Cascades on the Lattice

Transcription

1 Cascade Physics - Jlab 2005 Cascades on the Lattice Kostas Orginos College of William and Mary - JLab LHP Collaboration

2 LHPC collaborators R. Edwards (Jlab) G. Fleming (Yale) P. Hagler (Vrije Universiteit) C. Morningstar (CMU) J. Negele (MIT) A. Pochinsky (MIT) D. Renner (UofA) D. Richards (Jlab) W. Schroers (DESY)

3 Summary What can the Lattice do for you? How will we make it happen? What has been done? Some very preliminary results from LHPC Thanks to D. Richards

4 Particle Data Group

5 Lattice QCD Spectrum calculation: simplest thing to do Strange quarks don t decay stable cascades Better signal than protons (strange quark is heavy) Can vary quark masses Quantum numbers easy to identify

6 Difficulties Strong decays: Unstable particles Finite volume techniques Heavy quark masses: above threshold Broken rotational symmetry Angular momentum not a good quantum number Vacuum polarization effects Inefficient algorithms mass of up and down quarks too light! Chiral symmetry and lattice fermions

7 Lattice Operators 7/2 7/2 5/2 5/2 3/2 1/2 H G 2 G 1 hep-lat/ Basak et al.

8 Particle Data Group

9 Lattice QCD In continuous Euclidian space: Z = DqD qda µ e S[ q,q,a µ] O = 1 Z DqD qda µ O( q, q, A µ ) e S[ q,q,a µ] Lattice regulator: Gauge sector: U µ (x) = e iaa µ(x+ˆµ 2 )! q Pµ! Fermion sector: Z = du det( ) n f e β Nc ReT r[1 P µ,ν(x)] Uµ µ Fermion doubling Chiral symmetry breaking

10 Spectrum Correlation functions C(t) = J(t) J(0) J an interpolating field for some state Proton C(t) = Z 0 e M 0t +

11 Need to do Continuum extrapolation Chiral extrapolation Infinite volume extrapolation In all cases use Effective field theory Scale setting Heavy quark potential (Sommer scale) Rho mass (bad choice) Heavy quarkonia

12 What does it take 2+1 Dynamical flavors 2 light (up down) 1 heavy (strange) charm bottom top (treated in HQET as extrernal) Light quark masses m < 400MeV π Chiral extrapolations Finite volume corrections Numerical algorithm slows down (algorithm scaling ) 1 m 2.5 q Continuum extrapolations compute at several lattice spacings (algorithm scaling 1 ) a 7

13 The Berlin Wall Tflops years run A, B, C run D Ukawa m PS /m V Urbach (ILFTN 3)

14 Queching Z = du det( ) n f e β Nc ReT r[1 P µ,ν(x)] The computation simplifies if we ignore the fermion loops det( ) = 1 Uncontrolled approximation

15 Quenched spectrum m (GeV) K* φ N Λ Σ Ξ Σ* Ξ* Ω K K input φ input experiment 0.4 CP-PACS

16 Quenched Spectrum UKQCD

17 Recent Developments Cheap dynamical fermions (Kogut-Susskind) Taste breaking Improved KS action (Asqtad O(a 4, g 2 a 2 )) [KO, Sugar, Toussaint 99] MILC has generated lattices: Ready to milk the MILC Chiral symmetry on the lattice ( Domain wall fermions Overlap fermions O(a 2 ) errors) [Kaplan -- Shamir] [Neuberger, Narayanan] Costly for dynamical: RBC now starting Improvements: Improved gauge actions [KO with RBC 02] Mobius fermions [Brower, Neff, KO 04] Big Computers!

18 Domain Wall Fermions for QCD Formulate the 5D Wilson fermions with mass M 0 in s ɛ [1, L s ] q(r) Ls/2... Ls For 2 < M < 0, light chiral modes are bound on the walls. Only one Dirac fermion without doublers remains. q(r) Ls/2... Ls Fermion mass is introduced by explicitly coupling m f of the walls. [Shamir,Furman & Shamir] mf 8

19 Why Domain Wall Fermions Excellent chiral properties at finite lattice spacing: L s Exact chiral symmetry L s finite: Exponentially small chiral symmetry breaking Gauge action affects chiral symmetry [KO with RBC hep-lat/ ] Chiral extrapolations Simpler renormalization due to symmetry Can work close to the chiral limit Have O(a 2 ) errors Excellent scaling properties m/m ρ N K* N/DBW2 N/Wilson K * /DBW (a/r 0 ) 2

20 Scaling MILC and RBC data

21 Dynamical 2+1 flavors MILC

22 Quenched vs Dynamical f π f K 3M Ξ M N 2M Bs M Υ ψ(1p 1S) Υ(1D 1S) Υ(2P 1S) Υ(3S 1S) Υ(1P 1S) LQCD/Exp t (n f = 0) LQCD/Exp t (n f = 3) MILC, HPQCD, UKQCD

23 The LHPC program Domain wall fermions for valence (with hyp smeared links) Chiral symmetry Ward Identities Kogut-Susskind 2+1 Dynamical flavors Improved KS action (Asqtad: O(a 4, g 2 a 2 )) [KO, Sugar, Toussaint 99] MILC has generated lattices: Ready to milk the MILC Light quark masses: Lightest pion m π ~ 250MeV Volumes: 2.6 to 3.2 fm Future: Continuum extrapolation a=0.06fm in 1-2 years MILC lattice spacings: a=0.125fm, 0.09fm

24 The DWF quark masses Domain wall fermions for valence (hyp smeared links) We tune the DWF quark mass to the staggered Goldstone pion Unitarity violation Baer et.al.: tune to the taste singlet for m π Not clear it helps for other quantities ( ex. f π ) Unitarity is restored in the continuum in any case

25 8 IsoVector scalar correlator 8 6 m= m= C(t) C(t) 4 C(t) t t t 6 5 m= m= C(t) 0.05 C(t) t C(t) t t χpt calculation: Prelovsek LAT 05

26 Pion decay constant Fit the lower 4 points Scale used a = fm One loop χpt extrapolation: 130.6(1.8)MeV Systematic error: chiral extr. 3 MeV 2% from scale setting χ 2 /d.o.f. ~ 2 Need mixed χpt of Baer et.al.

27 LHPC dwf on MILC 2 Mass (GeV) Ξ 3/2+ Ξ 1/2 Δ N LHPC Preliminary N 1/2+ Ξ 1/2+ Ξ 3/2+ Δ 3/2+ Ξ 1/2 Σ 1/2+ Σ 3/ M π (GeV ) D. Richards

28 LHPC data vs Experiment Preliminary

29 Cascade - Nucleon mass splitting Mild quark mass dependence Small systematic error due to chiral extrapolation Other systematice errors cancel Preliminary Scale used a = 1588 MeV Latt./Exp. = 1.006(8)

30 Quenched vs Dynamical f π f K 3M Ξ M N 2M Bs M Υ ψ(1p 1S) Υ(1D 1S) Υ(2P 1S) Υ(3S 1S) Υ(1P 1S) LQCD/Exp t (n f = 0) LHPC: preliminary (no errorbars) LQCD/Exp t (n f = 3) MILC, HPQCD, UKQCD

31 Conclusions Lattice QCD can be very helpful in studying the cascade spectrum Not much has been done up to now The gold plated observable 3M Ξ - M N is well reproduced (MILC and LHPC). LHPC: Need to work on statistics and extrapolations Finer lattice spacing is on the way