Event Reconstruction and

Particle Identification

Yong LIU 刘 永

The University of Alabama PRC-US workshopBeijing, June 11-18, 2006

MiniB

NE

On Behalf of the MiniBooNE Collaboration

MiniBooNE Event Reconstruction and Particle Identification

Y.Liu, D.Perevalov, I.Stancu University of Alabama S.Koutsoliotas Bucknell University R.A.Johnson, J.L.Raaf University of Cincinnati T.Hart, R.H.Nelson, M.Tzanov M.Wilking, E.D.Zimmerman University of Colorado A.A.Aguilar-Arevalo, L.Bugel L.Coney, J.M.Conrad, Z. Djurcic, J.M.Link K.B.M.Mahn, J.Monroe, D.Schmitz M.H.Shaevitz, M.Sorel, G.P.Zeller Columbia University D.Smith Embry Riddle Aeronautical University L.Bartoszek, C.Bhat, S.J.Brice B.C.Brown, D. A. Finley, R.Ford, F.G.Garcia, P.Kasper, T.Kobilarcik, I.Kourbanis, A.Malensek, W.Marsh, P.Martin, F.Mills, C.Moore, E.Prebys, A.D.Russell , P.Spentzouris, R.J.Stefanski, T.Williams Fermi National Accelerator Laboratory D.C.Cox, T.Katori, H.Meyer, C.C.Polly R.Tayloe Indiana University

G.T.Garvey, A.Green, C.Green, W.C.Louis, G.McGregor, S.McKenney G.B.Mills, H.Ray, V.Sandberg, B.Sapp, R.Schirato, R.Van de Water N.L.Walbridge, D.H.White Los Alamos National Laboratory R.Imlay, W.Metcalf, S.Ouedraogo, M.O.Wascko Louisiana State University J.Cao, Y.Liu, B.P.Roe, H.J.Yang University of Michigan A.O.Bazarko, P.D.Meyers, R.B.Patterson, F.C.Shoemaker, H.A.Tanaka Princeton University P.Nienaber Saint Mary's University of Minnesota E.Hawker Western Illinois University A.Curioni, B.T.Fleming Yale University

MiniBooNECollaboration

MiniBooNE Event Reconstruction and Particle Identification

Global solar data and KamLAND S. Ahmed et al., Phys. Rev. Lett. 92, 181301 (2004)

Super-Kamiokande and K2K data G.Fogli et al., Phys. Rev. D 67, 093006 (2003)

LSNDA. Aguilar et. al., Phys. Rev. D 64, 112007 (2001)

The primary physics goal of MiniBooNE is to definitely confirm or rule out the oscillation signal seen by LSND experiment

e

PL m

Ee( ) s in ( ) s in (.

) ( . . . )% 2 22

21 27

0 264 0 067 0 045

Total excess = 87.9±22.4±6.0 (3.8σ)

MiniBooNE Event Reconstruction and Particle Identification

To achieve the MiniBooNE physics goal

Particle Identification performance

e efficiency ~ 50%contamination ~ .0 1%contamination 0

~ 1%is required in BooNE proposal (Dec. 7, 1997) and accordingly very good resolution of

by Event Reconstruction are desired.

position

direction

mass / energy 0

Poor event reconstruction => Poor Particle Identification

MiniBooNE Event Reconstruction and Particle Identification

12-meter diameter spherical tank1280 PMT in inner region240 PMT in outer veto region950,000 liters ultra pure mineral oil

MiniBooNE Event Reconstruction - Overview

Reconstruct what?• Position (x, y,

z, t)• Direction (ux,

uy, uz)• Energy/mass E/m

How to reconstruct?• Light model • Time likelihood -

position• Charge likelihood –

directionReconstruction

Performance• Position resolution• Direction resolution• Energy/Pi0 mass

resolution

MiniBooNE Event Reconstruction – light model

θc η

Directional Cherenkov light ρ

Isotropic Scintilation light φ

Point-like light source model

Event track

(x y z t)

(ux uy uz)

