Prospects for Spectroscopy Robert Edwards Jefferson Lab Exascale Computing January 2009 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAA

Private outline/notes What do we want? Use the requested bullets Current spectroscopy – iso –Actions? Chiral ferms bad – wiggles Clover good? Anisotropic program –Chiral ferms still bad –Operators and variational technology –Charmonium spectrum Excited Spectrum Overlaps – nature kind at dim=5 Excited transtion FF –Baryon spectrum –Costs Gauge Valence – overtaking gauge? Contractions not trivial Aniso switch over to Iso – want fine lattices Magic –No chiral ferms – can use clover –Can do magic of OPE w/o OPE – weak matelems (HEP) –Dist amps & sum-rules (structure) –Possibly do QCD light-cone directly (NP), qcdsf/detmold/keh-fei –Synergy HEP/NP –Costs – gauge (valence still expensive)

Physics Goals Exotic and excited state meson spectrum –Future JLab Hall D & GSI/Panda experiments –Photo-couplings & electromagnetic transition form-factors –Isoscalar spectrum –Also heavy quark spectrum – cross-over to HEP Baryon spectrum –Light quark and strange quarks E.g., many cascade states unknown parity –NP2012: Masses along with ground state and excited state transition form-factors up to 7 GeV 2 These are the simplest examples of views NOTE: spectrum & structure division arbitrary –Also consider 3D structure view of (excited) hadrons

Requirements Dynamical quarks: –Light quarks (u,d) – can be degenerate –Strange quark –Charm? Chiral extrapolation: problematic ! physical limit Multi-volume/decays Continuum extrapolation Disconnected contributions: –Isosinglets –3pt & 4-pt –Annihilation diagrams

Strange Quark Mass Decouple strange quark mass & lattice spacing “a” determinations Consider strange quark determination understood! Chiral PT extendable in (l_X, s_X) SU(3) stable hadron for scale X Physics observables (l_X, s_X) BMW, HadSpec 2008

Continuum Extrapolation Clover action - small discretization effects Chiral PT works well in ratio method BMW 2008 Ratio phys limit

Some Ground State Masses Some of the ground state masses Missing negative parity octet and decuplet – much more to do! BMW Collab, Science (2008)

Decays ½ mass from effective range expansion: finite box QCDSF ¼, n=100 2¼, n=110 2¼, n=111 m ¼ =250 MeV m ¼ =390 MeV physical ½

Decays ½ mass QCDSF 2008

More complicated decays Exotic 1 -+ : cascading decays as mass decreases:

More complicated decays Exotic 1 -+ : cascading decays as mass decreases : first 1 -+ ! b 1 ¼ S-wave [Dominant decay in flux-tube models]

More complicated decays Exotic 1 -+ : cascading decays as mass decreases : first 1 -+ ! b 1 ¼ S-wave [Dominant decay in flux-tube models] second b 1 ¼ ! !¼¼ S-wave

More complicated decays Exotic 1 -+ : cascading decays as mass decreases : first 1 -+ ! b 1 ¼ S-wave [Dominant decay in flux-tube models] second b 1 ¼ ! !¼¼ S-wave

More complicated decays Exotic 1 -+ : cascading decays: Also 1 -+ ! ½¼ P-wave [P-wave suppressed in flux-tube models] L=1 L=2.0fm Need multiple volumes Theory not well developed Will get to cost…

Nucleon spectrum (Experimental) NP2012 milestone: Spectrum & E&M transitions up to Q 2 = 7 GeV 2 Challenges/opportunities: –Compute excited energies –Compute decays ½+½+ 5/2 + 3/2 - 5/2 - 3/2 + ½-½- N¼¼ or ¢¼ N¼ or N´ or N(1440)¼ N¼¼ or ¢¼

Strange Quark Baryons Strange quark baryon spectrum poorly known Future: Narrow widths: easy(er) to extract (?) ¥ &  : unknown spin & parities Widths are small

