Lattice QCD Comes of Age y

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!”

BNL+JLab+FNAL+BG/L= O(10 Tflop/s)

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

Lattice QCD

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)

Alpha Strong

CKM projected improvement via Lattice Gauge

Before

After

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)

Axial Charge of the Nucleon

Lattice gA = 1.226 (84) Experiment gA = 1.295 (29)

Semi-leptonic Form Factor (prediction)

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:

Confinement length vs Pion Compton length

l

m-1

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

New fangled Algebraic-Adaptive Multigridfor Disconnected Diagrams

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

Conclusions

Not even the Beginning of the End ...,

perhaps the End of the Beginning”But

II. Postdictions Predictions

I. Search for signals Calibration of Errors

Coming of Age for Lattice Field theory:

III. To paraphrase W.C.“This is Not the End of Lattice Gauge Theory ...,