1. A Common Partial Wave Analysis
ComPWA
A Common Partial Wave Analysis
Framework for PANDA
Mathias Michel
Helmholtz Institute Mainz
On behalf of the ComPWA group
CHEP 2013, Amsterdam
October 15, 2013

2. understanding how hadrons are built
Hadron Spectroscopy
understanding how hadrons are built
What
happened
here? K+ K* π0 K-
What you see is
always the same K- K* π0 K+ π0 Ф K+ K-
Mathias Michel, HI Mainz

3. Mathias Michel, HI Mainz
Resonances K+ K* π0 K-
events
m2(K+0) K-
m2(K-0)
m2(K+0) K* π0 K+
events
events π0 Ф K+ K-
m2(K-0)
m2(K+K-)
Mathias Michel, HI Mainz

4. Mathias Michel, HI Mainz
Resonances 
K*(892) K+ K* π0 K-
events
m2(K+0) K-
m2(K-0)
m2(K+0) K* π0 K+
events
events π0 Ф K+ K-
m2(K-0)
m2(K+K-)
Mathias Michel, HI Mainz

5. Example: partial waves for inelastic scattering
Amplitude Analysis
PWA K+ K* π0 K-
Example: partial waves for inelastic scattering
The measured cross-section relates to the scattering matrix
Compose planar wave in terms of partial waves with given l
Calculating the scattered wave (outgoing - incoming) K-
𝑑𝛺 𝑑𝜃 = ∣ 𝑓 𝜃 2 ∣ K* π0 K+
𝑒 𝑖𝑘𝑟𝑐𝑜𝑠 𝜃 = 𝑙 2l+1 𝑖 𝑙 𝑗 𝑙 𝑘𝑟 𝑃 𝑙 cos𝜃 π0 Ф K+
𝑓 𝜃 = 1 𝑘 𝑙 2l+1 𝜂 𝑙 𝑒 2iδ 𝑙 −1 2l 𝑃 𝑙 cos𝜃 K-
Mathias Michel, HI Mainz

6. Mathias Michel, HI Mainz
ComPWA Challenges
PANDA physics program
→ various models needed
pp initial state at 1.5 – 15 GeV/c
→ high initial spin (≈ up to 6-7)
→ many possible waves
→ many parameters
High statistics
→ parallelization needed
Detector effects
→ distorted phasespace
Coupled channels
→ different efficiencies
Quality assurance
Why a common framework?
PWA tools on the market are specialised
→ not extendible to PANDA
PANDA is still years from data taking
→ start now and we could have a well
tested and reliable software ready
comparison of results from different
experiments possible
Mathias Michel, HI Mainz

7. Mathias Michel, HI Mainz
ComPWA Framework
Experiment C
Homebrew Amplitude
Experiment B
K-Matrix Amplitude
Experiment A
Helicity Amplitude
weight
event
amplitude
Likelihood
likelihood
Minuit2
Chi-Square
Geneva
Mathias Michel, HI Mainz

8. Mathias Michel, HI Mainz
ComPWA Framework
Data & MC
represents measurements
local and global values
multiple experiments (at once)
caching
Physics & Models
calculates amplitudes
various formalisms (helicity)
various models (isobar)
simple ways to add new
modules (wrapper)
weight
event
amplitude
Estimators
calculates discrepancy from
model to data
functiontree
combined fits and re-fits
documentation of procedure
Optimizer
varies model parameter
interface to external libraries
various algorithms (gradient
decent, genetic, swarm)
flexible strategies
likelihood
Mathias Michel, HI Mainz

9. Mathias Michel, HI Mainz
ComPWA Framework
Documentation
Controls
Data & MC
Physics & Models
weight
event
amplitude
Estimators
Optimizer
likelihood
Mathias Michel, HI Mainz

10. Mathias Michel, HI Mainz
FunctionTree
A = ∑ ( T*c*D )
𝐼= ∣ 𝑛 𝑇 𝑛 𝑟 𝑛 e 𝑖 𝜑 𝑛 𝐷 𝑛 ∣ 2 K*
Ф = T*c*D
T = Breit-Wigner Function
D = D-Wigner Function
r = Strength of Resonance
φ = Phase of Resonance T D c
glob.
par.
inv.
mass
res.
par.
Mathias Michel, HI Mainz

11. FunctionTree: Strategies
A = ∑ ( T*c*D )
Node
List of parents
List of children
My parameter
Strategy K*
Ф = T*c*D
Strategy pattern T D
execute function
input:
parameter list (children)
output:
calculated parameter c
glob.
par.
inv.
mass
res.
par.
Mathias Michel, HI Mainz

12. FunctionTree: Parameters
A = ∑ ( T*c*D )
Leaf
List of parents
List of children
My Parameter
Strategy K*
Ф = T*c*D
Observer pattern T D
Abstract
Parameter
Parameter
Observer c
glob.
par.
inv.
mass
res.
par.
Parameter
Leaf
Mathias Michel, HI Mainz

13. Test Environment: J/ψ→γπ0π0
Data/MC
represents measurements
local and global values
multiple experiments (at once)
caching
Physics & Models
calculates amplitudes
various formalisms (helicity)
various models (isobar)
simple ways to add new
modules (wrapper)
J/ψ→γπ0π0
Toy-MonteCarlo
complex sum of
relativistic Breit-Wigner
weight
event
Controls
user interface &
run manager
amplitude
manually
Estimators
calculates model result
combined fits and re-fits
documentation of procedure
Optimizer
varies model parameter
interface to external libraries
various algorithms (gradient
decent, genetic, swarm)
flexible strategies
likelihood
unbinned LogLH
Minuit gradient descent
Mathias Michel, HI Mainz

14. Mathias Michel, HI Mainz
J/ψ→γπ0π0 Model π0 π0 f π0
J/ψ ω π0
J/ψ γ γ
𝐼= ∣ 𝑛 𝑇 𝑛 𝑟 𝑛 e 𝑖 𝜑 𝑛 𝐷 𝑛 ∣ 2
T = Breit-Wigner Function
D = D-Wigner Function
r = Strength of Resonance
φ = Phase of Resonance
Mathias Michel, HI Mainz

15. Mathias Michel, HI Mainz
J/ψ→γπ0π0 phasespace
Mathias Michel, HI Mainz

16. Mathias Michel, HI Mainz
J/ψ→γπ0π0 generated ω
Hit & miss
MC using
PDG
parameter
f0(980)
f2(1270)
f0(1500)
f2'(1525)
f0(1710) ω
Mathias Michel, HI Mainz

17. Mathias Michel, HI Mainz
J/ψ→γπ0π0 first fit
Hit & miss
MC using
fitted
parameter
f0(980)
f2(1270)
f0(1500)
f2'(1525)
f0(1710)
result
optimal p0
0.990 p1
1.505 p2
1.720 p3
1.274 p4
1.525 ω
Mathias Michel, HI Mainz
startvalues: 0.95*optimal

18. Mathias Michel, HI Mainz
J/ψ→γπ0π0 ratio
f0(980)
f2(1270)
f0(1500)
f2'(1525)
f0(1710)
Mathias Michel, HI Mainz

19. Status & Outlook Language and Dependencies This is work in progress!
Boost
Boost.Build
Optional External Packages Used
Root
qft++
Minuit2
Geneva
Documentation
Doxygen
Doku Wiki
Version-Control
Git
This is work in progress!
Biggest ToDo's
go public
controls and configuration
documentation module
more physics cases
About Geneva
Geneva is available as Open Source
software (AGPL v3) from
and is also supported commercially
by Gemfony scientific
Contact
Mathias Michel, HI Mainz