-‐+, 2-‐+, 1-‐-‐



massive quasi-‐gluons Coulomb gauge transverse (no 3-‐body) 0++, 1++, 2++, 1+-‐

0-‐-‐, 1-‐+, ...1-‐-‐ “S-‐wave”


flux-‐tube model0-‐+, 1-‐+, 2-‐+, 1-‐-‐




0-‐-‐, 1-‐+, ...1-‐-‐ “S-‐wave”

Coulomb gauge transverse (incl. 3-‐body)

0+-‐, (2+-‐)2, ...

0-‐+, 1-‐+, 2-‐+, 1-‐-‐

1+-‐ “P-‐wave”


flux-‐tube model0-‐+, 1-‐+, 2-‐+, 1-‐-‐


without much data -‐ nothing much to constrain them ...



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.



as a sum of QCD eigenstates




e.g. 1-‐-‐two-‐point correlator matrix




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

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-‐-‐


1-‐-‐

hybrid?

(spin-singlet)


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-‐-‐


hybrid?


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-‐-‐


hybrid?


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


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-‐-‐


hybrid?


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


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


YES


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


addressing the small print

calculate at lighter quark masses increased computational cost

just a matter of time ...



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





-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.


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


Feng, Jansen, Renner



determining coupling to photons is relatively straighforward

t-‐channel meson exchange

p N

γM’

M

production modeling





p N

γM’

M

production modelingγ

M’

M

photocoupling / transition form-‐factor

lattice calculation of this





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


Jozef DudekOld Dominion University & Jefferson Lab

isoscalar mesons

isovector correlator :

isoscalar mesons


isoscalar (with just light quarks) correlator :

-‐2

isoscalar mesons


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

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



*complex

the spectrum should not be this simple

enhancements in the meson-‐meson scattering continuum

excited states should be resonances

real* resonances


in finite volume only discrete meson-‐meson states

but we aren’t seeing them !


*complex




real* resonances





*complex




0.4

0.6

0.8

1.0

1.2

1.4

1.6

increasingvolume

AB

real* resonances





*complex




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






E





⎭⎬⎫E





⎭⎬⎫ ⎫ ⎬ ｜ ⎭｜

E


‘solved’ by careful operator construction


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 ?



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

0-%012)+*%3#$4$5€¦ · $f"./+&! @;& 8&7$%"2$...

Documents