robert edwards jefferson lab - thomas jefferson national … · 2012-03-12 · determining the...
TRANSCRIPT
Determining the Hadron Spectrum Using Lattice QCD
Robert Edwards Jefferson Lab
Twin Approaches to Confinement Physics
2012
Collaborators (Hadron Spectrum Collaboration):
J. Dudek, P. Guo, B. Joo, D. Richards (JLab), S. Wallace (Maryland)
N. Mathur (Tata), L. Liu, M. Peardon, S. Ryan, C. Thomas (Trinity College)
Determining the Hadron Spectrum Using Lattice QCD
Robert Edwards Jefferson Lab
Twin Approaches to Confinement Physics
2012
Collaborators (Hadron Spectrum Collaboration):
J. Dudek, P. Guo, B. Joo, D. Richards (JLab), S. Wallace (Maryland)
N. Mathur (Tata), L. Liu, M. Peardon, S. Ryan, C. Thomas (Trinity College)
Recent publications:
“Hybrid baryons”, in press PRD, 1201.2349
“Helicity operators for mesons in flight”, PRD85, 1107.1930
“Lightest hybrid meson supermultiplet”, PRD84, 1106.5515
“Excited state baryon spectroscopy”, PRD84, 1104.5152
“Isoscalar meson spectroscopy”, PRD83, 1102.4299
“Phase shift of isospin-2 scattering”, PRD83, 1011.6352
“Toward the excited meson spectrum”, PRD82, 1004.4930
“Highly excited and exotic meson spectrum”, PRL103, 0909.0200
Where are the “Missing” Baryon Resonances?
3
• What are collective modes?
• Is there “freezing” of degrees of freedom?
• What is the structure of the states?
• Where is the glue?
Where are the “Missing” Baryon Resonances?
4
• What are collective modes?
• Is there “freezing” of degrees of freedom?
• What is the structure of the states?
• Where is the glue?
PDG uncertainty on
B-W mass
Nucleon & Delta spectrum
QM predictions
Where are the “Missing” Baryon Resonances?
5
• What are collective modes?
• Is there “freezing” of degrees of freedom?
• What is the structure of the states?
• Where is the glue?
PDG uncertainty on
B-W mass
Nucleon & Delta spectrum
2 2 1
QM predictions
1 1 0
Where are the “Missing” Baryon Resonances?
6
• What are collective modes?
• Is there “freezing” of degrees of freedom?
• What is the structure of the states?
• Where is the glue?
PDG uncertainty on
B-W mass
Nucleon & Delta spectrum
2 2 1
QM predictions
4 5 3 1
???
1 1 0 2 3 2 1
???
Spectrum from variational method
Matrix of correlators
“Rayleigh-Ritz method”
Diagonalize: eigenvalues ! spectrum
eigenvectors ! spectral “overlaps” Zin
Two-point correlator
9
Spectrum from variational method
Matrix of correlators
“Rayleigh-Ritz method”
Diagonalize: eigenvalues ! spectrum
eigenvectors ! spectral “overlaps” Zin
Two-point correlator
10
Each state optimal combination of ©i
Spectrum from variational method
Matrix of correlators
“Rayleigh-Ritz method”
Diagonalize: eigenvalues ! spectrum
eigenvectors ! spectral “overlaps” Zin
Benefit: orthogonality for near degenerate states
Two-point correlator
11
Each state optimal combination of ©i
Baryon operators
Construction : permutations of 3 objects
13
• Symmetric: •e.g., uud+udu+duu
• Antisymmetric: •e.g., uud-udu+duu-…
• Mixed: (antisymmetric & symmetric) •e.g., udu - duu & 2duu - udu - uud
1104.5152
Baryon operators
Construction : permutations of 3 objects
14
• Symmetric: •e.g., uud+udu+duu
• Antisymmetric: •e.g., uud-udu+duu-…
• Mixed: (antisymmetric & symmetric) •e.g., udu - duu & 2duu - udu - uud
1104.5152
Multiplication rules: • SymmetricAntisymmetric ! Antisymmetric
• MixedxMixed ! Symmetric©Antisymmetric©Mixed
•….
Baryon operators
Construction : permutations of 3 objects
15
• Symmetric: •e.g., uud+udu+duu
• Antisymmetric: •e.g., uud-udu+duu-…
• Mixed: (antisymmetric & symmetric) •e.g., udu - duu & 2duu - udu - uud
1104.5152
Multiplication rules: • SymmetricAntisymmetric ! Antisymmetric
• MixedxMixed ! Symmetric©Antisymmetric©Mixed
•….