(xi yi zi ti

qi )ri

• Predicted charge

cosηf(

cosη

)

• Cerenkov light - directional

• Scintillation light - isotopic

Assume Point-like light source model for e

• Model input parameter

1. Cerenkov angular distribution2. PMT angular response3. Cerenkov attenuation length4. Scintillation attenuation length5. Relative quantum efficiency

• Minimize with respective toCerenkov/Scintillation flux

iCER

ii CER

i

F E fr

r

(co s , ) (co s )

exp ( / )2

iSC I

ii sc i

i

fr

r

(co s )

exp ( / )2

i iC ER

iSC I

MiniBooNE Event Reconstruction - Charge Likelihood

P ne

n

n

( ; )!

P q P q n P nn

( ; ) ( ; ) ( ; )

0

The probability of measuring a charge q for a predicted charge μ

Three method to extract the charge likelihood

A. Fill 2-D histogram H(q, μ),

normalize q distribution for eachμbin, get –log versus μ for each q bin

C. Start from one PE charge response curve, generate P(q;n), assume Possion distribution, calculate P(q;μ), take –log

B. From hit/no-hit probability minimization procedure, get H(q, μ), then same As A.

MiniBooNE Event Reconstruction – Time likelihood

t t tr

ccorri

ii

n

( ) 0

T tE E

t t Ecer corr

c ccorr c( )

( , )exp

( , )[ ( , )]

1

2

1

2 2 02

T tE

E

E

t t E

E

ErfcE

E

t t E

E

sc i corrs

s

s

corr s

s

s

s

corr s

s

( )( , )

exp( , )

( , )

( , )

( , )

( , )

( , )

( , )

( , )

1

2 2

2 2

2

20

0

1. Corrected time

2. Cerenkov light tcorr(i) distribution

3. Scintillation light tcorr(i) distribution

4. Input: Cerenkov light – t0

cer ,σcer

Scintillation light – t0

sci ,σsci,τsci5. Total negative log time likelihood

L t T t T tcorri c

c scer corr

ic

s

c ssc i corr

is( ) log ( ( , ) ( , ))( ) ( ) ( )

MiniBooNE Event Reconstruction –Timing parameter

Cerenkov: look at hits in Cerenkov cone Scintillation: look at hits in backward directionGet tcorr=tcorr(μ,E), fit to CER and SCI T(tcorr), iteration

MiniBooNE Event Reconstruction – process chart

xi yi zi ti qi

x = ∑( xi qi ) / ∑qi t = ∑ qi (ti – |xi – x|/c) / ∑qi

Initial guess

Fast fitTLLK

x y z t dx = ∑qi (xi-x) /|xi-x|ux = dx / |dx|

d=R-|x| E=Qf(d)CER = c1 E SCI = c2 E

Full fitTLLK+QLLK

x y z t ux uy uzd=R-|x|

E=Qf(d)CER = c1 E SCI = c2 E

Flux fitTLLK+QLLK

Cer Sci fluxTrak fitTLLK+QLLK

Track length

Pi0 fitStep 1

x1=x y1=y z1=z t1=tux1=ux uy1=uy uz1=uz

ux2 uy2 uz2Cer1 Cer2

fcer e1 e2s1 = s(e1)s2 = s(e2)

x1 y1 z1 t1 fcer Θ1 φ1 s1 Θ2 φ2 s2 x y z t

Pi0 fitStep 2

sci1 = Cse e1sci2 = Cse e2

Cer1 Θ1 φ1 s1 Cer2 Θ2 φ2 s2

Pi0 fitStep 3

e1 = Cer1 / Ccee2 = Cer2 / Cce

Cer1 Cer2 Sci1 Sci2

Pi0cosine(γ1 γ2)e1 e2 Pi0mass

Calibrated data

MiniBooNE Event Reconstruction - performance

P r e l i m

i n a r y

MiniBooNE Event Reconstruction - performance

P r e l i m

i n a r y

ParticleID – do what?• Signal Events• Background Events

ParticleID - how to do?

• Variable - Construction and selection• Algorithm - Simple cuts/ANN/BoostingParticleID – reliable and powerful?

