Hadron Structure from Lattice QCD Robert Edwards Jefferson Lab DWF Valence on a Asqtad light sea Nucleon Properties: Spectrum Form Factors Pion Form Factor Radiative transitions - Hybrid meson decays

LHP Collaboration Dru Renner University of Arizona Richard Brower, James Osborn Boston University Rebecca Irwin, Michael Ramsey-Musolf CalTech Jimmy Juge, Adam Lichtl, Colin Morningstar, Carnegie Melon University Jozef Dudek, Robert Edwards, Nilmani Mathur, David Richards JLab Kostas Orginos, JLab/William & Mary Steve Wallace, Univ. Maryland Bojan Bistrovic, Jonathan Bratt, Patrick Dreher, Oliver Jahn, John Negele, Andrew Pochinsky, Dmitry Sigaev MIT Matthias Burkardt, Michael Engelhardt New Mexico State University George Fleming Yale Constantia Alexandrou, Antonios Tsapalis Cyprus, Wolfram Schroers DESY, Philippe de Forcrand EHT-Zurich, Philipp Hägler Tech.Munich

Spectrum - Group Theoretical Operators JLab Hall B: Baryon spectrum experiments Group theoretical construction of baryon interpolating fields Diagonalize cross-correlator matrix: find mass from each ev. Work in progress: Use in full QCD to extract multi-hadron states Asymmetric lattice – long time extent for plateaus and energy scale Need multi-volume techniques Effective mass: Nucleon G1g rep. (1/2)+ Small volume quenched Wilson fermion test case 8 Excited states!

Spectrum – Domain Wall Spectrum of Octet/Decuplet baryons Hybrid action - Domain wall fermions over Staggered sea quarks Only site site operators - no excited states Need  PT : less effected by chiral logs Previous on-going work using older (conventional) action will compute spectrum

Spectrum – Future Directions Calculating high lying excited states high priority for JLab lattice group Extraction of masses requires disentangling decay modes Requires full QCD Generation of new dynamical anisotropic configurations Only group pursuing this approach Also useful for simple vector/axial-vector current form-factors, e.g. Roper transition FF Scale of resources: One lattice spacing, several masses down to m = 200 MeV, Cost ~ 7 TFlop-yr . This year about 5.2 TFlop allocatable Doable in U.S. given expected growth in resources

Anatomy of a Matrix Element Calculation Jf,iy : Current with desired quantum numbers of state A,B Normalize: Compute ratio: Need propagator from t ! tf Want |h 0|Jy|ni|2 » dn,0 for best plateau

Proton Electromagnetic Form-Factors LT separation disagrees with polarization transfer New exp. at Q2 = 9 GeV2 Does lattice QCD predict the vanishing of GEp(Q2) around Q2 ~ 8 GeV2 ? Results use (hybrid) mixed action – DWF/staggered C. Perdrisat (W&M) , JLab Users Group Meeting, June 2005

Nucleon Electromagnetic Form-Factors J.J. Kelly (Maryland), PRC 70 Using covariance matrix (thanks to J.J. Kelly), these fits can be transformed into Dirac-Pauli with isospin decomposition

Isospin Decomposition of Nucleon FF

Nucleon Isovector F1 (or A10) Form Factor Dirac charge radius h r2iu-dch using dipole ansatz and Q2 · 1 GeV2 Chiral extrap. Using LNA and LA terms and finite-range regulator (PRL 86, 5011) Best fit:  ¼ 740 MeV As the pion mass approaches the physical value, the size approaches the correct value

Nucleon Isovector F1 at Higher Q^2 Breit frame at m ¼ 600 MeV Need more statistics as Q2 increases Both polarization transfer experiments and lattice data consistent with dipole ansatz up to 4 GeV2 Go to smaller lattice spacing to reach higher Q2

Nucleon Isovector GE at Higher Q^2 Fits of experimental data suggests GEu-d vanishes at Q2 ~ 4 GeV2 With m ¼ 600 MeV on 282 configs, the lattice points are consistent with something interesting happening around 4 GeV2 Need more lattice data and/or goto smaller lattice spacing

Nucleon Isovector Ratio F2/F1

Polarized Nucleon FF’s GA(Q2) and GP(Q2) Pion electroproduction at threshold (CCQE  n ! - p not shown) Pion electroproduction and muon capture - p !  n at rest J. Phys. G; Nucl. Part. Phys. 28

Nucleon Isovector Ratio GA/F1 Two experimental methods for GA(Q2) Electroproduction mA=1.069(16) CCQE mA=1.026(21) Lattice results favoring GA(Q2) from pion electroproduction at higher Q2

Nucleon Isovector Ratio GP/GA

Pion Electromagnetic Form Factor: F(Q2) Transition between perturbative and non-perturbative aspects of QCD Asymptotic normalization determined (?) Small Q2, vector-meson dominance provides faithful description Free of disconnected contributions – straightforward lattice calculation

Pion Form Factor: Experimental Results Existing data fit VMD monopole formulae too well. Where’s perturbative QCD? Because of simple valence structure, argued that PQCD should apply to lower Q2 than other hadrons PQCD calc. far off. Experimental interpretation problematic – must extrapolate to the pion pole Use lattice QCD!

