Outline

1. Recent progress in 3 p Partial Wave Analysis of E852 data Maciej Swat @ Indiana University Outline • 3p PWA overview • Computational challenges in Partial Wave Analysis • Comparison of new and old PWA software design - performance issues

2. PWA basics - isobar model- 3p t=(pp-pX)2 W1 W2 p - This is what we are looking for - production amplitudes p - iso We know how to calculate decay amplitudes Ab p+ X p - s=(pp+pp)2 p p Measured by experiment CGcoefficients andDlmm’’s Usually Breit Wigner propagator

3. 3p PWA results • Typical PWA fit involves: • ~1-3M events/’t’ bin • ~5-10 ‘t’ bins • ~80 mass bins • ~30-40 waves Intensity All waves a2(1320) Events/0.025 GeV/c2 a1 p2(1670) Mass [GeV/c2]

4. PWA implementation - Normalization Integrals in the isobar model For each event we have to: 1. Find helicity frame decay angles - W1, W2 2. Calculate decay amplitudes (involves Wigner D functions, CG coefficients,BW propagators). These amplitudes are model dependent. In particular ,the time to calculate a single decay amplitude depends on the model. 3.Find normalization integrals : Data file -10Mexperimental events Raw Monte Carlo file - 150M events Accepted Monte Carlo file - 40M events

5. OLD NEW Data sets Data sets All data events NI’s Gather partial results Master Distributed data Decay Amplitudes Decay Amplitudes All decay amplitudes Slaves calculate amplitudes “on the fly” and evaluate partial contributions to normalization integrals Legend Normalization Integrals PC-node Disk Storage

6. OLD NEW Performance comparison Assume 10 ‘t’ bins MC files Data files MC files Data files 150M 40M 10M 150M 40M 10M Calculate masses, angles, invariants, amplitudes. Store amplitudes.Fill normalization integrals tables. Calculate masses, angles, invariants, amplitudes. Fill normalization integrals tables. One has to handle ~5 000 files~300 GB disk space One has to handle ~15 files~30 MB disk space Total time:~150 hours of computer time Total time:~45 minutes of computer time Every time one changes data cut another 50 hours of computer time is required. Every time one changes data cut another 10 minutes of CPU time is required. Most of the time is spent doing Input/Output operations Input/Output operations are reduced to necessary minimum

7. OLD NEW PWA fits Decay Amplitudes Gather likelihood contributions Minuit runs only on master Master Fitted parameters ... bin 0 bin 1 bin 2 ... bin n Decay Amplitudes At every iteration of minimization routine master sends fitted parameters, slaves calculate likelihood and send the result back to the master bin 0 - bin n Use final parameters from bin k as the starting parameters for bin k+1. Have to re-read decay amplitudes for every bin.

8. OLD NEW PWA fitter features comparison Only two types of fits are possible as of now: 1. Bins are fitted independent from each other - fast, can use multiple CPU’s. 2 hours / t bin 2. Fit with parameters boot-strapping - has to be done on single machine , slow. 30 hours /t bin New fitter is scalable and one can do the following types of fits: 1. Bins are fitted independent from each other - fast, can use multiple CPU’s. 1-2 hours / t bin 2. Fit with parameters boot-strapping - has to be done on single machine , slow. 0.5 - 1 hours / t bin 3. Mass dependent PWA or any other type of fit where one would require to fit entire data sample at once (without dividingdata set into bins). CAUTION: Slow network connection between master and slaves can significantly degrade performance of the PWA fitter.

9. Tips,Tricks, Conclusions Ways to achieve good performance: 1. Write parallel code using e.g. Message Passing Interface (MPI) - a simple and easy to use library 2. Avoid reading from secondary storage 3. Compute things once and avoid redundancy Theoretical analysis - choice of model issues • Until now we have used only isobar model. • We have to study also other models, a lot of progress has been made in 70’s. • Try to represent data in model independent fashion - study moments