• Input – variable distribution and correlation Data/MC agree • Output Data/MC agree • The performance

MiniBooNE ParticleID - Overview

Forνe appearance search in MiniBooNE

Signal = oscillationνe CCQE events Background = everything else

Oscillation sensitivity study shows the most important backgrounds A. Intrinsic νe from K+, K0 and μ+ decay

- indistinguishable from signal

C. νμ CCQE

B. NC πo

D. Δ radiative decay

νμ + n/p νμ + n/p + πo

Δ N +γ

νμ + n μ- +

p

MiniBooNE ParticleID – Signal and Background

MiniBooNE ParticleID – π0 misID cases

0can be mis-identified as electron due to some physics

• High energy Pi0, Lorentz boost, two gamma direction close

• Very asymmetric Pi0 decay, one ring is too small

• Pi0 close to tank wall, one gamma convert behind PMTs

reason and detector limitation

0 0

0

V

V

e e

V

e e e e e e

e e

ParticleID basically based on event topology

e

μ

πo Real D

ata

Even

t D

isp

lay

MiniBooNE ParticleID

How to extract event topology from a set of PMT hits information

An Event = {(xk, yk, zk), tk, Qk} k = 1, 2, …, NTankHitsWhat we know is actually the space and time distribution of charge

The event topology is characterized by charge/hits fraction in space/time bins

θ

{(xk, yk, zk), tk, Qk}

rk

(x, y, z, t)

(ux, uy, uz)dtk = tk – rk/cn- t

Point-like model

θc

s

MiniBooNE ParticleID - space-time information

MiniBooNE ParticleID – Construct input variables

•Binning cosθin relative to event direction - record hits/PMT number, measured/predicted charge, time/charge likelihood in each cosθ bin

•Binning corrected time - record hits number, measured/predicted charge, time/charge likelihood in each corrected time bin

•Binning ring sharpness - record hits/PMT number, measured/predicted charge, time/charge likelihood in each ring sharpness bin

Take physically meaningful ratio in certain bin and combination of different bins Dimensionless quantity is preferred

How to construct the ParticleID variables

• Reconstruced physical observables: - e.g.πo mass, energy, track length and Cerenkov/scintillation light flux, production angle, etc.

• Reconstructed geometrical quantities: - e.g. radius r, u· r, and distance along track to wall,

etc.

• Difference of likelihood between different hypotheses fitting:

- electron/muon/pi0 fitting

Other ParticleID variables

These variables are very powerful !

MiniBooNE ParticleID – Other input variables

MiniBooNE ParticleID – Use how many inputs

How many variables do we need?

In ideal case, we can focus on the track instead of PMT hits. The least number of variables needed to describe one track is ~ 10• Radius r - from tank center to MGEP

• Angle α - between track and radial direction • Energy E • Light emision in unit length - parametrized by some parameters

(x, y, z, t)

(ux, uy, uz)

αr

At most, the number of variables we have

{(xh, yh, zh), th, Qh} × NTank PMTs = 5 × NTank PMTsBut they are highly correlated !

For πo events, twice as many variables needed.

MiniBooNE ParticleID – How to select variables

How to select ParticleID variables: reliability & efficiencyParticleID algorithm training and test have to

rely on Monte Carlo1. Does the variable distribution Data/MC agree ?

2. Does the correlation between variables Data/MC agree?

These two requirements ensure output Data/MC agree and so the reliability of ParticleID

3. Is the variable/combination powerful in separationToo many inputs may degrade the

ParticleID performance

Check with open box, cosmic ray calibration and NuMI data/MC

The events number in each node of the trees can test correlation between variables, and can be used to look at data/MC comparison naturally. Energy/geometry variable dependence.