Pion Form Factor –III Pion Form factor over Q2 commensurate with experiment Pion GPDs and transition form factors next

Spin Physics – Future Directions Currently, only done 1 lattice spacing of 3 Smaller lattice spacing gives access to higher Q2 Need for chiral fermions: Comparison to twist expansion requires derivative insertions – need action with good chiral symmetry to avoid mixings Scale of resources: 3 lattice spacings, several masses down to m = 250 MeV, Cost ~ 7 TFlop-yr . This year about 5.2 TFlop allocatable Doable in U.S. given expected growth in resources

JLab, GlueX and photocouplings GlueX plans to photoproduce mesons Especially exotic JPC mesons resonance, X exchange meson, M 21

Photoproduction of Exotics? Exotic quantum numbers 1-+, 0+-, 2+- may be explicable as hybrid meson states Photoproduction an untested method Relies upon reasonably large couplings e.g. Large in some model estimations (e.g., Close&Dudek PRL91, PRD69) 22

Lattice QCD estimation? Relatively straightforward in principle; evaluate three-point function with a vector current In practice, not so easy truly light quarks unfeasible (for now) transitions involve unstable states experimental data is limited and imprecise (even for conventional meson transitions) 23

charmonium Pragmatic approach Try out an untested method in a region where approximations are controllable and where there is good experimental data to compare with charmonium 24

Charmonium - expt. Multiple states below DD threshold have narrow widths Radiative transitions are big branching fractions Precision measurements 25

Charmonium - lattice States are small - small volumes OK Quenched theory not sick* - just not expt. Disconnected diagrams perturbatively suppressed Need a fine lattice spacing a-1 & 3 GeV * “one heavy flavour QCD”; will only notice non-unitary up near 6 GeV 26

First tests: VMD in Charmonium Many new techniques: test using conventional mesons Chiral fermions at charm scale – automatic O(a) improvement Quenched anisotropic lattices – as = 0.1fm, at = 0.033 fm Extraction of excited transition form-factors Warmup result: VMD does not hold in charmonium VMD ansatz bad fit Quark model inspired form works well Lack of VMD probably due to close proximity of (excited state) vector poles

V! S +  in Charmonium Form-factor decomposition of matrix-element Plot of time extracted FF versus current time-insertion Time plateaus: C1 E1

V ! S+ (E1) transition our ‘poster boy’ not used in the fit PDG CLEO lat.

V ! S +  (C1) transition

V ! P +  in Charmonium new CLEO-c number soon! Lattice calculation of V! P transition form factor Extrapolate using quark-model wavefunc phase space physical Crystal Ball expt. lattice New CLEO-c number soon! Dudek, Edwards, Richards, PRD, 2006 new CLEO-c number soon! new CLEO-c number soon! new CLEO-c number soon! new CLEO-c number soon! new CLEO-c number soon! new CLEO-c number soon! new CLEO-c number soon! new CLEO-c number soon! new CLEO-c number soon! new CLEO-c number soon! new CLEO-c number soon! new CLEO-c number soon! new CLEO-c number soon! new CLEO-c number soon! new CLEO-c number soon! new CLEO-c number soon! new CLEO-c number soon! new CLEO-c number soon! new CLEO-c number soon! new CLEO-c number soon! new CLEO-c number soon!

Quark potential model? Our fitting form inspired by NR potential model with rel. corrections: C1 params fairly consistent,  = 501(33), 502(38), 545(49) MeV 32

Photon Decays How does one compute a photon in an external state in QCD? Use LSZ reduction in Euclidean space and perturbation series for QED Effectively, all excited states of  summed with unknown weights Integrand is saturated by these sums

Photon Decays Decays of c! 2 and c0! 2 c possibly effected by hyperfine splitting. PDQ values very dispersed c! 2 c0 ! 2 Method can be used for 2 in GDH sum rule! Can have alternative low Q2 lattice calculation

Hybrid Decays – Future Directions Calculating hybrid photocoupling (also) a high priority for JLab lattice group Will use same gauge backgrounds as spectrum project Anisotropic lattice (lattice spacing in time direction compared to space) Also useful for simple vector/axial-vector current form-factors, e.g. Roper transition FF

Conclusions and Perspective Use of hybrid Asqtad/DWF calculation providing entry into pion-cloud regime for range of physical quantities – spectrum, nucleon and meson form factors and transition form factors, moments of PDF’s and GPD’s… Computations being extended both to smaller values of lattice spacing (a=0.9, 0.6 fm), and to lighter m = 250 MeV – reveal effects of pion cloud. Spectrum calculation on-going – high excited states appear possible First lattice calculation of radiative transistions. Determination of hybrid photocoupling next.

Extra Slides For the curious…

Partially Quenched Chiral Perturbation Theory Full QCD expensive! Leverage off cheap(er) valence calcs Correct low-energy constants, in principle Must be in domain of validity Extend partially quenched cPT to include O(a) terms Mixed actions Bär, Rupak, Shoresh, 2002, 2003

“Decay” in Quenched Approximation Dramatic behavior in isotriplet scalar particle a0!hp intermediate state Loss of positivity of a0 propagator from missing bubble insertions Quenched a0 has double pole in cPT Also appears in mh0 Bardeen, Duncan, Eichten, Thacker, 2000

Partially Quenched Singularity Non-positivity of a0 correlator (Partially) Quenched singularity (still) present at mp, valencea = mp, seaa Suggests not single staggered pion in chiral loops – taste breaking not neglible Need complete partial cPT Vary valence and sea masses Theory under development…

Rho!Pion Transition Form-Factor Electro-disintegration of deuteron intensively studied Isovector exchange currents identified Isoscalar exchange currents not clear h p(pf)|Jm|rk(pi)i » 2 V(Q2) pf pI / (mp+mr) Extracted coupling rough agreement to expt Need higher Q2 to discern VMD First lattice calc! Maris-Tandy (2002)