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Excited light meson spectroscopy from lattice QCD
With Jo Dudek, Robert Edwards, Mike Peardon, Bálint Joó, David Richards and the Hadron Spectrum Collaboration
Christopher Thomas, Jefferson Lab
PANIC11, MIT, Cambridge, MA, July 2011
Outline
1
• Introduction and motivation
• Excited isoscalar mesons
• Energy-dependent I=2 phase shift
• Summary and outlook
PR D83, 071504 (2011)PR D83, 111502 (2011)
Motivation
Upcoming experimental efforts in light meson sector (and charmonium)
2
GlueX and CLAS12 (JLab), BESIII, COMPASS, PANDA, ...
Motivation
Upcoming experimental efforts in light meson sector (and charmonium)
Quark-antiquark pair:
Parity: P = (-1)(L+1)
Charge Conj Sym: C = (-1)(L+S)
JPC = 0- + , 0+ + , 1- - , 1+ + , 1+ - , 2- - , 2+ + , 2- +, …
L
L2S+1LJ
½½
J = L S
3
GlueX and CLAS12 (JLab), BESIII, COMPASS, PANDA, ...
Probe low energy d.o.f. of QCD
Motivation
Upcoming experimental efforts in light meson sector (and charmonium)
Quark-antiquark pair:
Parity: P = (-1)(L+1)
Charge Conj Sym: C = (-1)(L+S)
JPC = 0- + , 0+ + , 1- - , 1+ + , 1+ - , 2- - , 2+ + , 2- +, …
L
L2S+1LJ
Exotics (JPC = 1 - +, 2 + -, ...)? – can’t just be a pair
e.g. hybrids, multi-mesons
½½
J = L S
4
GlueX and CLAS12 (JLab), BESIII, COMPASS, PANDA, ...
Probe low energy d.o.f. of QCD
Motivation
Upcoming experimental efforts in light meson sector (and charmonium)
Quark-antiquark pair:
Parity: P = (-1)(L+1)
Charge Conj Sym: C = (-1)(L+S)
JPC = 0- + , 0+ + , 1- - , 1+ + , 1+ - , 2- - , 2+ + , 2- +, …
L
L2S+1LJ
Exotics (JPC = 1 - +, 2 + -, ...)? – can’t just be a pair
e.g. hybrids, multi-mesons
½½
J = L S
5
GlueX and CLAS12 (JLab), BESIII, COMPASS, PANDA, ...
Motivation
Photoproduction at GlueX/CLAS12 (JLab @ 12 GeV)– systematic study of light mesons, particular interest in exotics
JLab
6
Motivation
Photoproduction at GlueX/CLAS12 (JLab @ 12 GeV)– systematic study of light mesons, particular interest in exotics
JLab
7
Use Lattice QCD to extract excited spectrum and photocouplings
10
Isoscalars
ms = mu = md [SU(3) sym]– eigenstates are octet, singlet
Isoscalars (I = 0) e.g. , ’, , Probe annihilation dynamics in QCD
11
Isoscalars
ms = mu = md [SU(3) sym]– eigenstates are octet, singlet
ms ≠ mu = md – physical states are a mixture
‘Ideal mixing’
Isoscalars (I = 0) e.g. , ’, , Probe annihilation dynamics in QCD
12
Isoscalars
ms = mu = md [SU(3) sym]– eigenstates are octet, singlet
ms ≠ mu = md – physical states are a mixture
‘Ideal mixing’
In general
Isoscalars (I = 0) e.g. , ’, , Probe annihilation dynamics in QCD
13
Isoscalars
ms = mu = md [SU(3) sym]– eigenstates are octet, singlet
ms ≠ mu = md – physical states are a mixture
‘Ideal mixing’
Experimentally , (1--) and f2(1270), f2’(1525) (2++) – close to ‘ideal’
, ’ (0-+) – closer to octet-singlet
In general
Isoscalars (I = 0) e.g. , ’, , Probe annihilation dynamics in QCD
14
Isoscalars
ms = mu = md [SU(3) sym]– eigenstates are octet, singlet
ms ≠ mu = md – physical states are a mixture
‘Ideal mixing’
Experimentally , (1--) and f2(1270), f2’(1525) (2++) – close to ‘ideal’
, ’ (0-+) – closer to octet-singlet
In general Can also mix with glueballs
Isoscalars (I = 0) e.g. , ’, , Probe annihilation dynamics in QCD
Calculate energies and matrix elements (“overlaps”, Z’s) from correlation functions of meson interpolating fields
Spectroscopy on the lattice
15