MiniBooNE ParticleID – Data/MC comparison

The input data/MC comparison

MiniBooNE ParticleID - Data/MC comparison

The input data/MC comparison

MiniBooNE ParticleID - Algorithm

Choose which algorithmANN=Artifical Neural NetworkSC=Simple Cuts BDT=Boosted decision tree

SC ANN BDT

Variable Number Up to ~10

~30

~200

Parameter to fit 0 ~1000

~10000

Control Parameters 0

~10

~3

PerformanceNot good

good

better

Boosting is preferred in MiniBooNE to get better sensitivitybut Simple Cuts method and ANN can provide cross check.

Reasonably more input variables may result in higher performance, but less input variables may be more reliable.

MiniBooNE ParticleID Boosting

Boosting – boosted decision tree

1.Boosting: how to split node – choose variable and cut Define GiniIndex = P (1 - P) ∑w(S+B) P =∑wS/∑w(S+B), w is event weight. For a pure background or signal node GiniIndex = 0

G = GiniIndexFather – ( GiniIndexLeftSon + GiniIndexRightSon )

2. Boosting: how to generate tree– choose node to split

Among the existing leaves, find the one which gives the biggest G and split it. Repeat this process to generate a tree of the chosen size.

A. Generate tree

Start here

variable = i

Cut = ci

variable(i)<ci variable(i)>=ci

Variable = k

Cut = ck

variable(k)<ck variable(k)>=ck

For a given node, determine which variable and cut value maximizes

MiniBooNE ParticleID – Boosted decision trees

B. Boost tree3. Boosting: how to boost tree

- Choose algorithm to change event weightTake ALL the events in a leaf as signal events if the polarity of that leaf is positive. Otherwise, take all the events as background events. Mark down those events which are misidentified. Reduce the weight of those correctly identified events while increase the weight of those misidentified evens. Then, generate the next tree.

4. Boosting: how to calculate output value - Sum over (polarity × tree weight) in all treesSee B. Roe et al. NIM A543 (2005) 577 and references therein for detail

C. Output

Define polarity of a node:polarity = + 1 if signal is more than backgroundpolarity = - 1 if background is more than signal

MiniBooNE ParticleID

Simple Cuts and Boosted Decision Tree

Simple Cuts

Generalization

Decision Tree

Improvement

Boosted Decision Tree

All events

Var1<c1 Var1>=c1

Var2>=c2Var2<c2

variable = i

Cut = c1

variable = 2

Cut = c2

Var1<c1 || (var1>=c1 && var2<c2)

Simple Cuts can be taken asOne Tree, Few Variables, Few Nodes

MiniBooNE ParticleID - conclusion on algorithm

Boosting is better than Artificial Neural Network

Boosting performance is higher in many variable (>20) caseand relatively insensitive to detector MC in comparison to ANN

Cascade Boosting is better than non-Cascade Boosting

Cascade Boosting training can improve 25~30% or evenmore relative to non-Cascade training, especially in low background contamination region

Combine individual separation outputs can improve further

By about 10~20%

Some conclusions based on our past experience

Cascade Boosting – build first boosting used as cut to select training events for second boosting, use second boosting

MiniBooNE ParticleID - Cascade Boosting

1st boosting - cascade

2nd boosting – cascade

Combine individual outputs

P r e l i m i n a r y

MiniBooNE ParticleID – Output data/MC comparison

The output data/MC comparison

MiniBooNE ParticleID – Output data/MC comparison

The output data/MC comparison

MiniBooNE ParticleID – How to play

Event counting

Energy or/and ParticleID spectrum fitting

Optimize PID cuts to maximize

N

N N

S

iB

iB

iii

( ) 2

After some precuts, do

Energy spectrum fit

PID output distribution fit

Energy and PID two dimensional fit

to get oscillation sensitivity

MiniBooNE Event Reconstruction and Particle Identification

MiniBooNE Event Reconstruction provides

Energy resolution ~ 14%Position resolution ~ 23cmDirection

resolution ~ 6oPi0 mass resolution ~ 23 MeV/c2

Based on the reconstruction information, with

• Boosted decision trees• Cascade training

• Combining specialist algorithms

a much better ParticleID than BooNE proposal required

has been achieved!

~ 67% electron efficiency 1% Pi0 contamination < 0.1% muon contamination

Conclusion