The Lattice QCD Program at Jefferson Lab. Huey-Wen Lin. JLab 7n cluster

Transcription

1 The Lattice QCD Program at Jefferson Lab Huey-Wen Lin JLab 7n cluster 1

2 Theoretical Support for Our Experimental Agenda 2

3 Theoretical Support for Our Experimental Agenda JLab Staff Joint appointments and others 3

4 Theoretical Support for Our Experimental Agenda Baryon and meson resonances (including exotics) Nucleon properties: axial coupling constants, charge radii, magnetic moments, structure functions, form factors, GPDs and polarizabilities. Extended to other hadrons. Meson photocoupling constants Pion-to-2photons decay Chiral perturbation theory for lattice data extrapolations Algorithms to improve lattice calculations Multiple-particle interactions and kaon condensation Charm and bottom baryon spectroscopy (long future ahead?) Time is too short 4

5 Outline Lattice QCD Overview Collaboration Efforts Old story and a new twist (Baryon spectroscopy, nucleon spin) Individual Projects Hyperon properties, large-q 2 form factors, pion decays, Roper-nucleon form factors, heavy-quark spectroscopy, etc Summary 5

6 Lattice QCD QCD observables are calculated from the path integral Strong-coupling regions: expansions no longer converge Lattice QCD is a discrete version of continuum QCD theory ψ(x+μ) U μ (x) ψ(x) Numerical integration to calculate the path integral Take a 0 and V in the continuum limit 6

7 Lattice Actions Symanzik Improvement Order-by-order in a improvement of the action and operators Systematic error due to discretization under control Gauge Actions Most gauge actions used today are O(a 2 ) improved Small discretization effects (~O(Λ 3 QCDa 3 )) due to gauge choices <1% systematic with current a Fermion Actions Most fermion actions are only O(a) improved (O(Λ 2 QCDa 2 )) ~4% Differences are benign once all systematics are included Different choices of fermion action are confined by limits of computational and human power + by personal interest Commonly used actions: domain-wall fermions, overlap fermions, Wilson/clover fermions, twisted-wilson fermions staggered fermions 7

8 Computational Requirements A wide variety of first-principles QCD calculations can be done: In 1970, Wilson started off by writing down the first actions Progress is limited by computational resources But assisted by advances in algorithms Computer power available for gaming in the 1980s: 8

9 Computational Requirements A wide variety of first-principles QCD calculations can be done: In 1970, Wilson started off by writing down the first actions Progress is limited by computational resources But assisted by advances in algorithms Computer power available today: Exciting progress during the last decade 9

10 Computational Requirements USQCD facilities: JLab, Fermilab, BNL Non-lattice resources open to USQCD: ORNL, LLNL, ANL NSF supercomputer and worldwide increase in computation facilities 10

11 Computational Requirements Gauge generation costs with the latest algorithms scale like Cost factor (DWF): a 6, L 5, M π 3 Norman Christ, LAT07 Most of the major 2+1-flavor gauge ensembles: M π < 300 MeV MILC (staggered): M π ~ 217 MeV PACS-CS (Clover action): M π ~ 156 MeV (but small volume) The Budapest-Marseille-Wuppertal (BMW) Collaboration: M π ~ 193 MeV, 3 lattice spacing, multiple volumes The Hadron Spectrum Collaboration (anisotropic clover): M π ~ 180, 220 MeV (on-going) RBC/UKQCD (DWF), M π ~ 210 MeV (on-going) Most of them have multiple lattice spacings and volumes A pion-mass extrapolation M π (M π ) phys (Bonus products: Low-Energy Constants) 11

12 Problems: Operators: Excited Resonances Assignment of particle quantum numbers? How do we create operators that maximize overlap with the low-lying states of interest and minimize mixing with other operators due to lattice artifacts? Euclidean space: Correlators with time-dependent form dominated by ground state; challenge for excited states 12

13 Hadron Spectrum Collaboration J. Bulava, C. Morningstar, J. Foley (Carnegie Mellon U.) S. Cohen, J. Dudek, R. Edwards, B. Joo, H.W. Lin, D. Richards, C. Thomas (Jefferson Lab.) E. Engelson, S. Wallace (U. Maryland) K.J. Juge (U. of Pacific) A. Lichtl (Brookhaven Nat. Lab.) N. Mathur (Tata Institute) M. Peardon, S. Ryan (Trinity Coll. Dublin) PI on USQCD proposal 13