Simple interpolating fields ( à C ¡ à ) ¡Ã limited to ½ +, ½ -, 3/2 +, 3/2 - Non-local operators: higher spins and excited states Extend to: ¡ D i à ¡ D j à ¡ D k à Excited Baryons Lattice Continuum G1G1 1/2, 7/2,… G2G2 5/2, 7/2,… H3/2, 7/2,... Operators: cubic lattice symmetries a M 5/2 m G2 mHmH Nature is kind! Action: chiral breaking dim=5, Lorentz invariant Masses possibly O(a) Splittings ~ O(a 2 ) Precocious scaling

Correlation matrix: Diagonalize Mass from eigenvalue Basis complete enough to capture excited states Small contamination as expected: Variational Method Luscher,Wolff; HadSpec PRD72:074501,2005, PRD72:094506,2005

Noisy signals – go anisotropic [Hadron Spectrum Collaboration] Why? COST!! Lower cost with only one fine lattice spacing instead of all 4. Anisotropic Lattice m  ~720MeV, a s =0.1fm,  =3 HadSpec PRD72:074501,2005, PRD72:094506,2005

N f =2 Nucleon Spectrum via Group Theory HadSpec 2009 N f =2, m  = 416 MeV, a s ~0.11fm N f =2, m  = 572 MeV

N f =2 Nucleon Spectrum via Group Theory Possible 5/2 - state HadSpec 2009 N f =2, m  = 416 MeV, a s ~0.11fm N f =2, m  = 572 MeV

Nucleon Spectrum Possible 5/2 - state: pattern similar to exp: Future: –As expected, most states decaying –Multiple volumes for decay analysis –Cost???

Nucleon Radiative Transition Exploratory: P11->Nucleon transition

Nucleon Radiative Transition Excited transition: large “pion cloud” effects ! small mass arXiv: m ¼ = 480, 720, 1100 MeV

Mesons New experimental efforts in meson spectroscopy GlueX aims to photoproduce hybrid mesons in Hall D. –CD4 in 2015 Compass (CERN) Panda (GSI) Lattice QCD: crucial role –Predict the spectrum –Compute production rates

Hybrid Photocouplings Compute photocouplings : gives rates Test in charmonium: useful in own right

Photocouplings at Q 2 = 0 Experimental & theoretical programs (e.g., EBAC) need form-factors as input Beyond Photocouplings pn °¤°¤ p n °¤°¤ ¼ ½ F ¼½ ( Q 2 ) or

Covariant derivatives operators: Excited Mesons Lattice Continuum A1A1 0,4... T1T1 1,3,4... T2T2 2,3,4... E2,4... A2A Operators: cubic lattice symmetries a M2M2 mEmE m T2 Splittings ~ O(a 2 )

Motivation J PC state: wavefunction –Short distance: sufficient derivatives – nonzero overlap –Long distance: different structure R Ã(R) 0

Charmonium Spectrum Dense spectrum of excited states – how to extract spins? spin-1 spin-2 spin-3 dim=1dim=3 dim=2dim= J/ψ ψ’ ψ (3770) ψ3ψ3 ψ3ψ3 PRD 77 (2008) Separate spin 1 and 3 (first time)

Variational method: gives eigenvectors Challenge: spin assignment in light quark sector with strong decays Lightest states in PC=++ –consider T 2 and E –Z’s for the operators should match in continuum Continuum Spin Identification? PRD 77 (2008)

Strategy for Excited Decays Variational results: use in 3-pt Excited sink: p=0 Ground source: p  0 Q2Q2  v (n)

Excited state decays Excited 0th 1st 2nd4th HadSpec 2009 Q2Q2 E1(Q 2 )

Hybrid decay Excited/exotic decays possible: go to light quarks

Light quarks N f =2+1: m ¼ = 580 MeV

Scalar mesons Long standing puzzle – 2-quarks, 4-quarks, molecules…?? Difficult experimentally Opportunity/challenge for lattice –Need N f =2+1 : ´ ’s prominent –Need disconnected, multi-hadron operators

Multi-hadrons Meson and baryon excited state energies obtainable 2-pt correlators: e.g., 2-mesons Different than in 3-pt Inversions on multiple time-slices/sources – Big cost: > 10x ??

