analysis of e852 data at indiana university ryan mitchell pwa workshop pittsburgh, pa february 2006
TRANSCRIPT
Outline
I. Overview of the Indiana 3π Analysis
II. PWA Formalism and Fitting Techniques
III. Limitations of the Current Method: 3 Case Studies
1pπππpπρpXpπ
pπππpπρpXpπ000
0
2005 Indiana 3π Analysis
PWA of two charge modes using 1995 E852 data:
1. “Charged Mode”π−p→π+π−π−p (2.6M events, after cuts)
2. “Neutral Mode”π−p→π−π0π0p (3.0M events, after cuts)
2pπππpfπpXpπ
pπππpfπpXpπ00
Isospin relationsprovide powerfulcross checks.
Raw Distributions After Cuts(no acceptance corrections)
a1
a2
π2
π2
a2
a1
f2(1270)
ρ(770)
3π mass distributionsshow the familiar a1(1260) a2(1320) π2(1670)resonances.
Dalitz plots showevidence ofisobar production.
Charged Mode Neutral Mode
f2(1270)
Setting up the Partial Wave Analysis
k
*k,k,
*k,k,
2
kk,k,tM, )(A)(AVV)(AV )(I
Expand the “angular distribution” in each mass and t bin into partial waves:
basisfunctions
complex fit parameters
incoherent sum(reflectivity)
coherent sum(JPC, isobars, M, L)
kinematics(angles,
2π masses)
Divide the data into bins of mass and t:
67 25MeV
Mass Bins
67 Mass Bins800 – 2500 MeV/c2
13 t Bins0.08 – 0.58 GeV2/c2
13 t Bins (1 standard)
Events in a t Bin~100’s of 1000’s
Events in a Fit~1’s to 10’s of 1000’s
PWA Results: Dominant Waves
Charged Mode Neutral Mode
2++1+(ρ)S 2++1+(ρ)S
1++0+(ρ)S 1++0+(ρ)S2−+0+(f2)S 2−+0+(f2)S
a2(1320)
a1(1260)
π2(1670)
• 35 Wave Fitº 21 Wave Fit
All Waves All Waves
PWA Results: A Minor Wave
Charged Mode Neutral Mode
4++1+(ρ)G 2++1+(ρ)S
a2(1320)a4(2040)
• 35 Wave Fitº 21 Wave Fit
2++1+(ρ)S 4++1+(ρ)G
Notice the difference in scales.(About a factor of 40)
Comparison of 2−+ and Exotic 1−+ Waves
• 35 Wave Fitº 21 Wave Fit
1−+1+(ρ)P 1−+1+(ρ)P1−+M−(ρ)P 1−+M−(ρ)P
2−+1+(ρ)F 2−+1+(ρ)F
1670 MeV/c2
Charged Mode
When additional 2−+ waves are not included,the intensity appears in the 1−+ waves.
2−+0+(ρ)F 2−+0+(ρ)F
Neutral Mode
Expanding the Intensity in Bins of M3π and t (and s):
2
kk,k,t,M )(AV )(I
3π
“DecayAmplitudes”(basis states)
“ProductionAmplitudes”(complex fit parameters)
incoherent sum
(spin flip,reflectivity,background,
etc.)
coherentsum(JPC,
isobars,etc.)
Kinematics(angles,
isobar masses,etc.)
CHOICES:
1. How to write A(Ω)?
2. Which terms addcoherently and whichincoherently?
3. Which and How Many terms are included?
Extensions
1. Don’t bin in M3π and/or t.
2. Include fit parameters inside A(Ω).
A(Ω) for 3π in the Isobar Model
r)L(-M)(isobaJ
MJ
M(isobar)LJ(isobar)LMJ
PC
PCεPC
A1)εP(
AΘ(M)A
0M0
0M1/2
0M1/2
Θ(M)
J,M SL
1. Each wave is characterized by JPCMε(isobar)L:
J: Spin of resonanceP: Parity of resonanceC: C-Parity of resonanceM: z projection of Jε: ReflectivityL: Orbital angular momentum of the resonance decayS: Spin of the Isobarθ1,φ1: Decay angles of the resonance (Gottfried- Jackson)θ2,φ2: Decay angles of the isobar (Helicity)FL(p1): Barrier factor for resonance decayFS(p2): Barrier factor for isobar decayBW(isobar): Breit-Wigner with isobar parameters
3. Transform to the “reflectivity” basis:
isobar)(BW)p(F)p(F
)0,,(D)0,,(DJ;SL0,
1)S2(1)L2()(A
2S1L
22*011
*JM
1/21/2
M(isobar)LJPC
S
2. Add a term for identical pions.
The Likelihood Fit
n
1i
inμ
dΩΩηΩI
)I(Ω
n!