Calculate energies and matrix elements (“overlaps”, Z’s) from correlation functions of meson interpolating fields
Spectroscopy on the lattice
16
Construct operators which only overlap with one spin in the continuum limit
Here up to 3 derivs and p = 0
definite JPC
‘Distillation’ technology for constructing on lattice PR D80 054506 (2009)
Calculate energies and matrix elements (“overlaps”, Z’s) from correlation functions of meson interpolating fields
Spectroscopy on the lattice
17
Construct operators which only overlap with one spin in the continuum limit
Here up to 3 derivs and p = 0
definite JPC
‘Distillation’ technology for constructing on lattice PR D80 054506 (2009)
Variational Method
18
Large basis of operators matrix of correlators
Generalised eigenvector problem:
Variational Method
19
Large basis of operators matrix of correlators
Generalised eigenvector problem:
Eigenvalues energies (t >> t0)
Variational Method
20
Large basis of operators matrix of correlators
Generalised eigenvector problem:
Eigenvalues energies
Also optimal linear combination of operators to overlap on to a state
Z(n) related to eigenvectors
(t >> t0)
Variational Method
21
Large basis of operators matrix of correlators
Generalised eigenvector problem:
Eigenvalues energies
Also optimal linear combination of operators to overlap on to a state
Z(n) related to eigenvectors
(t >> t0)
Var. method uses orthog of eigenvectors; don’t just rely on separating energies
23
Isoscalars in LQCD
Use variational method with large basis of operators
Basis doubled in size c.f. isovectors:
No glueball ops for now
24
Isoscalars in LQCD
Disconnected Wick contractionsq
q
q
q
q
q
Use variational method with large basis of operators
Basis doubled in size c.f. isovectors:
No glueball ops for now
JLab
25
Isoscalars in LQCD
Disconnected Wick contractionsq
q
q
q
q
q
Use variational method with large basis of operators
Basis doubled in size c.f. isovectors:
No glueball ops for now
Use GPUs for some parts of the computations
JLab
26
Isoscalars in LQCD
Disconnected Wick contractionsq
q
q
q
q
q
Use variational method with large basis of operators
Basis doubled in size c.f. isovectors:
No glueball ops for now
Use GPUs for some parts of the computations
Anisotropic lattices (as/at = 3.5), as 0.12 fm; 163 (2.0 fm)
Dynamical, Nf = 2+1, M 400 MeV
Lattice details in: PR D78, 054501; PR D79, 034502
27
Isoscalars
163 (Ls 2.0 fm)
PR D82, 034508 (2010)
Morningstar and Peardon PR D60, 034509 (1999)
PR D83, 111502 (2011)
28
Isoscalars
163 (Ls 2.0 fm)
PR D82, 034508 (2010)
Morningstar and Peardon PR D60, 034509 (1999)
PR D83, 111502 (2011)
29
Isoscalars
163 (Ls 2.0 fm)
First light isoscalar exotics in LQCD
PR D82, 034508 (2010)
Morningstar and Peardon PR D60, 034509 (1999)
PR D83, 111502 (2011)
30
Isoscalars
163 (Ls 2.0 fm)
First light isoscalar exotics in LQCD
PR D82, 034508 (2010)
Morningstar and Peardon PR D60, 034509 (1999)
PR D83, 111502 (2011)
S-wave
L
L½
½
J = L S
31
Isoscalars
163 (Ls 2.0 fm)
First light isoscalar exotics in LQCD
PR D82, 034508 (2010)
Morningstar and Peardon PR D60, 034509 (1999)
PR D83, 111502 (2011)
S-wave
L
L½
½
J = L S
- mass splitting = 21(5) MeV
32
Isoscalars
163 (Ls 2.0 fm)
First light isoscalar exotics in LQCD
PR D82, 034508 (2010)
Morningstar and Peardon PR D60, 034509 (1999)
PR D83, 111502 (2011)
S-wave
P-wave
L
L½
½
J = L S
- mass splitting = 21(5) MeV