Message so far Fine lattices (a < 0.04fm) crucial for u,d,s quark highly excited state spectroscopy, transitions, decays Current approach is anisotropic Not optimal for hadronic structure studies (light-cone interpretation) Go to fine lattice spacing isotropic What about costs? How does it help??

Small “a” – transformational ? OPE without OPE (Rome/Southampton/Washington) Weak-matrix elements need Small a -> compute Wilson coeffs in pert. theory Solve for renormalized operators –Avoid operator mixing & power divergent term [Rossi/Testa & Sharpe]: –a -1 ~ 8 GeV, so a ~ 0.025fm –Can use simple clover formulation – no chiral fermions –Avoid problems with heavy quarks in PT of c i

Synergy with Hadron Structure Hadron structure: also need OPE for hadronic tensor Variants: –Direct extraction and/or non-pt Wilson coeffs (QCDSF) –Connect with QCD sum-rules (QCDSF) –Fictitious heavy quark (Detmold/Lin)

Small ``a’’ – synergy of projects Isotropic lattices: a ~< 0.04fm –Potentially only need simple Clover formulation for HEP & NP –No chiral fermions – lower cost (10x ??) –Suitable for charm quarks - possibly bottom quarks??? –Light quarks (u,d,s): Current anisotropic program, a ~ 0.033fm Excited spectrum and transition FF’s –Suitable for hadron structure –Nuclear interactions: Helps with signal/noise – still need big/huge boxes

Scaling of costs Isotropic: m ¼ L = 4.2. Current aniso

Costs Physical limit: box sizes > 6fm ! m ¼ L > 4.2 Valence costs > gauge generation Number trajectories: dependent on problem (see Orginos) Lower bounds: (ignore future algorithm improvements): Anisotropic gauge: physical limit (6fm) ~ 0.1 PF-yr Isotropic gauge: physical limit (6fm): –a ~ 0.06fm: ~ 1 PF-yr –a ~ 0.04fm: ~ 10 PF-yr Overall factors: –Above only 10K traj (1K configs): need > 10x?? (baryons) –Valence inversions: need > 10x?? Summary: easily 10 PF-yr to 100 PF-yr

Backup slides Afterwards are backup slides

Spectroscopy - Roadmap First stage: a ~ 0.12 fm, spatial extents to 4 fm, pion masses to 220 MeV –Spectrum of exotic mesons –First predictions of  1 photocoupling –Emergence of resonances above two-particle threshold Second stage: two lattices spacings, pion masses to 180 MeV –Spectrum in continuum limit, with spins identified –Transition form factors between low-lying states Culmination: Goto a=0.10fm computation at two volumes at physical pion mass –Computation of spectrum for direct comparison with experiment –Identification of effective degrees of freedom in spectrum * Resources: USQCD clusters, ORNL/Cray XT4, ANL BG/P, NSF centers, NSF Petaflop machine (NCSA-2011)/proposal

Unsuitability of Chiral Fermions for Spectrum Chiral fermions lack a positive definite transfer matrix Results in unphysical excited states. Unphysical masses ~ 1/a, so separate in continuum limit Shown is the Cascade effective mass of DWF over Asqtad Upshot: chiral fermions not suited for high lying excited state program at currently achievable lattice spacings Source at t=10 Wiggles

PDG CLEO Photocouplings - II Anisotropic (DWF) study of transitions between conventional mesons, e.g. S !  V PRD73, Not used in the fit lat. Lattice Expt. Motivated by this work, CLEO-c reanalyzed their data