μeL
2
kk,k,tM, )(AV )(I
dΩΩηΩIμ
n
1ii dΩΩηΩI2))ln(I(Ω22ln(L)
Perform a likelihood fit in every bin of mass and t:
Minimize this function:This term is modifiedby acceptance
n: observed number of events in this binμ: expected number of events in this bin:
η(Ω): Acceptance
Likelihood Fit (acceptances)
k α α
N
1ii
*αk,iαk,
GEN
*αk,αk,
N
1i k
2
αiαk,αk,
GEN
N
1ii
GEN
ACC
ACC
ACC
ΩAΩAN
4πVV
ΩAVN
4π
ΩIN
4πdΩΩηΩI
NGEN: Generated MC Events (flat in angles)
NACC: Accepted MC Events
NDATA: Observed Data Events
“Normalization Integrals”
Minor note:V is rescaled during the fit:
ACC
GENDATA
N
NNVV
One-time sumover MC events.
MC
Master
Distributed data
Gather partial NI’s
NI’s
Slaves calculate amplitudes “on the fly” and evaluate partial contributions to normalization integrals
1. Normalization Integrals
Master Fitted
parameters
At every iteration of minimization the master sends the current parameters, and the slaves calculate the likelihood and send the result back to the master
2. The PWA Fit
Minuit runs on master
Data
GatherpartialLikelihood
NI’s
n
1ii dΩΩηΩI2))ln(I(Ω22ln(L)
BIG speed increase when data is CACHED.
III. Limitations of the Current Method
Three Case Studies:
1. The Effects of Barrier Factors
2. Incorporating the Deck Effect
3. Normalization Integral Files
Case I. The Effect of Barrier Factors
r)L(-M)(isobaJ
MJ
M(isobar)LJ(isobar)LMJ
PC
PCεPC
A1)εP(
AΘ(M)A
0M0
0M1/2
0M1/2
Θ(M)
J,M SL
1. Each wave is characterized by JPCMε(isobar)L:
J: Spin of resonanceP: Parity of resonanceC: C-Parity of resonanceM: z projection of Jε: ReflectivityL: Orbital angular momentum of the resonance decayS: Spin of the Isobarθ1,φ1: Decay angles of the resonance (Gottfried- Jackson)θ2,φ2: Decay angles of the isobar (Helicity)FL(p1): Barrier factor for resonance decayFS(p2): Barrier factor for isobar decayBW(isobar): Breit-Wigner with isobar parameters
3. Transform to the “reflectivity” basis:
isobar)(BW)p(F)p(F
)0,,(D)0,,(DJ;SL0,
1)S2(1)L2()(A
2S1L
22*011
*JM
1/21/2
M(isobar)LJPC
S
2. Add a term for identical pions.
What is the systematiceffect of this?
Case I. I Just Want to Modify a Barrier Factor
??
The code must be moretransparent.
We need more flexibilityin defining amplitudes:
• This is the HEART of the PWA.
• PWA should not be a physics black box.
• We need quick answers to simple questions of systematics.
Limitation 1.Black Box Physics
Case II: The Deck Effect
Proton
Pomeron
π π
π
πf2π
The 2-+0+(f2)S and 2-+0+(f2)D waves in 3π.
Why are they shifted in mass?
Fit with one resonance and the Deck Effect.
Preliminary work byAdam Szczepaniakand Jo Dudek.
Mass ≈ 1740 MeV/c2
“π2(1670)”
Case II. The Deck Effect
• Non-resonant amplitudes should be part of the PWA instead of being extracted from resonant amplitudes.
Proton
Pomeron
π π
π
πf2π
Limitation 2a:No Easy Way for “Users”to Define Amplitudes.
• Amplitudes like Deck could be more effective with fit parameters inside the amplitude.
Limitation 2b:Fit Parameters Always Multiplythe “Decay Amplitude”.
Case III. Normalization Integral Files
• When the data selection cuts change, or
the form of an amplitude changes, or
a Monte Carlo file changes, then
Normalization Integral files must be regenerated.
• With many versions of normalization integral files,
Organization becomes difficult.
• In November 2005, wrong normalization integral files set back the 3π analysis several weeks.
Limitation 3:Handling multiple NI fileseasily leads to confusion.
• Needs Improvement:– Black Box Physics
Separate physics and
computer science.
– Only Production Amplitudes in PWA Fit
– Normalization Integral Files
– Documenting Fits (CMU Database?)
– Viewing Results, Viewing correlations, etc.
Summary of Indiana PWA Experience
• Good Things:– Parallel Processing
– Caching Amplitudes
OTHER TALKS:
Matt: PWA Framework
Scott: Documentation
Adam: Phenomenology