Excited State Spectroscopy & QCD Hadron spectroscopy 2 - PowerPoint PPT Presentation

Excited State Spectroscopy & QCD

Hadron spectroscopy 2 • Determination of hadron spectrum of QCD a central goal in NP • Several experiments worldwide USQCD All-Hand’s Meeting | May 1, 2015

Spectrum - light meson experiments 3 USQCD All-Hand’s Meeting | May 1, 2015

Nuclear Physics & Jefferson Lab 4 • JLab finishing a $335M upgrade • Doubled beam energy • Added new Hall D (GlueX) USQCD All-Hand’s Meeting | May 1, 2015

Resonances 5 • Most hadrons are resonances - E.g., π N π N Im( E ) Re( E ) E (MeV) - Formally defined as a pole in a partial-wave scattering amplitude R t l ( s ) ∼ s 0 − s + . . . s 0 = s r 0 + s i 0 - Different channels should have same pole location - Pole structure gives decay information • Can we predict hadron properties from first principles? USQCD All-Hand’s Meeting | May 1, 2015

Isospin=1 ππ P-wave 6 expand angular dependence in partial waves PARTIAL WAVE AMPLITUDE elastic inelastic USQCD All-Hand’s Meeting | May 1, 2015

Isospin=1 ππ P-wave 7 RESONANT PHASE SHIFT USQCD All-Hand’s Meeting | May 1, 2015

ρ resonance 8 180 150 120 90 60 30 0 800 850 900 950 1000 1050 PDG USQCD All-Hand’s Meeting | May 1, 2015

π K / η K scattering amplitudes 9 D -WAVE π K → π K AMPLITUDE LASS D -WAVE 2.4 2.0 1.6 1.2 0.8 0.4 0 0.26 0.28 0.30 LASS, NPB296 493 USQCD All-Hand’s Meeting | May 1, 2015

π K / η K scattering amplitudes 9 D -WAVE π K → π K AMPLITUDE LASS D -WAVE 2.4 2.0 1.6 1.2 0.8 0.4 0 0.26 0.28 0.30 LASS, NPB296 493 USQCD All-Hand’s Meeting | May 1, 2015

S-wave π K/ η K more complicated 10 S -WAVE π K → π K AMPLITUDE LASS S -WAVE 1.2 1 0.8 0.6 0.4 0.2 0 0.18 0.20 0.22 0.24 0.26 180 150 120 90 60 30 0 LASS, NPB296 493 0.18 0.20 0.22 0.24 0.26 USQCD All-Hand’s Meeting | May 1, 2015

Major objective 11 • Compute decays (branching fractions) of exotic mesons: EXOTIC J PC USQCD All-Hand’s Meeting | May 1, 2015

Major objective - exotic meson decays 12 EXOTIC J PC • LQCD suggests existence of exotic mesons • Expt. determination requires measurement in many decay channels • Present LQCD calculations missing this info • Objective is to compute them ahead of expt. ➡ Guide expt. analysis ρπ b 1 π f 1 π JLab expt. beam has started η 0 π . . . USQCD All-Hand’s Meeting | May 1, 2015

What pion mass? 13 • Getting to the physical pion mass not the most pressing concern here • Need to establish feasibility of techniques for resonances USQCD All-Hand’s Meeting | May 1, 2015

What pion mass? 13 • Getting to the physical pion mass not the most pressing concern here • Need to establish feasibility of techniques for resonances - Hard to do with physical kinematics e.g. Some of the simple low-lying resonances: the number of open channels is too large to start here USQCD All-Hand’s Meeting | May 1, 2015

What pion mass? 13 • Getting to the physical pion mass not the most pressing concern here • Need to establish feasibility of techniques for resonances - Hard to do with physical kinematics e.g. Some of the simple low-lying resonances: the number of open channels is too large to start here • Development of three-body formalism required H ANSEN & S HARPE - MUCH PROGRESS USQCD All-Hand’s Meeting | May 1, 2015

LQCD workflow 14 USQCD All-Hand’s Meeting | May 1, 2015

LQCD workflow 14 Generate the configurations ! Leadership level ! 60K cores, 10’s TF-yr USQCD All-Hand’s Meeting | May 1, 2015

LQCD workflow 14 Generate the configurations ! Leadership level ! 60K cores, 10’s TF-yr Analyze Propagators 100K copies + 4 Kepler GPUs Q [ U ] − 1 t=0 t=T USQCD All-Hand’s Meeting | May 1, 2015

LQCD workflow 14 Generate the configurations ! Leadership level ! 60K cores, 10’s TF-yr Analyze Propagators 100K copies + 4 Kepler GPUs Q [ U ] − 1 Now also AMG! t=0 t=T USQCD All-Hand’s Meeting | May 1, 2015

LQCD workflow 14 Generate the configurations ! Leadership level ! 60K cores, 10’s TF-yr Analyze Propagators 100K copies + 4 Kepler GPUs Q [ U ] − 1 Now also AMG! t=0 t=T Contract Correlators 8 cores, CPUs • 100K – 1M copies t=0 t=T USQCD All-Hand’s Meeting | May 1, 2015

