Lattice QCD from the NuclearPhysics Perspective

J. W. Negele

SciDAC March 23 2004

White Paper: Nuclear Physics with Lattice QCD

http://www-ctp.mit.edu/~negele/WhitePaper.pdf

GOAL: Understand the structureand interactions of hadrons andthe properties of hadronic matterfrom first principles

• Quantitative calculation of

experimental observables

• Insight into how QCD works

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Introduction

How do hadrons arise from QCD?

• Lagrangian constrained by Lorentz invariance,gauge invariance and renormalizability:

• Deceptively simple Lagrangian producesamazingly rich and complex structure of stronglyinteracting matter in our universe

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Basic Ideas in Lattice QCD

• Evolution in Euclidean time

• Lattice Regularization

• Path Integral

• Stochastic solution

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Observables

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Computational Issues

• Fermion determinant - Full QCD

• Lattice spacing small

• Quark mass small

• Lattice volume large

Cost ≈ (mq)-4.5 ≈ (m�)-9

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Current Status

• Include Fermion determinant - Full QCD

• (m�)-9 limits calculations to “heavy pion world”

• Develop physics methodology

• Understand dependence on quark mass

• Terascale resources required for physicalregime

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Three Areas of QCD PhysicsLattice calculations essential to understandingphysics in each case

• Heavy Quark Systems

Confirm standard model or elucidate physicsbeyond it

• QCD Thermodynamics

Properties of hadronic matter under extremeconditions

Foundation for RHIC physics → LHC

• Hadron Structure

Quark and gluon structure of hadrons

Spectroscopy

Hadron-hadron interactions

Crucial to understand physics from Bates,Jlab, SLAC, Fermilab and RHIC-spin

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Impact on DOE Nuclear Physics Program

STAR and PHENIX detectors

RHIC at BNL

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Impact on DOE Nuclear Physics Program

SOS and HMS spectrometers

CEBAF at

JLab

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Hadron Structure

• Form factors

GE , GM Jlab

Strangeness FF Sample, Happex

• Transition form factors

N → ∆ - deformation Bates, JLab

• Parton Distributions RHIC spin, Hermes …

Quark distributions <x>q

Spin distribution - spin crisis ∆Σ ~ <1>∆q

Transversity distribution <1>δq

• Generalized Parton Distributions Jlab

Total quark angular momentum J

Transverse structure of nucleon

Transverse size → 0 as x → 1

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Electromagnetic Form Factors

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RMS Charge Radius

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Nucleon-Delta Transition Form Factor

• Calculate transition amplitudes

M1 dominates

C2 and E2 vanish if nucleon and deltaspherical

• Lattice calculations

hep-lat/030007018 Alexandrou, Tsapalis, J.N et. al.

M1/E2 expt

= -1.6 (.4)

Quenched

= -4.8 (1.1)

Full QCD

= -3.5 (1.2)

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Forward Matrix Elements

Parton distributions at Q = 5 GeV

Moments of parton distributions

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Momentum Fraction <x>

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<x>∆u-∆d

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Quark Angular Momentum

Connected diagram contributions

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Transverse Structure of Parton Distribution

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Smeared transverse structure

model (Burkardt hep-ph/0207047)

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Spectroscopy

• N* Spectroscopy JLab

Number and structure of states

• Exotics JLab

Glueballs

Exotic mesons - gluonic excitations

Pentaquark

• Hadronic Interactions

Heavy-light meson and baryon interactions

• Light quark exchange

• Gluon contributions

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Exotic Mesons

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Roper Resonance

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Pentaquarks

S = +1 five quark state

Diquark model - positive parity

Quark model - negative parity

Preliminary lattice calculations inheavy pion world

Θ (1540} observed at SPRing8, Jlab,…

Stepanyan et.al. hep-ex/0307018 Sasaki hep-lat/0310014

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QCD Thermodynamics

• Phase diagram of QCD

• Zero baryon density (µ = 0)

Transition to Quark Gluon Plasma

E(T), P(T)

• Non-zero baryon density (µ ≠ 0)

Critical point - RHIC signatures

Equation of state - neutron stars

Superconducting phases

• Quark number susceptibility

Event by event fluctuations

• Quark-antiquark potential

J/Ψ production

• Current correlation functions - spectral function

Dilepton and photon emission

Transport coefficients

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Quark Susceptibility

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Screening of Heavy Quark Potential

Kaczmarek et al hep-lat/0309121

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Spectral Functions

J/Ψ survives up to 2.25 TC

Petreczky et al hep-lat/0309012

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Fundamental aspects of QCD

Insight into how QCD works

• Confinement

Mechanism, flux tubes

• Chiral symmetry breaking

Instantons, zero modes

• Low energy effective theory

Parameters of chiral perturbation theory

• Structure of wave functions

Variational wave functions

Density-density correlation functions

• Configurations that dominate path integral

Instantons

• Dependence on parameters of QCD

Nc , Nf , gauge group, mq

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Long Term Effort

• Quantities for which we already have theoreticaland computational tools

Need 10’s of Teraflops - Petaflops for precisioncalculations at level of few percent

• Challenges with the potential for opening stillmore vistas

Example: Finite chemical potential

Cluster algorithms

• Need sustained effort at leading edge oftechnology curve

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Lattice QCD Initiative

Coherent National Plan

Cost optimized hardware: QCDOC and Clusters

SciDAC Computational Infrastructure

• Software development

Uniform optimized software for all platforms

• Cluster development

Hardware Plan

• 10 Tflops QCDOC at BNL in 04

Plan $1 per sustained Mflops in 04

General purpose machines $20-50

• 10 Tflops clusters at Jlab, FNAL in 05 and 06

• Joint high energy and nuclear physics funding

$4M committed in HEP

Seek Nuclear and ASCR support

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SciDAC Software

Uniform QCD physics software environment

Highly optimized for each platform

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FNAL Myrinet Cluster

• 128 Node dual Xeon

• 2.4 GHz P4

• Commissioned 1/03

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Jlab GigE Cluster

• 256 Node single Xeon

• 2.66 GHz P4

• 3 dual GigE cards

• $ 1950/node

• Commissioned 9/03

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Projected Cluster Performance

Staggered fermion inverter at FNAL

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Summary

• Lattice QCD poised to provide fundamentalunderstanding of hadrons and hadronic matter

• Essential tool for understanding contemporaryexperiments

• Demonstrated methodology in “heavy pion world”

• Computer technology ready for 10’s of Teraflops at$1/sustained Mflops.

• Sustained effort at leading edge of technologycurve provides outstanding opportunity forfundamental advances in Nuclear Physics