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
PWA basics - isobar model- 3p
t=(pp-pX)2
p-
W1
iso
X
p-
p-
W2
p+
s=(pp+pp)2
p
This is what we are We know how to
looking for calculate decay
production
amplitudes Ab
amplitudes
p
Measured by experiment
d
I (m X , W1 , W 2 , t ) 

dm X dW1dW 2dt

where
  a (m
b
2
X
, t )  Ab (W1 , W 2 , m iso )
b
b  {J , P , l , s, m}
Ab (W1 , W 2 , miso )  E J ,l , s ,m (W1 , W 2 ) * propagator (m iso )
CG coefficients and Dlmm’’s
Usually Breit Wigner propagator
3p PWA results
Intensity
a2(1320)
All waves
Typical PWA fit
involves:
• ~1-3M events/’t’ bin
Events/0.025 GeV/c2
• ~5-10 ‘t’ bins
• ~80 mass bins
• ~30-40 waves
p2(1670)
a1
Mass [GeV/c2]
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 :
NIb,b ' (m X , t ) 

Ab (W1 , W 2 , miso ) Ab ' (W1 , W 2 , miso )
*
events
Data file - 10M experimental events
Raw Monte Carlo file - 150M events
Accepted Monte Carlo file - 40M events
OLD
NEW
Data sets
Data sets
Gather
partial
results
NI’s
Master
Decay Amplitudes
Decay Amplitudes
Slaves calculate amplitudes “on the fly”
and evaluate partial contributions to
normalization integrals
Legend
Normalization Integrals
PC-node
Disk Storage
OLD
NEW
Performance comparison
Assume 10 ‘t’ bins
MC files
150M
Data files
40M
10M
MC files
150M
Data files
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
Every time one changes data cut another
50 hours of computer time is required.
Most of the time is spent doing
Input/Output operations
10 minutes of CPU time is required.
Input/Output operations are reduced
to necessary minimum
OLD
NEW
PWA fits
Decay Amplitudes
Gather
likelihood
contributions
Master
Minuit runs only
on master
...
bin 0
bin 1
bin 2
...
bin n
Decay Amplitudes
bin 0 - bin n
Use final parameters from bin k as the
starting parameters for bin k+1. Have to reread decay amplitudes for every bin.
At every iteration of minimization
routine master sends fitted parameters,
slaves calculate likelihood and send
the result back to the master
OLD
PWA fitter features comparison
NEW
Only two types of fits are possible as
of now:
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. 2 hours / t bin
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. 30 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 dividing data set into
bins).
CAUTION: Slow network
connection between master and
slaves can significantly degrade
performance of the PWA fitter.
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