excited state spectroscopy from lattice qcd robert edwards jefferson lab cern 2010 texpoint fonts...
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Excited State Spectroscopy from Lattice QCD
Robert Edwards Jefferson Lab
CERN 2010
Collaborators:J. Dudek, B. Joo, M. Peardon, D. Richards, C. Thomas, S. WallaceAuspices of the Hadron Spectrum Collaboration
Spectroscopy
Spectroscopy reveals fundamental aspects of hadronic physics– Essential degrees of freedom?– Gluonic excitations in mesons - exotic states of
matter?
• New spectroscopy programs world-wide– E.g., BES III (Beijing), GSI/Panda (Darmstadt)– Crucial complement to 12 GeV program at JLab.
• Excited nucleon spectroscopy (JLab)• JLab GlueX: search for gluonic excitations.
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Nuclear Physics & Jefferson Lab
• Lab doubling beam energy to 12GeV• Adding new experimental Hall
JLab undergoing a major upgrade
Future Hall D
Excited states: anisotropy+operators+variational
• Anisotropic lattices with Nf=2+1 dynamical (clover)fermions– Temporal lattice spacing at < as (spatial lattice spacing)– High temporal resolution ! Resolve noisy & excited states– Major project within USQCD – Hadron Spectrum Collab.
• Extended operators– Sufficient derivatives ! nonzero overlap at origin
• Variational method:– Matrix of correlators ! project onto excited states
PRD 78 (2008) & PRD 79 (2009)
PRD 76 (2007), PRD 77 (2008), 0909.0200
PRD 72 (2005), PRD 72 (2005), 0907.4516 (PRD), 0909.0200
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Nf=2+1 Anisotropic Clover
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Nf = 2 + 1 (u,d + s)
Using at m & »=3.5 : as = 0.1227(3)fm, (at)-1 ~ 5.640 GeV
0803.3960 & 0810.3588
Spin and Operator Construction
0905.2160 (PRD), 0909.0200 (PRL), 1004.4930 (PRD)
Gamma matrices and derivatives in circular basis:Couple to build any J,M via usual CG
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Construct all possible operators up to 3 derivatives (3 units orbital angular momentum)
Only using symmetries of continuum QCD
Subduce onto lattice irreps: “remembers” J
Distillation
0905.2160 (PRD), 1002.0818, Bulava (thesis 2010)
Replace smearing with low rank approximation
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Gauge covariant, mom. conservation (source & sink) ! reduced “noise”
Matrix elements of vk(t) ! propagators, mesons, baryons, etc. Make correlators
Stochastic variants (lower cost)
Spectrum from variational method
Matrix of correlators
Diagonalize: eigenvalues ! spectrum eigenvectors ! wave function overlaps
Benefit: orthogonality for near degenerate states
Two-point correlator
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Determining spin on a cubic lattice?
Spin reducible on lattice
Might be dynamical degeneracies
T2 E T2 E T2 E
mass
T1 T2 E A2
Spin 1, 2, 3, or 4 ?
Spin reduction & (re)identification
Variational solution:
Continuum
Lattice
Method: Check if converse is true
Exotic matter
Suggests (many) exotics within range of JLab Hall D
Previous work: charmonium photo-production rates high
Current work: (strong) decays
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Vector isoscalars (I=0)
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Nf=2+1, m¼ ~ 400MeV, L~2fm
light-strange (ls) basis
I = 0 Must include all disconnected diagrams
Baryon Spectrum
“Missing resonance problem”• What are collective modes?• What is the structure of the states?
– Major focus of (and motivation for) JLab Hall B– Not resolved experimentally @ 6GeV
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PDG uncertainty on B-W mass
Nucleon spectrum
Strange Quark Baryons
Strange quark baryon spectrum poorly known
Future:• Narrow widths: easy(er) to extract (?)
¥ & : unknown spin & parities Widths are small
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Light quark baryons in SU(6)
Conventional non-relativistic construction:
6 quark states in SU(6)
Baryons
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Relativistic operator construction: SU(12)
Relativistic construction: 3 Flavors with upper/lower components
Times space (derivatives)
Color contraction is Antisymmetric ! Totally antisymmetric operators
Dirac
More operators than SU(6): mixes orbital ang. momentum & Dirac spin
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Orbital angular momentum via derivatives
0905.2160 (PRD), 0909.0200 (PRL), 1004.4930
Couple derivatives onto single-site spinors:Enough D’s – build any J,M
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Use all possible operators up to 2 derivatives (2 units orbital angular momentum)
Only using symmetries of continuum QCD
Nucleon & Delta Spectrum
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[56,2+]D-wave [70,1-]
P-wave
[70,1-]P-wave
[56,2+]D-wave
Change at lighter quark mass? Decays!
Suggests spectrum at least as dense as quark model
[70,2+]D-wave
[20,1+]P-wave
“Roper”?
