Lattice QCD Comes of Agey

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Lattice QCD Comes of Agey
Richard C. Brower
XLIst Rencontres de Moriond March 18-25 2006 QCD
and Hadronic interactions at high energy
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QCD Theory Space!
Super String Theory Space!
String/Gravity
Strassler, Katz
N 1, nf 1
N 0
Asymptotically Free (UV/Short Distances)
Flux Tubes/Spectra (IR/Long Distances)
Ncolor
QCD
g2
Orginos
1/g2
Lattice

?B
kT
Schmidt,Levkova
Color Supercond (Dense quarks)
Chiral Restored (High Temp)
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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 Chemistry
• 193050 1980
• 0.1 flops ? 10 Mflops
• Gaussian Basis functions

• ab initio QCD
• 1980 50 2030?
• 10 Mflops ? 1000 Tflops
• Clever Multi-scale Variable?

Almost 20 Years ahead of schedule!
Fast Computers
Rigorous QCD Theoretical Analysis
Smart Algorithms
ab inition predictions
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BNLJLabFNALBG/L O(10 Tflop/s)
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USA SciDAC Software Group
UK Peter Boyle
Balint Joo
Software Coordinating Committee
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SciDAC QCD API
QDP (QCD Data Parallel)
QIO Binary DataFiles / XML Metadata
Level 2
Lattice Wide Operations, Data shifts
QLA (QCD Linear Algebra)
Level 1
QMP (QCD Message Passing)
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Lattice QCD
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Sources of Error

• Wrong theory --- no quark loops
• solution Keep Fermionic det Disconnected
  diagrams
• Finite lattice spacing a
• solution a lt .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

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Staggering ResultsRole of Determinant (aka Sea
Quarks)
This is real QCD --- No more excuses (except
Staggered Fermion with DetD¼ trick 4 ¼ taste
loops. Tasteful Chiral perturbation theory to
take a ? 0)
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Strong Coupling Constant
Lattice (data) vs Perturbation Theory (red/one
sigma band)
Lattice ?S(MZ) 0.1170 (12)
Experiment ?S(MZ) 0.1187 (20)
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Alpha Strong
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CKM projected improvement via Lattice Gauge
Before
After
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Properties of ? and K mesons
Rule out mu 0 by 5 sigma (Strong CP problem not
solved!)
lattice value is Vus 0.22190.0026,
experimental results Vus 0.2262(23)
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Axial Charge of the Nucleon
Experiment gA 1.295 (29)
Lattice gA 1.226 (84)
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Semi-leptonic Form Factor (prediction)
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Multi-scale Algorithms
QCD length scales
Log(mq)

• String Length
• 1000 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

Flavor u,d,s,c,b,t
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Confinement length vs Pion Compton length
m-1?
l?
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Quark loops Multi-time step HMC
In Hybrid Monte Carlo (HMC) simulations, the
determinant acts as a potential for
molecular evolutions Equilibrium by molecular
chaos Speed up by separating force terms and
using multiple step sizes

• Hasenbush Trick
• Rational Hybrid Monte Carlo

n times
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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)
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Multi-grid al 1980s failure pointUniversal
Autocorrelation ? F(m l?)
Gauss-Jacobi (Diamond), CG (circle), 3 level
(square star)
? 3 (cross) 10(plus) 100( square
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New fangled Algebraic-Adaptive Multigrid for
Disconnected Diagrams
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Exact Lattice Chiral Fermions (Taking the 5th
Dimension Seriously ?)
s 1
s 2
s M
s Ls
qL
QL
qR
QR
RIGHT
LEFT
qR
QR
QL
qL
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5-d Flavor Current ? 4-d Vector/Axial Current
4-d Ward-Takahashi Identities via decent
relations
Vector
Axial
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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
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Conclusions
Coming of Age for Lattice Field theory
I. Search for signals ? Calibration of Errors
II. Postdictions ? Predictions
III. To paraphrase W.C.
This is Not the End of Lattice Gauge Theory ...,
Not even the Beginning of the End ...,
perhaps the End of the Beginning
But