33
Isoscalars
163 (Ls 2.0 fm)
First light isoscalar exotics in LQCD
PR D82, 034508 (2010)
Morningstar and Peardon PR D60, 034509 (1999)
PR D83, 111502 (2011)
S-wave
P-wave
D-wave
L
L½
½
J = L S
- mass splitting = 21(5) MeV
34
Isoscalars
163 (Ls 2.0 fm)
First light isoscalar exotics in LQCD
PR D82, 034508 (2010)
Morningstar and Peardon PR D60, 034509 (1999)
PR D83, 111502 (2011)
S-wave
P-wave
D-wave
Large overlap with op [Di, Dj] F
L
L½
½
J = L S
- mass splitting = 21(5) MeV
35
Isoscalars
163 (Ls 2.0 fm)
First light isoscalar exotics in LQCD
PR D82, 034508 (2010)
Morningstar and Peardon PR D60, 034509 (1999)
PR D83, 111502 (2011)More interpretation of isovector and isoscalar results:“lowest hybrid meson supermultiplet” arXiv:1106.5515
S-wave
P-wave
D-wave
Large overlap with op [Di, Dj] F
L
L½
½
J = L S
- mass splitting = 21(5) MeV
Isoscalars
PR D82, 034508 (2010)
Morningstar and Peardon PR D60, 034509 (1999)
PR D83, 111502 (2011)
36
163 (Ls 2.0 fm)
Isoscalars
PR D82, 034508 (2010)
Morningstar and Peardon PR D60, 034509 (1999)
PR D83, 111502 (2011)
37
Most close to ideally mixed
163 (Ls 2.0 fm)
Isoscalars
PR D82, 034508 (2010)
Morningstar and Peardon PR D60, 034509 (1999)
PR D83, 111502 (2011)
38
Most close to ideally mixed
But - ’ = 42(1) , f1 – f1’ = 31(2) , 1-+ exotics
163 (Ls 2.0 fm)
What about multi-particle states?
41
Cubic box with periodic boundary conditions
Continuous spectrum
Infinite Volume
2m E
2m E
Finite Volume
Quantised momenta
Discrete spectrum
Infinite Volume
Finite Volume
What about multi-particle states?
43
Boxes – extracted meson levels (I=1)
Dashed lines – non-interacting two-meson levels
Nf = 3, M 700 MeV
What about multi-particle states?
44
Boxes – extracted meson levels (I=1)
No clear evidence for two-meson states
Dashed lines – non-interacting two-meson levels
Need ops that ‘look like’ two-mesons
Nf = 3, M 700 MeV
Scattering in a box
45
Euclidean time: can’t directly study dynamical properties like widths
Lüscher: (elastic) energy shifts in finite volume phase shift
Scattering in a box
46
2m E
Euclidean time: can’t directly study dynamical properties like widths
Lüscher: (elastic) energy shifts in finite volume phase shift
Scattering in a box
47
Map out phase shift resonance parameters (mass, width)2m E
Euclidean time: can’t directly study dynamical properties like widths
Lüscher: (elastic) energy shifts in finite volume phase shift
Extract phase shift at discrete E
I=2 spectrum
48
M 400 MeV
PR D83, 071504 (2011)
+ similar diagrams
‘Distillation’ for efficient computation
PR D80 054506 (2009)
I=2 spectrum
49
M 400 MeV
PR D83, 071504 (2011)
+ similar diagrams
‘Distillation’ for efficient computation
PR D80 054506 (2009)
I=2 spectrum
50
M 400 MeV
PR D83, 071504 (2011)
+ similar diagrams
‘Distillation’ for efficient computation
PR D80 054506 (2009)
Summary and Outlook
55
• Extensive isoscalar meson spectrum
• Exotics and non-exotic hybrids, high spin, excited states
• Flavour mixing angles
• Multi-meson operators – I=2 phase shift mapped out
Summary
Summary and Outlook
56
• Extensive isoscalar meson spectrum
• Exotics and non-exotic hybrids, high spin, excited states
• Flavour mixing angles
• Multi-meson operators – I=2 phase shift mapped out
Summary
• Include glueball operators; A1++ (0++) channel
• Other scattering channels – map out resonances
• Lighter pion masses, larger volumes, ...
Outlook