Color antisymmetric ! Require Space x [Flavor x Spin] symmetric
Baryon operators
Construction : permutations of 3 objects
16
• Symmetric: •e.g., uud+udu+duu
• Antisymmetric: •e.g., uud-udu+duu-…
• Mixed: (antisymmetric & symmetric) •e.g., udu - duu & 2duu - udu - uud
1104.5152
Multiplication rules: • SymmetricAntisymmetric ! Antisymmetric
• MixedxMixed ! Symmetric©Antisymmetric©Mixed
•….
©JM áCGC0s
¢i;j;k
h~Dii
h~Dij[ª]k
Space: couple covariant derivatives onto
single-site spinors - build any J,M
Color antisymmetric ! Require Space x [Flavor x Spin] symmetric
Baryon operators
Construction : permutations of 3 objects
17
• Symmetric: •e.g., uud+udu+duu
• Antisymmetric: •e.g., uud-udu+duu-…
• Mixed: (antisymmetric & symmetric) •e.g., udu - duu & 2duu - udu - uud
Classify operators by permutation symmetries:
• Leads to rich structure 1104.5152
Multiplication rules: • SymmetricAntisymmetric ! Antisymmetric
• MixedxMixed ! Symmetric©Antisymmetric©Mixed
•….
©JM áCGC0s
¢i;j;k
h~Dii
h~Dij[ª]k
Space: couple covariant derivatives onto
single-site spinors - build any J,M
Color antisymmetric ! Require Space x [Flavor x Spin] symmetric
Baryon operator basis
All possible 3-quark operators up to two covariant derivatives: some JP
19
Spatial symmetry classification: JP #ops E.g., spatial symmetries
J=1/2- 32 N 2PM ½- N 4PM ½-
J=3/2- 36 N 2PM 3/2- N 4PM 3/2-
J=5/2- 19 N 4PM 5/2-
J=1/2+ 32 N 2SS ½+ N 2SM ½+ N 2PM ½+
N 4DM½+
N 2PA ½+ N 4PM ½+
J=3/2+
36 N 2DS3/2+
N 2DM3/2+ N 2PA 3/2+
N 2PM 3/2+
N 4SM3/2+ N 4DM3/2+
N 4PM 3/2+
J=5/2+ 19 N 2DS5/2+ N 2DM5/2+
N 4DM5/2+
N 4PM 5/2+
J=7/2+ 4 N 4DM7/2+
e.g., Nucleons: N 2S+1L¼ JP
Baryon operator basis
All possible 3-quark operators up to two covariant derivatives: some JP
20
Spatial symmetry classification: JP #ops E.g., spatial symmetries
J=1/2- 32 N 2PM ½- N 4PM ½-
J=3/2- 36 N 2PM 3/2- N 4PM 3/2-
J=5/2- 19 N 4PM 5/2-
J=1/2+ 32 N 2SS ½+ N 2SM ½+ N 2PM ½+
N 4DM½+
N 2PA ½+ N 4PM ½+
J=3/2+
36 N 2DS3/2+
N 2DM3/2+ N 2PA 3/2+
N 2PM 3/2+
N 4SM3/2+ N 4DM3/2+
N 4PM 3/2+
J=5/2+ 19 N 2DS5/2+ N 2DM5/2+
N 4DM5/2+
N 4PM 5/2+
J=7/2+ 4 N 4DM7/2+
e.g., Nucleons: N 2S+1L¼ JP
By far the largest operator basis ever used for
such calculations
Hold on, what are those PM ??