14 Operator Design Baryon field Classify states according to symmetry properties Projection onto irreducible representations of finite groups Number of operators: S. Basak et al., Phys. Rev. D72, (2005) 14

15 Increase resolution Dynamical Anisotropic Lattices N f = 2+1 anisotropic clover action available ensemble list m π (MeV) ~ 1600 ~ 660 ~ 1340 ~ 850 R. Edwards et al., Phys. Rev. D 78, (2008) HWL et al., Phys. Rev. D 79, (2009) M π ~180 and 220 MeV are in progress at LLNL ~

16 Dynamical Anisotropic Lattices Preliminary octet masses extrapolation using modified NLO HBXPT Dimensionless quantities to avoid lattice-spacing ambiguities Mass ratios with {l,s} Ξ coordinates A. Thomas et al., in preparation l Ξ 16

17 N f = 0 Study: Nucleon N f = 0, anisotropic Wilson action, V = , a s ~ 0.1 fm, a s /a t ~ 3, M π ~ 700 MeV A. Lichtl, hep-lat/ Exp (GeV) Lat (a t 1 ) 17

18 N f = 0 Study: Delta N f = 0, anisotropic Wilson action, V = , a s ~ 0.1 fm, a s /a t ~ 3, M π ~ 700 MeV J. Bulava et al., [hep-lat] Exp (GeV) Lat (a t 1 ) 18

19 N f = 2 Study: Nucleon J. Bulava et al., Phys. Rev. D79, (2009) N f = 2, anisotropic Wilson action, V = , a s ~ 0.1 fm, a s /a t ~ 3, M π ~ 416 MeV Exp (GeV) Lat (a t 1 ) 19

20 N f = 2+1 Study: Nucleon N f = 2+1, anisotropic clover action, V = , a s ~ 0.1 fm, a s /a t ~ 3.5, M π ~ 366 MeV Very Preliminary Exp (GeV) 20

21 Strange Baryons Strange baryons are of special interest; challenging even to experiment Example from PDG Live: 21

22 N f = 2+1 Study: Hyperons Highly excited states can be extracted from future dynamical anisotropic lattices From isotropic N f = 2+1 Mixed action: DWF on staggered sea M π ~ MeV, L ~ 2.5 fm Local operator only Naïve chiral extrapolation HWL et al., [hep-lat] From the pattern: spin identification Ξ(1690): 1/2 Ω(2250): 3/2 Ω(2380): 1/2 Ω(2470): 1/2 22

23 More on Cascades Nilmani et al. N f = 2, anisotropic Wilson action, V = , a s ~ 0.1 fm, a s /a t ~ 3, M π ~ 572 MeV N f = 2+1 is also in progress 23

24 Nucleon Spin Using GFF and Ji s sum rule Xiang-Dong Ji, Phys. Rev. Lett., 78:610 (1997) Decomposition according to quark flavor: LHPC: N f = 2+1 mixed action, M π ~ MeV Ph. Hagler et. al, Phys. Rev. D77, (2008). L u +d ~ 0 J d ~ 0 M π2 (GeV 2 ) 24

25 Nucleon Spin Using GFF and Ji s sum rule Xiang-Dong Ji, Phys. Rev. Lett., 78:610 (1997) Decomposition according to spin and orbital angular momentum: LHPC: N f = 2+1 mixed action, M π ~ MeV QCDSF: N f = 2 clover action, M π ~ MeV LHPC, QCDSF LHPC, QCDSF M π2 (GeV 2 ) Ph. Hagler et. al, Phys. Rev. D77, (2008); M. Ohtani et al, PoS (Lat2007)

26 Nucleon Spin J u -J d plot with experimental bands 26

27 Octet Axial Couplings Full-QCD with pion mass: MeV HWL, K. Orginos, Phys.Rev.D79: (2009) Including first lattice calculation of g ΞΞ and g ΣΣ. Systematic errors: finite volume + finite a XPT: 0.35 < g ΣΣ < 0.55; 0.18 < g ΞΞ < 0.36 Large-N c : 0.30 < g ΣΣ < 0.36; 0.26 < g ΞΞ < 0.30 Global coupling constants: D = 0.715(06)(29), F = 0.453(05)(19) Constrained fit for g A Huey-Wen Lin CIPANP

