# Presentation: 120669

## What is QCD?

- Quantum ChromoDynamics is the theory of the strong force
- the strong force describes the binding of quarks by gluons to make particles such as neutrons and protons
- The strong force is one of the four fundamental forces in the Standard Model of Physics– the others are:
- Gravity
- Electromagnetism
- The Weak force
- The 2004 Physics Nobel prize was awarded to David J. Gross, H. David Politzer, and Frank Wilczek**  **for their work leading to QCD

## The Four Fundamental Forces

## Quarks and Gluons in QCD

- 	The QCD quark action expresses the strong interaction between quarks and gluons:

- where the Dirac “dslash” operator,

- depends on the gluons, *A****(x)* as well as the quarks ***(x).*

##  Lattice QCD – Numerical Simulation of QCD

- Space and time are discretized on a four dimensional lattice.
- On a parallel computer, the lattice is divided among all the nodes.

*An illustration of how a 16**3** space lattice is partitioned into 8 sub-lattices.*

## Quarks and Gluons in lattice QCD

- Complex 3x1 quarks vectors, ***(x)*, are defined at lattice sites. * *
- Complex 3x3 gluon matrices,  *U****(x)*, are defined on each lattice link.

## Quark and Gluon Interactions

- A simple discretized form of the Dirac operator is

- Quark and gluon interactions are represented by the algebra of complex 3x3 (gluon) matrices and 3x1 (quark) vectors at adjacent sites.

- The dominant computation is repeated inversion of the (sparse matrix) Dirac operator via the Conjugate Gradient method.

## Why do Lattice QCD?

- Many QCD problems can only be simulated numerically, using Lattice QCD
- To test the Standard Model, physicists take experimental data and compare to the theoretical predictions of QCD
- Differences may indicate new physics, for example, explaining why the universe is dominated by matter and has so little anti-matter

## Testing the Standard Model

- Regions of different colors correspond to different constraints from theory and experiment
- The intersection of the colored regions is allowed by the Standard Model

## Testing the Standard Model

- New B-factory  experiments, such as BaBar at SLAC and Belle at KEK, will reduce the experimental errors, shrinking the areas of each region

## Testing the Standard Model

- Even tighter constraints will result from better theoretical calculations from Lattice QCD
- If the regions don’t overlap, there must be new physics!

## Machines for Lattice QCD

- Lattice QCD codes require:
- excellent single and double precision floating point performance
- majority of Flops are consumed by small complex matrix-vector multiplies (SU3 algebra)
- high memory bandwidth (principal bottleneck)
- low latency, high bandwidth communications
- typically implemented with MPI or similar message passing APIs

## Memory Bandwidth Limits Performance

## Lattice QCD Clusters at Fermilab

| Cluster | QCD | Pion | Kaon |
| --- | --- | --- | --- |
| Nodes | 128 | 520 | 600 |
| Processor | 2.8 GHz Pentium 4E | 3.2 GHz Pentium 940 | 2.0 GHz Dual Opteron 270 |
| Network | Myrinet 2000 | Infiniband 4X (SDR) | Infiniband 4X (DDR) |
| Performance | 0.14 Tflop/s | 0.86 Tflop/s | 2.6 Tflop/s |

## Performance Trends – Clusters

## For More Information

- Fermilab lattice QCD portal:	http://lqcd.fnal.gov/
- US lattice QCD portal:	http://www.lqcd.org/