The GlueX Exper iment and Lattice QCDThe GlueX Exper iment! GlueX will use r eal 9 GeV pho tons t o pho topr oduce mesons! vir tuall y no dat a on pho topr oduction of meson resonances

LHP ‘06 - GlueX & Lattice QCD - J. Dudek

The GlueX Experiment and Lattice QCD

Jo Dudek, Jefferson LabLHP ‘06


The Physics of GlueX

! GlueX will explore the meson spectrum with a mass reach over 2.5 GeV

! major feature is the search for exotic quantum-numbered mesons

! e.g. not accessible to a fermion-antifermion state

! likely origin for such states in QCD is hybrid mesons - i.e. quark-antiquark states with excited gluonic field

0!!

, 0+!

, 1!+

, 2+!

. . .JPC

=


The GlueX Experiment

! GlueX will use real 9 GeV photons to photoproduce mesons

! virtually no data on photoproduction of meson resonances exists

SLAC bubble chamber

19 GeV photons (1991)40 evts

3 2.4

CLAS

5.5 GeV photons (2005)

m(!!!) / GeV

4000 evts

m(!!!) / GeV1


GlueX Details

! GlueX will hugely surpass these statistics

! 106 !!! events per 10 MeV bin in 3 months running

! ~ 1 PetaByte per year

! detector designed to have good coverage over full 4!

! aids the required Partial Wave Analysis

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1 1.2 1.4 1.6 1.8 2 2.2 2.4{1++ 0+ "!s2++ 1+ "!D 2-+ 0+ f2!s0-+ 0+ f0!s

!X ! !2++

reducing model dependence actively researched


GlueX Photon Beam & Detector

this guy trying to work

out who stole the other

half of the detector

acceptance estimates


Exotics in Experiment

! bulk of relevant exotic searches done by E852 using a 18 GeV pion beam & dominantly

! !p ! !"N

!!

"

2++

1!+

60016,000

2++

1!+

3,000

1,000

!0"

a2

a2

1!+

1.0 1.4 1.8 1.0 1.4 1.8

!1(1400), #~400 MeV or non-

resonant interaction ?no clear sign of a resonance in the P-wave intensity


Exotics in E852

!p ! !!

""p

a2

?

1!+

2++

broad enhancement in

P-wave intensity

D-wave structure not

understood so phase

comparison unconstrained

taken at face value,

intensity gives

!1(1600), #~350 MeV

non-resonant origin

cannot be ruled out


Exotics in E852

! two analyses of , more recent has higher statistics

!p ! !!!p

1500

E852 (2001) grey points use a more truncated wave-set lacking some

waves2!+

claimed explanation of difference is !2(1670)

missing waves being assigned to exotic wave by PWA


E852 Exotics cont...

!p ! !!!!!p

1!+(b1!)S

2++(!")S

4++(!")D

1!+(b1!)S

phase

exotic enhancement in the 1.65 GeV region

low event statistics limit the PWA to a small

number of waves

1!+

! 2++


E852 Exotics cont...

!p ! "!!!p

1++(f1!)P

2!+(f1!)D

1!+(f1!)S

exotic enhancement in

the 1.7 GeV region


Exotics in Experiment

! E852 results suggestive, but situation unclear overall

! GlueX poised to continue the good work of hybrid-hunting with a new production mechanism and much greater statistics


Models of Gluonic Excitations

! the flux-tube model has historically dominated the field

! has a rather complete phenomenological coverage

! mass spectrum estimates (Isgur & Paton)

! hadronic decay widths (Isgur, Kokoski, Close, Page ...)

! photocouplings (Close & JJD)

!m !

!

1

r

"

⇒ “S+P” rule

AH

AC

!"

b

mq

! O(1)

mH ! 2 GeV

1!+

, 0+!

, 2+! + non-exotics

!1 $ ! b1

!1 $ ! "~


Lightest 1-+ from Lattice QCD

! summary of world simulation data

0 0.5 1 1.5m! / GeV

0

1

2

3

m!

1 / G

eV

m !m ss

quenched

NF=2, NF=3

NF=2+1

mostly old studies w/

coarse lattice spacings


Lightest 1-+ from Lattice QCD

! JLab effort over next two years aim to significantly improve this picture

two lattice spacings, as = 0.10, 0.125 fm

two volumes V = 2.4, 3.2 fm 1/at = 6 GeV

0 0.5 1 1.5m! / GeV

0

1

2

3

m!

1 / G

eV

m !m ss

dynamical (NF=2+1)

anisotropic Clover

dynamical

& partially quenched points


Wider Meson Spectrum

! GlueX will be a meson spectrometer of broad scope

! JLab lattice QCD spectrum program has same aim

! excited states in a given JPC via variational method

! large set of JPC using big operator basis

e.g. baryon sector

work by LHPC claims

9 excited states !

!!!

Dµ ! !!!

Dµ

!

D! !!!! !!Fµ!!+ two-meson style operators


Photocouplings

! GlueX will photoproduce mesons

! couplings virtually unknown even for conventional mesons - clear target for Lattice QCD predictions

!

p N

resonance, X

‘exchange’

meson, M

!!M |X"photocoupling


Lattice Method

! three-point functions with vector current

!(tf , t ; !pf , !q) =!

