Prospects for Spectroscopy

Robert Edwards Jefferson Lab

Exascale ComputingJanuary 2009

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 GeV2

• 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 method a @ 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 2008

2¼, n=100

2¼, n=110

2¼, n=111

m¼=250 MeVm¼=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-+ ! b1¼ S-wave [Dominant decay in flux-tube models]

More complicated decays

• Exotic 1-+: cascading decays as mass decreases :

• first 1-+ ! b1¼ S-wave [Dominant decay in flux-tube models]

• second b1¼ ! !¼¼ S-wave

More complicated decays

• Exotic 1-+: cascading decays as mass decreases :

• first 1-+ ! b1¼ S-wave [Dominant decay in flux-tube models]

• second b1¼ ! !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=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 Q2 = 7 GeV2

• Challenges/opportunities:– Compute excited energies– Compute decays

½+ 5/2+ 3/2- 5/2-3/2+ 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 (Ã C ¡ Ã)¡Ã limited to ½+, ½-, 3/2+, 3/2-

• Non-local operators: higher spins and excited states

• Extend to: ¡ Dià ¡ Djà ¡ DkÃ

Excited Baryons

Lattice Continuum

G1 1/2, 7/2,…

G2 5/2, 7/2,…

H 3/2, 7/2,...

Operators: cubic lattice symmetries

a

M5/2mG2

mH Nature is kind! Action: chiral breaking dim=5, Lorentz

invariant Masses possibly O(a) Splittings ~ O(a2) 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, as=0.1fm, =3

HadSpec PRD72:074501,2005, PRD72:094506,2005

Nf=2 Nucleon Spectrum via Group Theory

HadSpec 2009

NNff=2, m=2, m= 416 MeV, a= 416 MeV, ass~0.11fm~0.11fm NNff=2, m=2, m= 572 MeV= 572 MeV

Nf=2 Nucleon Spectrum via Group Theory

• Possible 5/2- state

HadSpec 2009

NNff=2, m=2, m= 416 MeV, a= 416 MeV, ass~0.11fm~0.11fm NNff=2, m=2, m= 572 MeV= 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:0810.5141

m¼ = 480, 720, 1100 MeV

MesonsNew 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 Q2= 0

• Experimental & theoretical programs (e.g., EBAC) need form-factors as input

Beyond Photocouplings

p n

°¤

p n

°¤

¼

½

F¼½(Q2)or

• Covariant derivatives operators:

Excited Mesons

Lattice Continuum

A1 0,4...

T1 1,3,4...

T2 2,3,4...

E 2,4...

A2 3...

Operators: cubic lattice symmetries

a

M2mE

mT2

Splittings ~ O(a2)

Motivation

JPC 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-1spin-2spin-3

dim=1 dim=3 dim=3 dim=2 dim=1

30973097

36863686

37703770

J/ψJ/ψ

ψ’ψ’ψ(3770)ψ(3770)

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 T2 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

Q2

v(n)

Excited state decaysExcited

0th 1st

2nd 4th

HadSpec 2009

Q2

E1(Q2)

Hybrid decay

Excited/exotic decays possible: go to light quarks

Light quarks

Nf=2+1: m¼ = 580 MeV

Scalar mesons• Long standing puzzle – 2-quarks, 4-quarks, molecules…??• Difficult experimentally

• Opportunity/challenge for lattice

– Need Nf=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 ci

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: m¼ L = 4.2

. Current aniso

Costs

• Physical limit: box sizes > 6fm ! m¼ 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

PDGCLEO

Photocouplings - II

Anisotropic (DWF) study of transitions between conventional mesons, e.g. S ! V PRD73, 074507

Not used in the fit

lat.

Lattice

Expt.

Motivated by this work, CLEO-c reanalyzed their data