Operators featuring explicit glue
At two derivatives & L=1, have operators featuring a chromomagnetic B field
21
Operators featuring explicit glue
At two derivatives & L=1, have operators featuring a chromomagnetic B field
22
Occurs only in Mixed spatial symmetry with L=1 ! PM with positive parity
Hybrid operator: is 0 unless in a nontrivial background gauge field A 0
Operators featuring explicit glue
At two derivatives & L=1, have operators featuring a chromomagnetic B field
23
Occurs only in Mixed spatial symmetry with L=1 ! PM with positive parity
Note: Antisymmetric PA operators not of this form. Is not 0 if A = 0
Hybrid operator: is 0 unless in a nontrivial background gauge field A 0
Just a basis
Spectral decomposition
Choose a random linear combination of operators
Recall: two-point correlator matrix
26
Just a basis
Spectral decomposition
Choose a random linear combination of operators
Recall: two-point correlator matrix
27
Spectral “overlaps” Zin change
Energies En unchanged
Spin identified Nucleon & Delta spectrum
m¼ ~ 396MeV
28
arXiv:1104.5152, 1201.2349 Statistical errors < 2%
Spin identified Nucleon & Delta spectrum
m¼ ~ 396MeV
29
arXiv:1104.5152, 1201.2349 Statistical errors < 2%
Spin identified Nucleon & Delta spectrum
m¼ ~ 396MeV
30
arXiv:1104.5152, 1201.2349 Statistical errors < 2%
2 2 1 1 1
Spin identified Nucleon & Delta spectrum
m¼ ~ 396MeV
31
arXiv:1104.5152, 1201.2349 Statistical errors < 2%
2 2 1 1 1
4 5 3 1 2 3 2 1
Spin identified Nucleon & Delta spectrum
m¼ ~ 396MeV
32
arXiv:1104.5152, 1201.2349 Statistical errors < 2%
2 2 1 1 1
4 5 3 1 2 3 2 1
Spin identified Nucleon & Delta spectrum
m¼ ~ 396MeV
33
arXiv:1104.5152, 1201.2349 Statistical errors < 2%
2 2 1 1 1
4 5 3 1 2 3 2 1
??? ???
Spin identified Nucleon & Delta spectrum
m¼ ~ 396MeV
34
arXiv:1104.5152, 1201.2349 Statistical errors < 2%
2 2 1 1 1
4 5 3 1 2 3 2 1
??? ???
SU(6)xO(3) counting
No parity doubling
Spin identified Nucleon & Delta spectrum
m¼ ~ 396MeV
35
arXiv:1104.5152, 1201.2349 Discern structure: spectral overlaps
Spin identified Nucleon & Delta spectrum
m¼ ~ 396MeV
36
arXiv:1104.5152, 1201.2349 Discern structure: spectral overlaps
[56,0+]
S-wave
[56,0+]
S-wave
Spin identified Nucleon & Delta spectrum
m¼ ~ 396MeV
37
arXiv:1104.5152, 1201.2349 Discern structure: spectral overlaps
[56,0+]
S-wave
[56,0+]
S-wave [70,1-]
P-wave
[70,1-]
P-wave
Spin identified Nucleon & Delta spectrum
39
Discern structure: spectral overlaps
2SS 2SM 4SM 2DS
2DM 4DM
2PA [56’,0+], [70,0+], [56,2+],
[70,2+], [20,1+]
13 levels/ops
Significant mixing in J+
Spin identified Nucleon & Delta spectrum
40
Discern structure: spectral overlaps
2SS 2SM 4SM 2DS
2DM 4DM
2PA [56’,0+], [70,0+], [56,2+],
[70,2+], [20,1+]
13 levels/ops
2SM 4SS 2DM
4DS [56’,0+], [70,0+],
[56,2+], [70,2+]
8 levels/ops
Significant mixing in J+
Spin identified Nucleon & Delta spectrum
41
2SS 2SM 4SM 2DS
2DM 4DM
2PA [56’,0+], [70,0+], [56,2+],
[70,2+], [20,1+]
13 levels/ops
2SM 4SS 2DM
4DS [56’,0+], [70,0+],
[56,2+], [70,2+]
8 levels/ops
No “freezing” of
degrees of
freedom
Hybrid baryons
42
Negative parity structure replicated: gluonic components (hybrid baryons)
[70,1+]
P-wave
[70,1-]
P-wave
Hybrid baryons
43
Negative parity structure replicated: gluonic components (hybrid baryons)
[70,1+]
P-wave
[70,1-]
P-wave
Predicted by Barnes & Close, 1983
See talk by J. Dudek
Hadronic decays
Plot the non-interacting meson levels as a guide
45
Current spectrum calculations:
no evidence of multi-particle levels
Hadronic decays
Plot the non-interacting meson levels as a guide
46
Current spectrum calculations:
no evidence of multi-particle levels
Require multi-particle operators
• (lattice) helicity construction
• annihilation diagrams
Hadronic decays
Plot the non-interacting meson levels as a guide
47
Current spectrum calculations:
no evidence of multi-particle levels
Require multi-particle operators
• (lattice) helicity construction
• annihilation diagrams
Extract δ(E) at discrete E
Spectrum of finite volume field
Solutions
Quantization condition when -L/2 < z < L/2
Same physics in 4 dim version (but messier)
Provable in a QFT (and relativistic)
Two spin-less bosons: Ã(x,y) = f(x-y) ! f(z)
The idea: 1 dim quantum mechanics
Finite volume scattering
49
E.g. just a single elastic resonance
e.g.