!x,!y

e!i!pf ·!xei!q·!y !"f (!x, tf )jµ(!y, t)"i(!0, 0)"

!!

n,m

e!Efn (tf!t)"0|!f (0)|fn("pf )#

!"fn(!pf )|jµ(0)|im(!pi)#

!"im(!pi)|"i(0)|0#e!Eint

transition

matrix element

covariant transition

matrix element to be

extracted

energies and overlap

factors extracted from

fits to two-point functions three-point function

calculation performed via a

sequential-sink construction

smeared interpolators!!!


Charmonium

! before calculating with light quarks for GlueX we’d like to test the technology

! charmonium is ideal

! excellent exptal data

! near-stable states

! quenched might be‘tolerable’

quenched aniso. %=3

1/at ~ 6 GeV

DWF (mcat ~ 0.15)

300 cfgs.


! transverse E1(Q2) and longitudinal C1(Q2)!S(!pS)|jµ(0)|V (!pV , r)" =

!!1(Q2)

!

E1(Q2)

"

!(Q2)"µ(!pV , r) # "(!pV , r).pS

#

pµV pV .pS # m2

V pµS

$

%

+C1(Q2)&

q2mV "(!pV , r).pS

"

pV .pS(pV + pS)µ # m2

SpµV # m2

V pµS

%

'

.

not used

in the fit

E1(Q2) = E1(0)

!

1 + Q2

!2

"

e!

Q2

16"2

PDG

CLEO

lat.

!c0 ! J/"#

!S(!pS)|jµ(0)|V (!pV , r)" =

E1(Q2)


! transverse E1(Q2), M2(Q2) and longitudinal C1(Q2) !A(!pA, rA)|jµ(0)|V (!pV , rV )" = i

4!

2!(Q2)"µ!"#(pA # pV )#$

$

!

E1(Q2)(pA + pV )"

"

2mA[""( !pA, rA).pV ]"!( !pV , rV ) + 2mV ["(!pV , rV ).pA]""!(!pA, rA)#

+ M2(Q2)(pA + pV )"

"

2mA[""( !pA, rA).pV ]"!( !pV , rV ) # 2mV ["(!pV , rV ).pA]""!(!pA, rA)#

+C1(Q2)

$

q2

"

# 4!(Q2)""!(!pA, rA)""(!pV , rV )

+ (pA + pV )"

%

(m2A # m2

V + q2)[""(!pA, rA).pV ] "!(!pV , rV ) + (m2A # m2

V # q2)["(!pV , rV ).pA] ""!( !pA, rA)&#

'

.

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Q2 (GeV

2)

-0.25

-0.2

-0.15

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-0.05

0

a tM

2(Q2 )

spat. pf = (000) !c1 snk.


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Q2 (GeV

2)

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0.35

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a tE

1(Q2 )



PDG phys. massPDG lat. massCLEO phys. massCLEO lat. mass

!c1 ! J/"#

E1(Q2) M2(Q2)


Summary

! GlueX is a major component of the JLab 12 GeV upgrade

! will exceed total world meson production data in a few years

! search for exotic mesons a main focus

! JLab lattice QCD program aligned with GlueX aims

! dynamical 2+1 anisotropic Clover lattices to be used for spectrum, decay and photocoupling studies at low pion masses


Hadronic Decays

! some recent lattice progress on this important topic

! Lüscher method study : Cook & Fiebig

! use volume dependence where m(!) + m(b1) < m(!1) or m(!) + m(a1) < m(&1)

quenched 103x24 & 123x24 with Wilson quarks

m(!) ~ 1800 MeV

very large extrapolation

to level crossing

0 0.5 1 1.5m! / GeV

0

1

2

3

m!

1 / G

eV

m !m ss

~ m b 1 + m !

~ m " + 2 m !

*


CLAS PWA

16,000

80,000

16,000

exotic maybe 1-2% of 1++ in pion prod, appears to be about 20% here


Hadronic Decays cont.

! some recent lattice progress on this important topic

! alternative approach due to Michael & McNeile

! tune quark masses to m(!) + m(b1) " m(!1)


Lightest 0+- from Lattice QCD


quenched

0 0.5 1 1.5m! / GeV

0

1

2

3

mb 0 /

GeV

m !m ss


Lightest 2+- from Lattice QCD


quenched

0 0.5 1 1.5m! / GeV

0

1

2

3

mb 2 /

GeV

m !m ss


Lattice QCD & model testing

! quark masses will decrease in the future, but even now we can make good use of lattice data

! we can compare lattice QCD calculations with ‘heavier’ quarks vs model calculations with ‘heavier’ quarks


Exotics in E852

! two analyses of , more recent has higher statistics

!p ! !!!p

1500

40,0002++(!")D1+

E852 (2001) grey points use a more truncated waveset lacking some

waves2!+

claimed explanation of difference is !2(1670)

leaking into exotic wave


0 2 4 6 8 10 12 14 16 18 20 22 24t

0.67

0.68

0.69

0.7

0.71

0.72

0.73

0.74

0.75

0.76

mef

f

g.s.

1st ex?

meff

Variational Method

! traditional method

! variational method e.g. baryon sector

work by LHPC

9 excited states !

g.s.

1st ex

2nd ex

3rd ex4th ex

Documents

The GlueX Exper iment and Lattice QCDThe GlueX Exper iment! GlueX will use r eal 9 GeV pho tons t o pho topr oduce mesons! vir tuall y no dat a on pho topr oduction of meson resonances