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Lattice QCD Comes of AgeyLattice QCD Comes of Agey
Richard C. Brower
XLIst Rencontres de Moriond March 18-25 2006QCD and Hadronic interactions at high energy
QCD Theory Space!
Color Supercond(Dense quarks)
Asymptotically Free (UV/Short Distances)
String/Gravity
Flux Tubes/Spectra(IR/Long Distances)
Chiral Restored(High Temp)
Ncolor
1/g2g2
kTB
N = 1, nf = 1N = 0
*Lattice*
Strassler, Katz
Orginos
Schmidt,Levkova
IIB
IIA
D=11 SGRA
HO
HE I
N = 2
N = 1
M-theory
Super String Theory Space!
Comparison of Chemistry & QCD : K. Wilson (1989 Capri):
“lattice gauge theory could also require a 108 increase in computer power AND
spectacular algorithmic advances before useful interactions with experiment ...”
• ab initio Chemistry1. 1930+50 = 19802. 0.1 flops 10 Mflops3. Gaussian Basis functions
• ab initio QCD1. 1980 + 50 = 2030?*2. 10 Mflops 1000 Tflops3. Clever Multi-scale Variable?
*Fast Computers + Rigorous QCD Theoretical AnalysisSmart Algorithms +
= ab inition predictions
“Almost 20 Years ahead of schedule!”
Arizona Doug Toussaint MIT Andrew Pochinsky
Dru Renner (Eric Gregory)
North Carolina
Daniel Reed (Celso Mendes)
BU R. Brower(CHAIR) * Ying Zhang *
James Osborn (Hartmut Neff)
JLab Robert Edwards *
BNL Chulwoo Jung Chip Watson *
Kostantin Petrov Jie Chen
Columbia Bob Mawhinney * Walt Akers
FNAL Don Holmgren * Utah Carleton DeTar *
Jim Simone Francesca Maresca
Eric Neilsen
Amitoj Singh
USA SciDAC SoftUSA SciDAC Softwware Groupare Group
* Software Coordinating Committee
UK Peter Boyle Balint Joo
Optimized Dirac Operators, InvertersLevel 3
QDP (QCD Data Parallel)
Lattice Wide Operations, Data shifts
Level 2
QMP (QCD Message Passing)
QLA (QCD Linear Algebra)Level 1
QIOBinary DataFiles / XML Metadata
SciDAC QCD API SciDAC QCD API
C/C++, implemented over MPI, nativeQCDOC, M-via GigE mesh
Optimised for P4 and QCDOC
Exists in C/C++
ILDG collab
Sources of Error Wrong “theory” --- no quark loops
solution: Keep Fermionic det & Disconnected diagrams
Finite lattice spacing a solution: a < .1 fermi + O(a2) asymptotic freedom
Light quark limit mu/d/ms O(1/20) solution: Chiral pert. theory + Exact Lattice Chiral Symmetry
Finite space-time volume solution: Big memory computer
Monte Carlo 1/N1/2 sampling error solution: Algorithms + $’s
Staggering Results:Role of Determinant (aka Sea Quarks)
This is real QCD --- No more excuses (except Staggered Fermion with Det[D]¼ trick: 4 * ¼ taste loops. Tasteful Chiral perturbation theory to take a 0)
Strong Coupling Constant
Lattice: S(MZ) = 0.1170 (12) Experiment: S(MZ) = 0.1187 (20)
Lattice (data) vs Perturbation Theory (red/one sigma band)
Properties of and K mesons
Rule out mu = 0 by 5 sigma (Strong CP problem not solved!)
lattice value is |Vus| = 0.2219±0.0026, experimental results: |Vus| = 0.2262(23)
Multi-scale Algorithms
String Length1000 Mev ( » 0.2 fm)
Quarks Masses: (197 fm Mev) 2, 8, 100, 1200, 4200, 175,000 Mev
Nuclear: scattering length/effective range asinglet = - 23.714 fm ( » 8 Mev) & r = 2.73 atriplet = 5.425 fm ( » 36 Mev) & r = 1.749 fm
Deuteron Binding = 50 Mev. (» 4 fm)
Finite T, finite etc
Log(
mq)
Flavor: u,d,s,c,b,t
QCD length scales:
Quark loops: Multi-time step HMC
Hasenbush Trick:
Rational Hybrid Monte Carlo:
In Hybrid Monte Carlo (HMC) simulations, the determinant acts as a potential for molecularevolutions: Equilibrium by “molecular chaos”: Speed up by separating force terms and using multiple step sizes:
n times
Wilson Fermions with Multi-time step trick(moving the Berlin Wall)
Wilson is Almost as efficient as Staggered BUT respects flavor sym
(Urbach, Jansen, Shindler, Wegner, hep-lat/0506011)
Multi-grid al 1980’s failure point:Universal Autocorrelation: = F(m l)
Gauss-Jacobi (Diamond), CG (circle), 3 level (square & star)
= 3 (cross) 10(plus) 100( square
s = 1 s = 2 s = M s = Ls
qL
qR
QL
QRqL
qRQR
QL
LEFTRIGHT
Exact Lattice Chiral Fermions: (Taking the 5th Dimension Seriously ?)
5-d Flavor Current 4-d Vector/Axial Current
Vector:
Axial:
4-d Ward-Takahashi Identities via decent relations:
“QCD and a Holographic Model of Hadrons” Erlich, Katz, Son, Stephanov, hep-ph/05011 (fit “qcd, mq, ”)
Remarkably similar to AdS/CFT approach to Flavor Currents
* constrained fit