Hadronic decays
Plot the non-interacting meson levels as a guide
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Current spectrum calculations:no evidence of multi-particle levels
Require multi-particle operators • (lattice) helicity construction • annihilation diagrams
Extract δ(E) at discrete E
Phase Shifts: demonstration¼¼ isospin=2 Extract δ0(E) at discrete E
No discernible pion mass dependence
Hardware: JLab GPU ClustersGPU clusters: ~530 cards
Quads 2.4 GHz Nehalem 48 GB memory / node 117 nodes x 4 GPUs -> 468 GPUs
Singles 2.4 GHz Nehalem 24 GB memory / node 64 nodes x 1 GPU -> 64 GPUs
Prospects
• Strong effort in excited state spectroscopy– New operator & correlator constructions ! high lying states– Finite volume extraction of resonance parameters – promising– Progress! Still much more to do
• Initial results for excited state spectrum:– Suggests baryon spectrum at least as dense as quark model– Suggests multiple exotic mesons within range of Jlab’s Hall D
• Resonance determination:– Start at heavy masses: have some “elastic scattering”– Use larger volumes & smaller pion masses (m¼ ~230MeV)
– Now: multi-particle operators & annihilation diagrams (gpu-s)– Need multi-channel finite-volume analysis for (in)elastic
scattering
• Future:– Transition FF-s, photo-couplings (0803.3020, 0902.2214)
Distillation: mesons
• Smearing in correlator: use low-rank approximation
• Correlator
• Factorizes: operators and perambulators
• A posteriori evaluation of C(2) after ¿arxiv:0905.2160
Perambulators
• Current calculation (243x128, m¼ ~ 230MeV)• Solve: [all space sites]• Perambulator
• High angular momentum (J = 4), want N = 128• All time-sources -> 64K inversions / config• Can construct all possible source/sink multi-particles
• Ideally suited for GPU-s: – 300 configs on 180 GPU-s -> 4 months @ 185
GF/gpu
Hadronic & Nuclear Physics with LQCD
• Hadronic spectroscopy– Hadron resonance determinations– Exotic meson spectrum (JLab 12GeV )
• Hadronic structure– 3-D picture of hadrons from gluon & quark spin+flavor distributions– Ground & excited E&M transition form-factors (JLab 6GeV+12GeV+Mainz)– E&M polarizabilities of hadrons (Duke+CERN+Lund)
• Nuclear interactions– Nuclear processes relevant for stellar evolution– Hyperon-hyperon scattering– 3 & 4 nucleon interaction properties [Collab. w/LLNL] (JLab+LLNL)
• Beyond the Standard Model– Neutron decay constraints on BSM from Ultra Cold Neutron source (LANL)
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Gauge Generation: Cost Scaling• Cost: reasonable statistics, box size and “physical” pion
mass• Extrapolate in lattice spacings: 10 ~ 100 PF-yr
PF-years
State-of-Art
Today, 10TF-yr
2011 (100TF-yr)
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Computational Requirements
Gauge generation : Analysis
Current calculations• Weak matrix elements: 1 : 1• Baryon spectroscopy: 1 : 10• Nuclear structure: 1 : 4
Computational Requirements: Gauge Generation : Analysis 10 : 1 (2005) 1 : 3 (2010)
Core work: Dirac inverters - use GPU-s
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Modern GPU Characteristics• Hundreds of simple cores: high flop rate• SIMD architecture (single instruction, multiple data)• Complex (high bandwidth) memory hierarchy
• Gaming cards: no memory Error-Correction (ECC) – reliability issue
• I/O bandwidth << Memory bandwidth
Commodity Processors x86 CPU NVIDIA GT200 New Fermi GPU
#cores 8 240 480
Clock speed 3.2 GHz 1.4 GHz 1.4 GHz
Main memory bandwidth 20 GB/s 160 GB/s(gaming card)
180 GB/s(gaming card)
I/O bandwidth 7 GB/s(dual QDR IB)
3 GB/s 4 GB/s
Power 80 watts 200 watts 250 watts
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Determining spin on a cubic lattice?
Spin reducible on lattice
Might be dynamical degeneracies
H G2 H G2H G2
mass
G1 H G2
Spin 1/2, 3/2, 5/2, or 7/2 ?
Spin reduction & (re)identification
Variational solution:
Continuum
Lattice
Method: Check if converse is true
Spectrum of finite volume field theory
Missing states: “continuum” of multi-particle scattering states
Infinite volume: continuous spectrum
2mπ 2mπ
Finite volume: discrete spectrum
2mπ
Deviation from (discrete) free energies depends upon interaction - contains information about scattering phase shift
ΔE(L) ↔ δ(E) : Lüscher method
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Finite volume scattering
Reverse engineer Use known phase shift - anticipate spectrum
E.g. just a single elastic resonancee.g.
Lüscher method - essentially scattering in a periodic cubic box (length L)- finite volume energy levels E(δ,L)
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Finite volume scattering: Lϋscher method
Excited state spectrum at a single volume
Discrete points on the phase shift curve
Do more volumes, get more points
energylevelsL ~ 2.9 fm
e.g. L ~ 2.9 fm
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The interpretation
“non-interacting basis states”
DOTS:Finite volume QCD energy eigenvalues
LINES:Non-interacting two-particle states have known energies
Level repulsion - just like quantum mechanical pert. theory
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Where are the Form Factors??
• Previous efforts– Charmonium: excited state E&M transition FF-s (0909.0200)
– Nucleon: 1st attempt: E&M Roper->N FF-s (0803.3020)
• Spectrum first!– Basically have to address “what is a resonance’’ up front– (Simplistic example): FF for a strongly decaying state:
linear combination of states
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energylevels
Spin identified Nucleon spectrum
Where is the “Roper”? Thresholds & decays: need multi-particle ops
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m¼ ~ 520MeV
Phenomenology: Nucleon spectrum
Looks like quark model?
[70,1-]P-wave
[56,2+]D-wave
[70,2+]D-wave
[20,1+]P-wave
m¼ ~ 520MeV
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Discern structure: wave-function overlaps
Phenomenology: Nucleon spectrum
[70,1-]P-wave
Looks like quark model?
[56,2+]D-wave
[70,2+]D-wave
[20,1+]P-wave
m¼ ~ 520MeV
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Discern structure: wave-function overlaps