At some L , have discrete excited energies
•T-matrix amplitudes ! partial waves
• Finite volume energy levels E(L) $ δ(E)
Scattering in a periodic cubic box (length L)
• Discrete energy levels in finite volume
Resonances
1011.6352, 1203.????
Scattering of composite objects in non-perturbative field theory
isospin=2 ¼¼
δ0(E) & δ2(E)
Resonances
1011.6352, 1203.????
Scattering of composite objects in non-perturbative field theory m¼=481 MeV
m¼=421 MeV
m¼=330 MeV
m¼=290MeV
isospin=2 ¼¼
δ0(E) & δ2(E)
isospin=1 ¼¼
Feng, et.al, 1011.5288
sin2(δ1(E))
Resonances Scattering of composite objects in non-perturbative field theory m¼=481 MeV
m¼=421 MeV
m¼=330 MeV
m¼=290MeV
isospin=1 ¼¼
Feng, et.al, 1011.5288
Manifestation of “decay” in
Euclidean space
Can extract pole position
Resonances Scattering of composite objects in non-perturbative field theory m¼=481 MeV
m¼=421 MeV
m¼=330 MeV
m¼=290MeV
isospin=1 ¼¼
Feng, et.al, 1011.5288
g½¼¼
m¼2 (GeV2)
Extracted coupling: stable in pion mass
Stability a generic feature
of couplings??
Hadronic decays
54
Some candidates: determine phase shift
Somewhat elastic
S11! [N¼]S
+[N´]S ¢![N¼]P
Hadronic decays – the full job
55
Need a lattice program of “amplitude analysis” - lots of room for help!
Summary & prospects
Results for baryon excited state spectrum: • No “freezing” of degrees of freedom nor parity doubling
• Broadly consistent with non-relativistic quark model
• Extra bits interpreted as hybrid baryons • Add multi-particle ops ! baryon spectrum becomes denser
57
Summary & prospects
Results for baryon excited state spectrum: • No “freezing” of degrees of freedom nor parity doubling
• Broadly consistent with non-relativistic quark model
• Extra bits interpreted as hybrid baryons • Add multi-particle ops ! baryon spectrum becomes denser
58
Short-term plans: resonance determination! • Lighter pion masses (230MeV available) • Extract couplings in multi-channel systems (with ¼, ´, K…)
Summary & prospects
Results for baryon excited state spectrum: • No “freezing” of degrees of freedom nor parity doubling
• Broadly consistent with non-relativistic quark model
• Extra bits interpreted as hybrid baryons • Add multi-particle ops ! baryon spectrum becomes denser
59
T-matrix “poles” from Euclidean space?
Short-term plans: resonance determination! • Lighter pion masses (230MeV available) • Extract couplings in multi-channel systems (with ¼, ´, K…)
Summary & prospects
Results for baryon excited state spectrum: • No “freezing” of degrees of freedom nor parity doubling
• Broadly consistent with non-relativistic quark model
• Extra bits interpreted as hybrid baryons • Add multi-particle ops ! baryon spectrum becomes denser
60
T-matrix “poles” from Euclidean space?
Short-term plans: resonance determination! • Lighter pion masses (230MeV available) • Extract couplings in multi-channel systems (with ¼, ´, K…)
Yes! [with caveats] • Also complicated
• But all Minkowski information is there
Summary & prospects
Results for baryon excited state spectrum: • No “freezing” of degrees of freedom nor parity doubling
• Broadly consistent with non-relativistic quark model
• Extra bits interpreted as hybrid baryons • Add multi-particle ops ! baryon spectrum becomes denser
61
T-matrix “poles” from Euclidean space?
Short-term plans: resonance determination! • Lighter pion masses (230MeV available) • Extract couplings in multi-channel systems (with ¼, ´, K…)
Yes! [with caveats] • Also complicated
• But all Minkowski information is there
Optimistic: see confluence of methods (an “amplitude analysis”) • Develop techniques concurrently with decreasing pion mass