28 Octet Axial Couplings Most lattice calculations performed on g A SU(3) constrained fit gives Lin et al. smaller extrapolated statistical error than LHPC Lighter m π, finer a, multiple V essential for precise calculation SU(3) symmetry breaking δ SU(3) / x 2 Quadratic behaviour is observed Not predicted by any theorem nor chiral perturbation theory 20% breaking at physical point coincidence? Huey-Wen Lin CIPANP

29 Hyperon Properties Hyperon projects: including the form factors, charge radii, magnetic moments (HWL, K. Orginos, Phys.Rev.D79: (2009)) and semi-leptonic decays Mixed action with pion mass MeV Predictions for Ξ and Σ + charge radii to be 0.67(5) and 0.306(15) fm 2 respectively. Including Λ hyperon and decuplet-octet transition 29

30 Strangeness in the Nucleon s s G E -G M plots HAPPEX: Phys.Rev.Lett.98: (2007) SAMPLE, PVA4,HAPPEX,G0: Phys.Rev.Lett. 97, (2006) Indirect lattice calculation D. Leinweber et al., Phys.Rev.Lett.97: (2006); D. Leinweber et al., Phys.Rev.Lett.94: (2005); HWL, [hep-lat] (SPIN 2008) Recent direct lattice calculation M. Deka: et al., Phys.Rev.D79: (2009) { 0.017(25)(07), (16)(8)} at Q 2 = 0 30

31 Higher-Q 2 Nucleon Form Factors N f = 0 anisotropic lattices, M π ~ 480, 720, 1080 MeV HWL et al., Phys. Rev. D78, (2008); HWL et al. [ ] G E p G M p /μ p G M n /μ n G E n (GeV 2 ) 31

32 Higher-Q 2 Nucleon Form Factors N f = 2+1 anisotropic lattices, M π ~ 580, 875 MeV G E p Preliminary G E n G M p /μ p G M n /μ n 32

33 π γγ Saul D. Cohen et al., Primakoff effect; photoproduction (e.g. PrimEx) Work in progress M π ~ 725 MeV for exploratory study Preliminary results in arxiv: [hep-lat] Extend to other mesons 33

34 Charmed Baryons Liuming Liu et al. (see the poster) preliminary results in arxiv: [hep-lat] Example results (more on her poster) Prediction: Ω cc (j=1/2): 3734(03)(25) MeV 34

35 Bottom Baryons Inconsistency between the CDF and DØ results in Ω b mass Our Ω b agrees with the CDF result Mass prediction for Ξ b to be 5955(27) MeV 35

36 Nucleon-Roper Form Factors First lattice study on quenched lattices Proton-P MeV Pion Neutron-P 11 Possible decaying state (circled above) 200 configurations give us reasonable signal Lower pion mass will shift the time-like region to space-like region HWL et. al, Phys.Rev.D78: (2008) 36

37 Nucleon-Roper Form Factors N f = 2+1 anisotropic lattices, M π ~ 580, 875 MeV Very Preliminary Proton-P 11 Neutron-P 11 Need higher precision! 37

38 Precision Baryon Calculation Recent demonstration by NPLQCD on 366 MeV 2+1f HSC anisotropic clover lattices < 0.2% accuracy S. Beane et. al., [hep-lat] Brute force! Used 292,500 sets of measurements on 1194 gauge configurations and a full year of a collaboration s resources for one pion mass, lattice spacing and volume. Can we find a smarter way of doing the calculation? 38

39 Quark Distillation To Improve A new technique to improve the contraction time and signal First peek at baryon signals: Noise-to-signal scales like N p NPLQCD, [hep-lat] M N M. Peardon et. al. (HSC), [hep-lat] G 1g 1 st excited p = 1.74(19) p = 0.41(3) G 1u ground p = 1.20(23) More computational resources 39

40 Summary Lab experimental program is a great motivation for theoretical interests Wide range of spectroscopy calculations and form factors within the lattice group here at JLab IT support at the lab is crucial: more physics done and less machinery operations Workshops within the lab are helpful for learning the latest results and communicating Variety: Given sufficient computational resources and human effort, one can contribute many different kinds of theory support for the lab s experiments and more JLab provides unique opportunities for Lattice QCD calculations 40