Nucleon Resonances from Lattice QCD Robert Edwards Jefferson Lab GHP April 2009 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAA

Hadron Spectrum Collaboration University of Pacific J Juge JLAB S Cohen J Dudek R Edwards B Joo H-W Lin D Richards C Thomas CMU J Bulava J Foley C Morningstar UMD E Engelson S Wallace Tata (India) N Mathur

Physics Goals Exotic and excited state meson spectrum E.g., 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 (lX, sX) SU(3) stable hadron for scale X Physics observables (lX, sX) BMW, HadSpec 2008

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

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

No-go Theorem Scattering matrix elements: only from finite volume Euclidean correlation functions (except at threshold) [Maiani-Testa] 3-d box with size L, spectrum of states discrete – even above threshold Scattering lengths inferred Missing negative parity octet and decuplet – much more to do!

Decays ½ mass from effective range expansion: finite box QCDSF 2008 physical ½ 2¼, n=111 2¼, n=110 2¼, n=100 m¼=390 MeV m¼=250 MeV QCDSF 2008

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=2.0fm L=1 Need multiple volumes Theory not well developed Will get to cost… L=1

Nucleon spectrum (Experimental) ½+ 5/2+ 3/2- 5/2- 3/2+ ½- NP2012 milestone: Spectrum & E&M transitions up to Q2 = 7 GeV2 Challenges/opportunities: Compute excited energies Compute decays 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

Variational Method Correlation matrix: Diagonalize Mass from eigenvalue Basis complete enough to capture excited states Small contamination as expected: Diagonalization gives ~ <state out| Tt | state in>, T transfer matrix Luscher,Wolff; HadSpec PRD72:074501,2005, PRD72:094506,2005

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

Nf=2 Nucleon Spectrum via Group Theory HadSpec 2009 Nf=2, m= 416 MeV, as~0.11fm Nf=2, m= 572 MeV ½+ 3/2+, 5/2+ 5/2- ½- 3/2+, 5/2+ 5/2- ½+ 3/2+, 5/2+ 5/2- ½- 3/2+, 5/2+ 5/2-

Nf=2 Nucleon Spectrum via Group Theory Possible 5/2- state HadSpec 2009 Nf=2, m= 416 MeV, as~0.11fm Nf=2, m= 572 MeV 5/2- ½+ 3/2+, 5/2+ 5/2+ ½- 3/2-, 5/2- 5/2- ½+ 3/2+, 5/2+ 5/2+ ½- 3/2-, 5/2- 5/2-

Nucleon Spectrum Possible 5/2- state: pattern similar to exp: Future: As expected, most states decaying Multiple volumes for decay analysis 3/2-, 5/2- ½- 5/2- 3/2-, 5/2- ½- 5/2-

Strategy for Excited Decays Variational results: use in 3-pt Excited sink: p=0 Ground source: p 0 Q2  v(n)

Nucleon Form-Factors (Ground state) Nf=0 anisotropic lattices, M¼ = 480, 720, 1080 MeV

Nucleon Form-Factors (Ground state) Nf=2+1 anisotropic lattices, M¼ = 580, 875 MeV

Nucleon Radiative Transition Nf=0 exploratory: P11->Nucleon transition

Nucleon Radiative Transition Excited transition: large “pion cloud” effects ! small mass m¼ = 480, 720, 1100 MeV PRD 2008

Nucleon Radiative Transition Nf=2+1 anisotropic lattices, M¼ = 580, 875 MeV Does not use derivative operators:

Multi-hadrons Meson and baryon excited state energies obtainable 2-pt correlators: e.g., 2-mesons Different than in 3-pt Two-particle signals suppressed relative to single particle?

Current and future work Some efforts underway Strange quark spectrum (hybrids) and radiative transitions Excited light baryon spectrum (N, ¢, ¥, §, ¤) [showed first versions in N and ¥ (Mathur)] Radiative transitions for P11(1440), S11(1535), D13(1520) Q2 <~ 5 GeV2 Need to disentangle decay states: Two-meson states, I=1 & 0 Meson-baryon