Excited State Spectroscopy from Lattice QCD Robert Edwards Jefferson Lab CERN 2010 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A AA A A A Collaborators: J. Dudek, B. Joo, M. Peardon, D. Richards, C. Thomas, S. Wallace Auspices 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. 2

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 N f =2+1 dynamical (clover)fermions –Temporal lattice spacing a t < a s (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), PRD 72 (2005), PRD 72 (2005), (PRD),

N f =2+1 Anisotropic Clover 5 N f = (u,d + s) Using a t m  & »=3.5 : a s = (3)fm, (a t ) -1 ~ GeV &

Spin and Operator Construction (PRD), (PRL), (PRD) Gamma matrices and derivatives in circular basis: Couple to build any J,M via usual CG 6 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 (PRD), , Bulava (thesis 2010) Replace smearing with low rank approximation 7 Gauge covariant, mom. conservation (source & sink) ! reduced “noise” Matrix elements of v k (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 8

Determining spin on a cubic lattice? Spin reducible on lattice Might be dynamical degeneracies T 2 E mass T 1 T 2 E A 2 Spin 1, 2, 3, or 4 ?

Spin reduction & (re)identification Variational solution: Continuum Lattice Method: Check if converse is true

Spin (re)identification Z values: spin 3 N f =3 Well identified: suggests small rotational breaking

Isovector Meson Spectrum 12 N f =

Isovector Meson Spectrum 13 N f =3 1D 2P S 2S 1P 3S 1G ??

Isovector Meson Spectrum 14 N f =2+1, m ¼ ~ 520MeV, L~2fm Similar to Nf=3

Exotic matter Exotics: world summary 15

Exotic matter Suggests (many) exotics within range of JLab Hall D Previous work: charmonium photo-production rates high Current work: (strong) decays 16

Vector isoscalars (I=0) 17 N f =2+1, m ¼ ~ 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 6GeV 18 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 19

Light quark baryons in SU(6) Conventional non-relativistic construction: 6 quark states in SU(6) Baryons 20

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 21

Orbital angular momentum via derivatives (PRD), (PRL), Couple derivatives onto single-site spinors: Enough D’s – build any J,M 22 Use all possible operators up to 2 derivatives (2 units orbital angular momentum) Only using symmetries of continuum QCD

Nucleon & Delta Spectrum 23

Nucleon & Delta Spectrum 24 [ 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 25 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: demonstration ¼¼ isospin=2 Extract δ 0 (E) at discrete E No discernible pion mass dependence

Phase Shifts: demonstration ¼¼ isospin=2 δ 2 (E)

Hardware: JLab GPU Clusters GPU 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

Inverter Strong Scaling: V=32 3 x256 Local volume on GPU too small (I/O bottleneck) 3 Tflops 29

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 (m ¼ ~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 ( , )

Backup slides The end 31

Interpretation of Meson Spectrum Future: probe with photon decays

Distillation: mesons Smearing in correlator: use low-rank approximation Correlator Factorizes: operators and perambulators A posteriori evaluation of C (2) after ¿ arxiv:

Distillation: annihilation diagrams Two-meson creation op Correlator arxiv:

Perambulators Current calculation (24 3 x128, m ¼ ~ 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 -> 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) 36

Bridges in Nuclear Physics NP Exascale 37

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) 38

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 39

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 Processorsx86 CPUNVIDIA GT200New Fermi GPU #cores Clock speed3.2 GHz1.4 GHz Main memory bandwidth20 GB/s160 GB/s (gaming card) 180 GB/s (gaming card) I/O bandwidth7 GB/s (dual QDR IB) 3 GB/s 4 GB/s Power80 watts200 watts250 watts 40

Science / Dollar for (Some) LQCD Capacity Apps 41

Isovector Meson Spectrum

Determining spin on a cubic lattice? Spin reducible on lattice Might be dynamical degeneracies H G 2 mass G 1 H G 2 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 2m π Finite volume: discrete spectrum 2m π Deviation from (discrete) free energies depends upon interaction - contains information about scattering phase shift ΔE(L) ↔ δ(E) : Lüscher method 45

Finite volume scattering Reverse engineer Use known phase shift - anticipate spectrum E.g. just a single elastic resonance e.g. Lüscher method - essentially scattering in a periodic cubic box (length L) - finite volume energy levels E(δ,L) 46

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 energy levels L ~ 2.9 fm e.g. L ~ 2.9 fm 47

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 48

The interpretation energy levels 49

Where are the Form Factors?? Previous efforts –Charmonium: excited state E&M transition FF-s ( ) –Nucleon: 1 st attempt: E&M Roper->N FF-s ( ) Spectrum first! –Basically have to address “what is a resonance’’ up front –(Simplistic example): FF for a strongly decaying state: linear combination of states 50 energy levels

Phase Shifts: demonstration ¼¼ isospin=2 Extract δ 0 (E) at discrete E

Phase Shifts: demonstration 52

Spin identified Nucleon spectrum m ¼ ~ 520MeV 53 Statistical errors < 2%

Spin identified Nucleon spectrum Where is the “Roper”? Thresholds & decays: need multi-particle ops 54 m ¼ ~ 520MeV

Phenomenology: Nucleon spectrum Looks like quark model? [ 70,1 - ] P-wave [ 56,2 + ] D-wave [ 70,2 + ] D-wave [ 20,1 + ] P-wave m ¼ ~ 520MeV 55 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 m ¼ ~ 520MeV 56 Discern structure: wave-function overlaps

Spin identified ¢ spectrum [ 70,1 - ] P-wave [ 56,2 + ] D-wave Spectrum slightly higher than nucleon 57