LQCD workflow 14 Generate the configurations ! Leadership level ! 60K cores, 10’s TF-yr Analyze Propagators 100K copies + 4 Kepler GPUs Q [ U ] − 1 Now also AMG! t=0 t=T Contract Correlators 8 cores, CPUs • 100K – 1M copies t=0 t=T USQCD All-Hand’s Meeting | May 1, 2015

LQCD workflow 14 Generate the Few big jobs configurations ! Leadership level Few big files ! 60K cores, 10’s TF-yr Analyze Propagators 100K copies + 4 Kepler GPUs Q [ U ] − 1 Now also AMG! t=0 t=T Contract Many small jobs Correlators 8 cores, CPUs • 100K – 1M copies Many big files I/O movement t=0 t=T USQCD All-Hand’s Meeting | May 1, 2015

LQCD workflow 15 Generate the configurations ~25% ! Leadership level ! 60K cores, 10’s TF-yr Leadership level ~75% Analyze Propagators 100K copies + 4 Kepler GPUs Throughput mode Q [ U ] − 1 Now also AMG! t=0 t=T Contract Correlators 8 cores, CPUs • 100K – 1M copies > 5% New analysis cost t=0 t=T USQCD All-Hand’s Meeting | May 1, 2015

Scattering in a finite cubic volume 16 • Expect a discrete spectrum in a finite periodic volume e.g. free particle quantized momentum • For an interacting theory L ÜSCHER … elastic scattering known phase-shift function Discrete energies Discrete values in a finite-volume of the phase-shift USQCD All-Hand’s Meeting | May 1, 2015

Scattering in a finite cubic volume 17 • Experimental ππ I =1 P -wave scattering amplitude P -WAVE PHASE SHIFT 150 CUBIC BOX SPECTRUM 100 1.0 50 0.9 0.4 0.6 0.8 1.0 1.2 0.8 0.7 0.6 0.5 0.4 0.3 10.0 15.0 20.0 25.0 30.0 35.0 USQCD All-Hand’s Meeting | May 1, 2015

ππ P -wave phase-shift 18 180 150 120 90 60 30 0 0.14 0.15 0.16 0.17 0.18 0.19 PRD87 034505 (2013) USQCD All-Hand’s Meeting | May 1, 2015

ππ P -wave phase-shift 18 180 150 120 90 60 30 0 0.14 0.15 0.16 0.17 0.18 0.19 PRD87 034505 (2013) USQCD All-Hand’s Meeting | May 1, 2015

ρ resonance 19 180 150 120 90 60 30 0 800 850 900 950 1000 1050 PDG USQCD All-Hand’s Meeting | May 1, 2015

Coupled-channel scattering 20 H E , JHEP 0507 011 H ANSEN , PRD86 016007 B RICENO , PRD88 094507 • Finite-volume formalism recently derived (multiple methods) G UO , PRD88 014051 phase known scattering matrices in space functions matrix partial-wave space … • However, this is one equation for multiple unknowns (per energy level) for N channels - parameterize the energy dependence of t - try to describe a spectrum globally “Energy-dependent” analysis USQCD All-Hand’s Meeting | May 1, 2015

π K / η K scattering & kaon resonances 21 • Example of coupled-channel scattering • Compute finite-volume spectrum PRL 113 182001 PRD 91 054008 USQCD All-Hand’s Meeting | May 1, 2015

π K / η K scattering & kaon resonances 21 • Example of coupled-channel scattering WICK CONTRACTIONS • Compute finite-volume spectrum PRL 113 182001 PRD 91 054008 USQCD All-Hand’s Meeting | May 1, 2015

π K / η K scattering & kaon resonances 21 • Example of coupled-channel scattering WICK CONTRACTIONS • Compute finite-volume spectrum PRL 113 182001 PRD 91 054008 Large combinatoric factors - contractions expensive USQCD All-Hand’s Meeting | May 1, 2015

π K / η K scattering & kaon resonances 22 • Rest frame “ S -wave” spectrum 0.28 0.24 0.20 0.16 16 20 24 USQCD All-Hand’s Meeting | May 1, 2015

π K / η K scattering & kaon resonances 23 • Parameterize the t -matrix in a unitarity conserving way - vary the parameters, solving for the spectrum in each irreducible representation & momentum Want pole mass and couplings of t-matrix USQCD All-Hand’s Meeting | May 1, 2015

π K / η K scattering 24 USQCD All-Hand’s Meeting | May 1, 2015

π K / η K scattering 24 USQCD All-Hand’s Meeting | May 1, 2015

Singularity content 25 • t -matrix poles as least model-dependent characterization of resonances 600 1000 1200 1400 1600 800 scalar narrow tensor vector -100 virtual resonance bound-state bound-state -300 -500 broad scalar resonance PRL 113 182001 PRD 91 054008 USQCD All-Hand’s Meeting | May 1, 2015

Impact on experiment 26 Approved expt: second phase of GlueX program . . . USQCD All-Hand’s Meeting | May 1, 2015

Impact on experiment 27 Science case for JLab CLAS12 expt NSAC report prominently featuring exotic meson spectroscopy project New NSAC report in writing now… USQCD All-Hand’s Meeting | May 1, 2015